Boundary-Layer Receptivity and Integrated Transition Prediction

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Choudhari, Meelan

2005-01-01

The adjoint parabold stability equations (PSE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fidelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.

Application of Adjoint Methodology to Supersonic Aircraft Design Using Reversed Equivalent Areas

NASA Technical Reports Server (NTRS)

Rallabhandi, Sriram K.

2013-01-01

This paper presents an approach to shape an aircraft to equivalent area based objectives using the discrete adjoint approach. Equivalent areas can be obtained either using reversed augmented Burgers equation or direct conversion of off-body pressures into equivalent area. Formal coupling with CFD allows computation of sensitivities of equivalent area objectives with respect to aircraft shape parameters. The exactness of the adjoint sensitivities is verified against derivatives obtained using the complex step approach. This methodology has the benefit of using designer-friendly equivalent areas in the shape design of low-boom aircraft. Shape optimization results with equivalent area cost functionals are discussed and further refined using ground loudness based objectives.

Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2006-01-01

A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design variables such as the free stream parameters and the planform shape of an isolated wing. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Factors under consideration include the computation of mesh sensitivities that provide a reliable approximation of the objective function gradient, as well as the computation of surface shape sensitivities based on a direct-CAD interface. We present detailed gradient verification studies and then focus on a shape optimization problem for an Apollo-like reentry vehicle. The goal of the optimization is to enhance the lift-to-drag ratio of the capsule by modifying the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design.

Towards Seismic Tomography Based Upon Adjoint Methods

NASA Astrophysics Data System (ADS)

Tromp, J.; Liu, Q.; Tape, C.; Maggi, A.

2006-12-01

We outline the theory behind tomographic inversions based on 3D reference models, fully numerical 3D wave propagation, and adjoint methods. Our approach involves computing the Fréchet derivatives for tomographic inversions via the interaction between a forward wavefield, propagating from the source to the receivers, and an `adjoint' wavefield, propagating from the receivers back to the source. The forward wavefield is computed using a spectral-element method (SEM) and a heterogeneous wave-speed model, and stored as synthetic seismograms at particular receivers for which there is data. We specify an objective or misfit function that defines a measure of misfit between data and synthetics. For a given receiver, the differences between the data and the synthetics are time reversed and used as the source of the adjoint wavefield. For each earthquake, the interaction between the regular and adjoint wavefields is used to construct finite-frequency sensitivity kernels, which we call event kernel. These kernels may be thought of as weighted sums of measurement-specific banana-donut kernels, with weights determined by the measurements. The overall sensitivity is simply the sum of event kernels, which defines the misfit kernel. The misfit kernel is multiplied by convenient orthonormal basis functions that are embedded in the SEM code, resulting in the gradient of the misfit function, i.e., the Fréchet derivatives. The misfit kernel is multiplied by convenient orthonormal basis functions that are embedded in the SEM code, resulting in the gradient of the misfit function, i.e., the Fréchet derivatives. A conjugate gradient algorithm is used to iteratively improve the model while reducing the misfit function. Using 2D examples for Rayleigh wave phase-speed maps of southern California, we illustrate the construction of the gradient and the minimization algorithm, and consider various tomographic experiments, including source inversions, structural inversions, and joint source-structure inversions. We also illustrate the characteristics of these 3D finite-frequency kernels based upon adjoint simulations for a variety of global arrivals, e.g., Pdiff, P'P', and SKS, and we illustrate how the approach may be used to investigate body- and surface-wave anisotropy. In adjoint tomography any time segment in which the data and synthetics match reasonably well is suitable for measurement, and this implies a much greater number of phases per seismogram can be used compared to classical tomography in which the sensitivity of the measurements is determined analytically for specific arrivals, e.g., P. We use an automated picking algorithm based upon short-term/long-term averages and strict phase and amplitude anomaly criteria to determine arrivals and time windows suitable for measurement. For shallow global events the algorithm typically identifies of the order of 1000~windows suitable for measurement, whereas for a deep event the number can reach 4000. For southern California earthquakes the number of phases is of the order of 100 for a magnitude 4.0 event and up to 450 for a magnitude 5.0 event. We will show examples of event kernels for both global and regional earthquakes. These event kernels form the basis of adjoint tomography.

Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization

NASA Technical Reports Server (NTRS)

Arian, Eyal; Salas, Manuel D.

1997-01-01

We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as "inadmissible." For example, a cost functional which depends on the density, rather than on the pressure, is considered "inadmissible" for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian functional when deriving the adjoint equations. These terms are obtained from the restriction of the interior PDE to the control surface. Demonstrations of the explicit derivation of the adjoint equations for "inadmissible" cost functionals are given for the potential, Euler, and Navier-Stokes equations.

Use of adjoint methods in the probabilistic finite element approach to fracture mechanics

NASA Technical Reports Server (NTRS)

Liu, Wing Kam; Besterfield, Glen; Lawrence, Mark; Belytschko, Ted

1988-01-01

The adjoint method approach to probabilistic finite element methods (PFEM) is presented. When the number of objective functions is small compared to the number of random variables, the adjoint method is far superior to the direct method in evaluating the objective function derivatives with respect to the random variables. The PFEM is extended to probabilistic fracture mechanics (PFM) using an element which has the near crack-tip singular strain field embedded. Since only two objective functions (i.e., mode I and II stress intensity factors) are needed for PFM, the adjoint method is well suited.

Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization

NASA Technical Reports Server (NTRS)

Green, Lawrence; Carle, Alan; Fagan, Mike

1999-01-01

Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop limit is reached, or no further design improvement is possible due to active design variable bounds and/or constraints. The resulting shape parameters are then used by the grid generation code to define a new wing surface and computational grid. The lift-to-drag ratio and its gradient are computed for the new design by the automatically-generated adjoint codes. Several optimization iterations may be required to find an optimum wing shape. Results from two sample cases will be discussed. The reader should note that this work primarily represents a demonstration of use of automatically- generated adjoint code within an aerodynamic shape optimization. As such, little significance is placed upon the actual optimization results, relative to the method for obtaining the results.

Adjoint shape optimization for fluid-structure interaction of ducted flows

NASA Astrophysics Data System (ADS)

Heners, J. P.; Radtke, L.; Hinze, M.; Düster, A.

2018-03-01

Based on the coupled problem of time-dependent fluid-structure interaction, equations for an appropriate adjoint problem are derived by the consequent use of the formal Lagrange calculus. Solutions of both primal and adjoint equations are computed in a partitioned fashion and enable the formulation of a surface sensitivity. This sensitivity is used in the context of a steepest descent algorithm for the computation of the required gradient of an appropriate cost functional. The efficiency of the developed optimization approach is demonstrated by minimization of the pressure drop in a simple two-dimensional channel flow and in a three-dimensional ducted flow surrounded by a thin-walled structure.

Adjoint method and runaway electron avalanche

DOE PAGES

Liu, Chang; Brennan, Dylan P.; Boozer, Allen H.; ...

2016-12-16

The adjoint method for the study of runaway electron dynamics in momentum space Liu et al (2016 Phys. Plasmas 23 010702) is rederived using the Green's function method, for both the runaway probability function (RPF) and the expected loss time (ELT). The RPF and ELT obtained using the adjoint method are presented, both with and without the synchrotron radiation reaction force. In conclusion, the adjoint method is then applied to study the runaway electron avalanche. Both the critical electric field and the growth rate for the avalanche are calculated using this fast and novel approach.

Adjoint-Based Mesh Adaptation for the Sonic Boom Signature Loudness

NASA Technical Reports Server (NTRS)

Rallabhandi, Sriram K.; Park, Michael A.

2017-01-01

The mesh adaptation functionality of FUN3D is utilized to obtain a mesh optimized to calculate sonic boom ground signature loudness. During this process, the coupling between the discrete-adjoints of the computational fluid dynamics tool FUN3D and the atmospheric propagation tool sBOOM is exploited to form the error estimate. This new mesh adaptation methodology will allow generation of suitable meshes adapted to reduce the estimated errors in the ground loudness, which is an optimization metric employed in supersonic aircraft design. This new output-based adaptation could allow new insights into meshing for sonic boom analysis and design, and complements existing output-based adaptation techniques such as adaptation to reduce estimated errors in off-body pressure functional. This effort could also have implications for other coupled multidisciplinary adjoint capabilities (e.g., aeroelasticity) as well as inclusion of propagation specific parameters such as prevailing winds or non-standard atmospheric conditions. Results are discussed in the context of existing methods and appropriate conclusions are drawn as to the efficacy and efficiency of the developed capability.

Self-adjoint realisations of the Dirac-Coulomb Hamiltonian for heavy nuclei

NASA Astrophysics Data System (ADS)

Gallone, Matteo; Michelangeli, Alessandro

2018-02-01

We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the Kreĭn-Višik-Birman extension scheme, or also on Grubb's universal classification theory, as opposite to previous works within the standard von Neumann framework. This let the boundary condition of self-adjointness emerge, neatly and intrinsically, as a multiplicative constraint between regular and singular part of the functions in the domain of the extension, the multiplicative constant giving also immediate information on the invertibility property and on the resolvent and spectral gap of the extension.

Efficient Construction of Discrete Adjoint Operators on Unstructured Grids by Using Complex Variables

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Kleb, William L.

2005-01-01

A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Kleb, William L.

2005-01-01

A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

Self-consistent adjoint analysis for topology optimization of electromagnetic waves

NASA Astrophysics Data System (ADS)

Deng, Yongbo; Korvink, Jan G.

2018-05-01

In topology optimization of electromagnetic waves, the Gâteaux differentiability of the conjugate operator to the complex field variable results in the complexity of the adjoint sensitivity, which evolves the original real-valued design variable to be complex during the iterative solution procedure. Therefore, the self-inconsistency of the adjoint sensitivity is presented. To enforce the self-consistency, the real part operator has been used to extract the real part of the sensitivity to keep the real-value property of the design variable. However, this enforced self-consistency can cause the problem that the derived structural topology has unreasonable dependence on the phase of the incident wave. To solve this problem, this article focuses on the self-consistent adjoint analysis of the topology optimization problems for electromagnetic waves. This self-consistent adjoint analysis is implemented by splitting the complex variables of the wave equations into the corresponding real parts and imaginary parts, sequentially substituting the split complex variables into the wave equations with deriving the coupled equations equivalent to the original wave equations, where the infinite free space is truncated by the perfectly matched layers. Then, the topology optimization problems of electromagnetic waves are transformed into the forms defined on real functional spaces instead of complex functional spaces; the adjoint analysis of the topology optimization problems is implemented on real functional spaces with removing the variational of the conjugate operator; the self-consistent adjoint sensitivity is derived, and the phase-dependence problem is avoided for the derived structural topology. Several numerical examples are implemented to demonstrate the robustness of the derived self-consistent adjoint analysis.

Adjoint-Based Aerodynamic Design of Complex Aerospace Configurations

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.

2016-01-01

An overview of twenty years of adjoint-based aerodynamic design research at NASA Langley Research Center is presented. Adjoint-based algorithms provide a powerful tool for efficient sensitivity analysis of complex large-scale computational fluid dynamics (CFD) simulations. Unlike alternative approaches for which computational expense generally scales with the number of design parameters, adjoint techniques yield sensitivity derivatives of a simulation output with respect to all input parameters at the cost of a single additional simulation. With modern large-scale CFD applications often requiring millions of compute hours for a single analysis, the efficiency afforded by adjoint methods is critical in realizing a computationally tractable design optimization capability for such applications.

Design optimization using adjoint of Long-time LES for the trailing edge of a transonic turbine vane

NASA Astrophysics Data System (ADS)

Talnikar, Chaitanya; Wang, Qiqi

2017-11-01

Adjoint-based design optimization methods have been applied to low-fidelity simulation methods like Reynolds Averaged Navier-Stokes (RANS) and are useful for designing fluid machinery components. But to reliably capture the complex flow phenomena involved in turbomachinery, high fidelity simulations like large eddy simulation (LES) are required. Unfortunately due to the chaotic dynamics of turbulence, the unsteady adjoint method for LES diverges and produces incorrect gradients. Using a viscosity stabilized unsteady adjoint method developed for LES, the gradient can be obtained with reasonable accuracy. In this paper, design of the trailing edge of a gas turbine inlet guide vane is performed with the objective to reduce stagnation pressure loss and heat transfer over the surface of the vane. Slight changes in the shape of trailing edge can significantly impact these quantities by altering the boundary layer development process and separation points. The trailing edge is parameterized using a linear combination of 5 convex designs. Bayesian optimization is used as a global optimizer with the objective function evaluated from the LES and gradients obtained using the viscosity adjoint method. Results from the optimization, performed on the supercomputer Mira, are presented.

Ambient-noise Tomography of the Southern California Lithosphere

NASA Astrophysics Data System (ADS)

Basini, P.; Liu, Q.; Tape, C.

2012-12-01

We exploit the stacked ambient noise cross-correlation functions (NCF) to improve the 3-D velocity structures of southern California crust and upper mantle. NCFs are extracted between pairs of seismic stations as approximations to 3D Greens functions based on the assumption of diffuse wavefields. Thanks to the dense instrumental coverage in south California a high number (around 13000) of NCFs are available that allow us to reach anunprecedented high imaging resolution. The 3-D crustal model m16 of Tape et al. (2009) which describes the detailed crustal variation of southern California region is incorporated into the starting model of our adjoint tomographic inversions. The use of 3D initial model help reduce the nonlinearity of the inverse problem and the number of required iterations. We iteratively improve the velocity model by combining spectral-element (SEM) simulations of seismic wave propagation with Frechet derivatives computed by adjoint methods. The multi-taper traveltime misfit function that quantifies the difference between NCFs (measured over the windows of predominantly surface waves at the period range of 10-20 seconds) and 3D Greens functions for the current model also defines the adjoint sources which produces the necessary Frechet derivatives (sensitivity kernels) through an adjoint simulation. Interesting mantle heterogeneities are revealed due to the improved depth resolution of surface waves. The quality of inversion results may be assessed through the misfit between NCFs and Greens functions for the final model in terms of traveltime, amplitude as well as full waveform. An independent set of earthquakes data and synthetics may also be introduced to verify the final mode.

The fast neutron fluence and the activation detector activity calculations using the effective source method and the adjoint function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hep, J.; Konecna, A.; Krysl, V.

2011-07-01

This paper describes the application of effective source in forward calculations and the adjoint method to the solution of fast neutron fluence and activation detector activities in the reactor pressure vessel (RPV) and RPV cavity of a VVER-440 reactor. Its objective is the demonstration of both methods on a practical task. The effective source method applies the Boltzmann transport operator to time integrated source data in order to obtain neutron fluence and detector activities. By weighting the source data by time dependent decay of the detector activity, the result of the calculation is the detector activity. Alternatively, if the weightingmore » is uniform with respect to time, the result is the fluence. The approach works because of the inherent linearity of radiation transport in non-multiplying time-invariant media. Integrated in this way, the source data are referred to as the effective source. The effective source in the forward calculations method thereby enables the analyst to replace numerous intensive transport calculations with a single transport calculation in which the time dependence and magnitude of the source are correctly represented. In this work, the effective source method has been expanded slightly in the following way: neutron source data were performed with few group method calculation using the active core calculation code MOBY-DICK. The follow-up neutron transport calculation was performed using the neutron transport code TORT to perform multigroup calculations. For comparison, an alternative method of calculation has been used based upon adjoint functions of the Boltzmann transport equation. Calculation of the three-dimensional (3-D) adjoint function for each required computational outcome has been obtained using the deterministic code TORT and the cross section library BGL440. Adjoint functions appropriate to the required fast neutron flux density and neutron reaction rates have been calculated for several significant points within the RPV and RPV cavity of the VVER-440 reacto rand located axially at the position of maximum power and at the position of the weld. Both of these methods (the effective source and the adjoint function) are briefly described in the present paper. The paper also describes their application to the solution of fast neutron fluence and detectors activities for the VVER-440 reactor. (authors)« less

Sensitivity of Lumped Constraints Using the Adjoint Method

NASA Technical Reports Server (NTRS)

Akgun, Mehmet A.; Haftka, Raphael T.; Wu, K. Chauncey; Walsh, Joanne L.

1999-01-01

Adjoint sensitivity calculation of stress, buckling and displacement constraints may be much less expensive than direct sensitivity calculation when the number of load cases is large. Adjoint stress and displacement sensitivities are available in the literature. Expressions for local buckling sensitivity of isotropic plate elements are derived in this study. Computational efficiency of the adjoint method is sensitive to the number of constraints and, therefore, the method benefits from constraint lumping. A continuum version of the Kreisselmeier-Steinhauser (KS) function is chosen to lump constraints. The adjoint and direct methods are compared for three examples: a truss structure, a simple HSCT wing model, and a large HSCT model. These sensitivity derivatives are then used in optimization.

A modified adjoint-based grid adaptation and error correction method for unstructured grid

NASA Astrophysics Data System (ADS)

Cui, Pengcheng; Li, Bin; Tang, Jing; Chen, Jiangtao; Deng, Youqi

2018-05-01

Grid adaptation is an important strategy to improve the accuracy of output functions (e.g. drag, lift, etc.) in computational fluid dynamics (CFD) analysis and design applications. This paper presents a modified robust grid adaptation and error correction method for reducing simulation errors in integral outputs. The procedure is based on discrete adjoint optimization theory in which the estimated global error of output functions can be directly related to the local residual error. According to this relationship, local residual error contribution can be used as an indicator in a grid adaptation strategy designed to generate refined grids for accurately estimating the output functions. This grid adaptation and error correction method is applied to subsonic and supersonic simulations around three-dimensional configurations. Numerical results demonstrate that the sensitive grids to output functions are detected and refined after grid adaptation, and the accuracy of output functions is obviously improved after error correction. The proposed grid adaptation and error correction method is shown to compare very favorably in terms of output accuracy and computational efficiency relative to the traditional featured-based grid adaptation.

Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.

2006-01-01

Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.

A new mathematical adjoint for the modified SAAF -SN equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunert, Sebastian; Wang, Yaqi; Martineau, Richard

2015-01-01

We present a new adjoint FEM weak form, which can be directly used for evaluating the mathematical adjoint, suitable for perturbation calculations, of the self-adjoint angular flux SN equations (SAAF -SN) without construction and transposition of the underlying coefficient matrix. Stabilization schemes incorporated in the described SAAF -SN method make the mathematical adjoint distinct from the physical adjoint, i.e. the solution of the continuous adjoint equation with SAAF -SN . This weak form is implemented into RattleSnake, the MOOSE (Multiphysics Object-Oriented Simulation Environment) based transport solver. Numerical results verify the correctness of the implementation and show its utility both formore » fixed source and eigenvalue problems.« less

Linear Array Ambient Noise Adjoint Tomography Reveals Intense Crust-Mantle Interactions in North China Craton

NASA Astrophysics Data System (ADS)

Zhang, Chao; Yao, Huajian; Liu, Qinya; Zhang, Ping; Yuan, Yanhua O.; Feng, Jikun; Fang, Lihua

2018-01-01

We present a 2-D ambient noise adjoint tomography technique for a linear array with a significant reduction in computational cost and show its application to an array in North China. We first convert the observed data for 3-D media, i.e., surface-wave empirical Green's functions (EGFs) to the reconstructed EGFs (REGFs) for 2-D media using a 3-D/2-D transformation scheme. Different from the conventional steps of measuring phase dispersion, this technology refines 2-D shear wave speeds along the profile directly from REGFs. With an initial model based on traditional ambient noise tomography, adjoint tomography updates the model by minimizing the frequency-dependent Rayleigh wave traveltime delays between the REGFs and synthetic Green functions calculated by the spectral-element method. The multitaper traveltime difference measurement is applied in four-period bands: 20-35 s, 15-30 s, 10-20 s, and 6-15 s. The recovered model shows detailed crustal structures including pronounced low-velocity anomalies in the lower crust and a gradual crust-mantle transition zone beneath the northern Trans-North China Orogen, which suggest the possible intense thermo-chemical interactions between mantle-derived upwelling melts and the lower crust, probably associated with the magmatic underplating during the Mesozoic to Cenozoic evolution of this region. To our knowledge, it is the first time that ambient noise adjoint tomography is implemented for a 2-D medium. Compared with the intensive computational cost and storage requirement of 3-D adjoint tomography, this method offers a computationally efficient and inexpensive alternative to imaging fine-scale crustal structures beneath linear arrays.

Finite-fault source inversion using adjoint methods in 3D heterogeneous media

NASA Astrophysics Data System (ADS)

Somala, Surendra Nadh; Ampuero, Jean-Paul; Lapusta, Nadia

2018-04-01

Accounting for lateral heterogeneities in the 3D velocity structure of the crust is known to improve earthquake source inversion, compared to results based on 1D velocity models which are routinely assumed to derive finite-fault slip models. The conventional approach to include known 3D heterogeneity in source inversion involves pre-computing 3D Green's functions, which requires a number of 3D wave propagation simulations proportional to the number of stations or to the number of fault cells. The computational cost of such an approach is prohibitive for the dense datasets that could be provided by future earthquake observation systems. Here, we propose an adjoint-based optimization technique to invert for the spatio-temporal evolution of slip velocity. The approach does not require pre-computed Green's functions. The adjoint method provides the gradient of the cost function, which is used to improve the model iteratively employing an iterative gradient-based minimization method. The adjoint approach is shown to be computationally more efficient than the conventional approach based on pre-computed Green's functions in a broad range of situations. We consider data up to 1 Hz from a Haskell source scenario (a steady pulse-like rupture) on a vertical strike-slip fault embedded in an elastic 3D heterogeneous velocity model. The velocity model comprises a uniform background and a 3D stochastic perturbation with the von Karman correlation function. Source inversions based on the 3D velocity model are performed for two different station configurations, a dense and a sparse network with 1 km and 20 km station spacing, respectively. These reference inversions show that our inversion scheme adequately retrieves the rise time when the velocity model is exactly known, and illustrates how dense coverage improves the inference of peak slip velocities. We investigate the effects of uncertainties in the velocity model by performing source inversions based on an incorrect, homogeneous velocity model. We find that, for velocity uncertainties that have standard deviation and correlation length typical of available 3D crustal models, the inverted sources can be severely contaminated by spurious features even if the station density is high. When data from thousand or more receivers is used in source inversions in 3D heterogeneous media, the computational cost of the method proposed in this work is at least two orders of magnitude lower than source inversion based on pre-computed Green's functions.

Finite-fault source inversion using adjoint methods in 3-D heterogeneous media

NASA Astrophysics Data System (ADS)

Somala, Surendra Nadh; Ampuero, Jean-Paul; Lapusta, Nadia

2018-07-01

Accounting for lateral heterogeneities in the 3-D velocity structure of the crust is known to improve earthquake source inversion, compared to results based on 1-D velocity models which are routinely assumed to derive finite-fault slip models. The conventional approach to include known 3-D heterogeneity in source inversion involves pre-computing 3-D Green's functions, which requires a number of 3-D wave propagation simulations proportional to the number of stations or to the number of fault cells. The computational cost of such an approach is prohibitive for the dense data sets that could be provided by future earthquake observation systems. Here, we propose an adjoint-based optimization technique to invert for the spatio-temporal evolution of slip velocity. The approach does not require pre-computed Green's functions. The adjoint method provides the gradient of the cost function, which is used to improve the model iteratively employing an iterative gradient-based minimization method. The adjoint approach is shown to be computationally more efficient than the conventional approach based on pre-computed Green's functions in a broad range of situations. We consider data up to 1 Hz from a Haskell source scenario (a steady pulse-like rupture) on a vertical strike-slip fault embedded in an elastic 3-D heterogeneous velocity model. The velocity model comprises a uniform background and a 3-D stochastic perturbation with the von Karman correlation function. Source inversions based on the 3-D velocity model are performed for two different station configurations, a dense and a sparse network with 1 and 20 km station spacing, respectively. These reference inversions show that our inversion scheme adequately retrieves the rise time when the velocity model is exactly known, and illustrates how dense coverage improves the inference of peak-slip velocities. We investigate the effects of uncertainties in the velocity model by performing source inversions based on an incorrect, homogeneous velocity model. We find that, for velocity uncertainties that have standard deviation and correlation length typical of available 3-D crustal models, the inverted sources can be severely contaminated by spurious features even if the station density is high. When data from thousand or more receivers is used in source inversions in 3-D heterogeneous media, the computational cost of the method proposed in this work is at least two orders of magnitude lower than source inversion based on pre-computed Green's functions.

Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe

2013-01-01

This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.

2010-01-01

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Adjoint-Based Design of Rotors using the Navier-Stokes Equations in a Noninertial Reference Frame

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.

2009-01-01

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated using comparisons with a complex-variable technique, and a number of single- and multi-point optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Doppler Temperature Coefficient Calculations Using Adjoint-Weighted Tallies and Continuous Energy Cross Sections in MCNP6

NASA Astrophysics Data System (ADS)

Gonzales, Matthew Alejandro

The calculation of the thermal neutron Doppler temperature reactivity feedback co-efficient, a key parameter in the design and safe operation of advanced reactors, using first order perturbation theory in continuous energy Monte Carlo codes is challenging as the continuous energy adjoint flux is not readily available. Traditional approaches of obtaining the adjoint flux attempt to invert the random walk process as well as require data corresponding to all temperatures and their respective temperature derivatives within the system in order to accurately calculate the Doppler temperature feedback. A new method has been developed using adjoint-weighted tallies and On-The-Fly (OTF) generated continuous energy cross sections within the Monte Carlo N-Particle (MCNP6) transport code. The adjoint-weighted tallies are generated during the continuous energy k-eigenvalue Monte Carlo calculation. The weighting is based upon the iterated fission probability interpretation of the adjoint flux, which is the steady state population in a critical nuclear reactor caused by a neutron introduced at that point in phase space. The adjoint-weighted tallies are produced in a forward calculation and do not require an inversion of the random walk. The OTF cross section database uses a high order functional expansion between points on a user-defined energy-temperature mesh in which the coefficients with respect to a polynomial fitting in temperature are stored. The coefficients of the fits are generated before run- time and called upon during the simulation to produce cross sections at any given energy and temperature. The polynomial form of the OTF cross sections allows the possibility of obtaining temperature derivatives of the cross sections on-the-fly. The use of Monte Carlo sampling of adjoint-weighted tallies and the capability of computing derivatives of continuous energy cross sections with respect to temperature are used to calculate the Doppler temperature coefficient in a research version of MCNP6. Temperature feedback results from the cross sections themselves, changes in the probability density functions, as well as changes in the density of the materials. The focus of this work is specific to the Doppler temperature feedback which result from Doppler broadening of cross sections as well as changes in the probability density function within the scattering kernel. This method is compared against published results using Mosteller's numerical benchmark to show accurate evaluations of the Doppler temperature coefficient, fuel assembly calculations, and a benchmark solution based on the heavy gas model for free-gas elastic scattering. An infinite medium benchmark for neutron free gas elastic scattering for large scattering ratios and constant absorption cross section has been developed using the heavy gas model. An exact closed form solution for the neutron energy spectrum is obtained in terms of the confluent hypergeometric function and compared against spectra for the free gas scattering model in MCNP6. Results show a quick increase in convergence of the analytic energy spectrum to the MCNP6 code with increasing target size, showing absolute relative differences of less than 5% for neutrons scattering with carbon. The analytic solution has been generalized to accommodate piecewise constant in energy absorption cross section to produce temperature feedback. Results reinforce the constraints in which heavy gas theory may be applied resulting in a significant target size to accommodate increasing cross section structure. The energy dependent piecewise constant cross section heavy gas model was used to produce a benchmark calculation of the Doppler temperature coefficient to show accurate calculations when using the adjoint-weighted method. Results show the Doppler temperature coefficient using adjoint weighting and cross section derivatives accurately obtains the correct solution within statistics as well as reduce computer runtimes by a factor of 50.

Inverse Regional Modeling with Adjoint-Free Technique

NASA Astrophysics Data System (ADS)

Yaremchuk, M.; Martin, P.; Panteleev, G.; Beattie, C.

2016-02-01

The ongoing parallelization trend in computer technologies facilitates the use ensemble methods in geophysical data assimilation. Of particular interest are ensemble techniques which do not require the development of tangent linear numerical models and their adjoints for optimization. These ``adjoint-free'' methods minimize the cost function within the sequence of subspaces spanned by a carefully chosen sets perturbations of the control variables. In this presentation, an adjoint-free variational technique (a4dVar) is demonstrated in an application estimating initial conditions of two numerical models: the Navy Coastal Ocean Model (NCOM), and the surface wave model (WAM). With the NCOM, performance of both adjoint and adjoint-free 4dVar data assimilation techniques is compared in application to the hydrographic surveys and velocity observations collected in the Adriatic Sea in 2006. Numerical experiments have shown that a4dVar is capable of providing forecast skill similar to that of conventional 4dVar at comparable computational expense while being less susceptible to excitation of ageostrophic modes that are not supported by observations. Adjoint-free technique constrained by the WAM model is tested in a series of data assimilation experiments with synthetic observations in the southern Chukchi Sea. The types of considered observations are directional spectra estimated from point measurements by stationary buoys, significant wave height (SWH) observations by coastal high-frequency radars and along-track SWH observations by satellite altimeters. The a4dVar forecast skill is shown to be 30-40% better than the skill of the sequential assimilaiton method based on optimal interpolation which is currently used in operations. Prospects of further development of the a4dVar methods in regional applications are discussed.

Adjoint optimization of natural convection problems: differentially heated cavity

NASA Astrophysics Data System (ADS)

Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.

2017-12-01

Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here for the first time.

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Diskin, Boris; Yamaleev, Nail K.

2009-01-01

An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

Crustal wavespeed structure of North Texas and Oklahoma based on ambient noise cross-correlation functions and adjoint tomography

NASA Astrophysics Data System (ADS)

Zhu, H.

2017-12-01

Recently, seismologists observed increasing seismicity in North Texas and Oklahoma. Based on seismic observations and other geophysical measurements, some studies suggested possible links between the increasing seismicity and wastewater injection during unconventional oil and gas exploration. To better monitor seismic events and investigate their mechanisms, we need an accurate 3D crustal wavespeed model for North Texas and Oklahoma. Considering the uneven distribution of earthquakes in this region, seismic tomography with local earthquake records have difficulties to achieve good illumination. To overcome this limitation, in this study, ambient noise cross-correlation functions are used to constrain subsurface variations in wavespeeds. I use adjoint tomography to iteratively fit frequency-dependent phase differences between observed and predicted band-limited Green's functions. The spectral-element method is used to numerically calculate the band-limited Green's functions and the adjoint method is used to calculate misfit gradients with respect to wavespeeds. 25 preconditioned conjugate gradient iterations are used to update model parameters and minimize data misfits. Features in the new crustal model M25 correlates with geological units in the study region, including the Llano uplift, the Anadarko basin and the Ouachita orogenic front. In addition, these seismic anomalies correlate with gravity and magnetic observations. This new model can be used to better constrain earthquake source parameters in North Texas and Oklahoma, such as epicenter location and moment tensor solutions, which are important for investigating potential relations between seismicity and unconventional oil and gas exploration.

Source Parameter Estimation using the Second-order Closure Integrated Puff Model

DTIC Science & Technology

The sensor measurements are categorized as triggered and non-triggered based on the recorded concentration measurements and a threshold...concentration value. Using each measured value, sources of adjoint material are created from the triggered and non-triggered sensors, and the adjoint transport...equations are solved to predict the adjoint concentration fields. The adjoint source strength is inversely proportional to the concentration measurement

Application of Parallel Adjoint-Based Error Estimation and Anisotropic Grid Adaptation for Three-Dimensional Aerospace Configurations

NASA Technical Reports Server (NTRS)

Lee-Rausch, E. M.; Park, M. A.; Jones, W. T.; Hammond, D. P.; Nielsen, E. J.

2005-01-01

This paper demonstrates the extension of error estimation and adaptation methods to parallel computations enabling larger, more realistic aerospace applications and the quantification of discretization errors for complex 3-D solutions. Results were shown for an inviscid sonic-boom prediction about a double-cone configuration and a wing/body segmented leading edge (SLE) configuration where the output function of the adjoint was pressure integrated over a part of the cylinder in the near field. After multiple cycles of error estimation and surface/field adaptation, a significant improvement in the inviscid solution for the sonic boom signature of the double cone was observed. Although the double-cone adaptation was initiated from a very coarse mesh, the near-field pressure signature from the final adapted mesh compared very well with the wind-tunnel data which illustrates that the adjoint-based error estimation and adaptation process requires no a priori refinement of the mesh. Similarly, the near-field pressure signature for the SLE wing/body sonic boom configuration showed a significant improvement from the initial coarse mesh to the final adapted mesh in comparison with the wind tunnel results. Error estimation and field adaptation results were also presented for the viscous transonic drag prediction of the DLR-F6 wing/body configuration, and results were compared to a series of globally refined meshes. Two of these globally refined meshes were used as a starting point for the error estimation and field-adaptation process where the output function for the adjoint was the total drag. The field-adapted results showed an improvement in the prediction of the drag in comparison with the finest globally refined mesh and a reduction in the estimate of the remaining drag error. The adjoint-based adaptation parameter showed a need for increased resolution in the surface of the wing/body as well as a need for wake resolution downstream of the fuselage and wing trailing edge in order to achieve the requested drag tolerance. Although further adaptation was required to meet the requested tolerance, no further cycles were computed in order to avoid large discrepancies between the surface mesh spacing and the refined field spacing.

Modeling Finite Faults Using the Adjoint Wave Field

NASA Astrophysics Data System (ADS)

Hjörleifsdóttir, V.; Liu, Q.; Tromp, J.

2004-12-01

Time-reversal acoustics, a technique in which an acoustic signal is recorded by an array of transducers, time-reversed, and retransmitted, is used, e.g., in medical therapy to locate and destroy gallstones (for a review see Fink, 1997). As discussed by Tromp et al. (2004), time-reversal techniques for locating sources are closely linked to so-called `adjoint methods' (Talagrand and Courtier, 1987), which may be used to evaluate the gradient of a misfit function. Tromp et al. (2004) illustrate how a (finite) source inversion may be implemented based upon the adjoint wave field by writing the change in the misfit function, δ χ, due to a change in the moment-density tensor, δ m, as an integral of the adjoint strain field ɛ x,t) over the fault plane Σ : δ χ = ∫ 0T∫_Σ ɛ x,T-t) :δ m(x,t) d2xdt. We find that if the real fault plane is located at a distance δ h in the direction of the fault normal hat n, then to first order an additional factor of ∫ 0T∫_Σ δ h (x) ∂ n ɛ x,T-t):m(x,t) d2xdt is added to the change in the misfit function. The adjoint strain is computed by using the time-reversed difference between data and synthetics recorded at all receivers as simultaneous sources and recording the resulting strain on the fault plane. In accordance with time-reversal acoustics, all the resulting waves will constructively interfere at the position of the original source in space and time. The level of convergence will be deterimined by factors such as the source-receiver geometry, the frequency of the recorded data and synthetics, and the accuracy of the velocity structure used when back propagating the wave field. The terms ɛ x,T-t) and ∂ n ɛ x,T-t):m(x,t) can be viewed as sensitivity kernels for the moment density and the faultplane location respectively. By looking at these quantities we can make an educated choice of fault parametrization given the data in hand. The process can then be repeated to invert for the best source model, as demonstrated by Tromp et al. (2004) for the magnitude of a point force. In this presentation we explore the applicability of adjoint methods to estimating finite source parameters. Fink, M. (1997), Time reversed acoustics, Physics Today, 50(3), 34--40. Talagrand, O., and P.~Courtier (1987), Variational assimilation of meteorological observations with the adjoint vorticity equatuation. I: Theory, Q. J. R. Meteorol. Soc., 113, 1311--1328. Tromp, J., C.~Tape, and Q.~Liu (2004), Waveform tomography, adjoint methods, time reversal, and banana-doughnut kernels, Geophys. Jour. Int., in press

Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing

NASA Astrophysics Data System (ADS)

Blonigan, Patrick J.

2017-11-01

This paper presents a discrete adjoint version of the recently developed non-intrusive least squares shadowing (NILSS) algorithm, which circumvents the instability that conventional adjoint methods encounter for chaotic systems. The NILSS approach involves solving a smaller minimization problem than other shadowing approaches and can be implemented with only minor modifications to preexisting tangent and adjoint solvers. Adjoint NILSS is demonstrated on a small chaotic ODE, a one-dimensional scalar PDE, and a direct numerical simulation (DNS) of the minimal flow unit, a turbulent channel flow on a small spatial domain. This is the first application of an adjoint shadowing-based algorithm to a three-dimensional turbulent flow.

Frozen Gaussian approximation for 3D seismic tomography

NASA Astrophysics Data System (ADS)

Chai, Lihui; Tong, Ping; Yang, Xu

2018-05-01

Three-dimensional (3D) wave-equation-based seismic tomography is computationally challenging in large scales and high-frequency regime. In this paper, we apply the frozen Gaussian approximation (FGA) method to compute 3D sensitivity kernels and seismic tomography of high-frequency. Rather than standard ray theory used in seismic inversion (e.g. Kirchhoff migration and Gaussian beam migration), FGA is used to compute the 3D high-frequency sensitivity kernels for travel-time or full waveform inversions. Specifically, we reformulate the equations of the forward and adjoint wavefields for the purpose of convenience to apply FGA, and with this reformulation, one can efficiently compute the Green’s functions whose convolutions with source time function produce wavefields needed for the construction of 3D kernels. Moreover, a fast summation method is proposed based on local fast Fourier transform which greatly improves the speed of reconstruction as the last step of FGA algorithm. We apply FGA to both the travel-time adjoint tomography and full waveform inversion (FWI) on synthetic crosswell seismic data with dominant frequencies as high as those of real crosswell data, and confirm again that FWI requires a more sophisticated initial velocity model for the convergence than travel-time adjoint tomography. We also numerically test the accuracy of applying FGA to local earthquake tomography. This study paves the way to directly apply wave-equation-based seismic tomography methods into real data around their dominant frequencies.

Learning a trajectory using adjoint functions and teacher forcing

NASA Technical Reports Server (NTRS)

Toomarian, Nikzad B.; Barhen, Jacob

1992-01-01

A new methodology for faster supervised temporal learning in nonlinear neural networks is presented which builds upon the concept of adjoint operators to allow fast computation of the gradients of an error functional with respect to all parameters of the neural architecture, and exploits the concept of teacher forcing to incorporate information on the desired output into the activation dynamics. The importance of the initial or final time conditions for the adjoint equations is discussed. A new algorithm is presented in which the adjoint equations are solved simultaneously (i.e., forward in time) with the activation dynamics of the neural network. We also indicate how teacher forcing can be modulated in time as learning proceeds. The results obtained show that the learning time is reduced by one to two orders of magnitude with respect to previously published results, while trajectory tracking is significantly improved. The proposed methodology makes hardware implementation of temporal learning attractive for real-time applications.

On the Implementation and Performance of Iterative Methods for Computational Electromagnetics

DTIC Science & Technology

1985-12-01

based on F3 only if L is self-adjoint and positive definite in the sense of Griffel [651. Each of the above functionals gives rise to a different...New York: Wiley, 1960. [65] D. H. Griffel , Applied Functional Analysis. New York: Wiley, 1981. [661 R. Fletcher and C. M. Reeves, "Functional

Sensitivity Analysis of Multidisciplinary Rotorcraft Simulations

NASA Technical Reports Server (NTRS)

Wang, Li; Diskin, Boris; Biedron, Robert T.; Nielsen, Eric J.; Bauchau, Olivier A.

2017-01-01

A multidisciplinary sensitivity analysis of rotorcraft simulations involving tightly coupled high-fidelity computational fluid dynamics and comprehensive analysis solvers is presented and evaluated. An unstructured sensitivity-enabled Navier-Stokes solver, FUN3D, and a nonlinear flexible multibody dynamics solver, DYMORE, are coupled to predict the aerodynamic loads and structural responses of helicopter rotor blades. A discretely-consistent adjoint-based sensitivity analysis available in FUN3D provides sensitivities arising from unsteady turbulent flows and unstructured dynamic overset meshes, while a complex-variable approach is used to compute DYMORE structural sensitivities with respect to aerodynamic loads. The multidisciplinary sensitivity analysis is conducted through integrating the sensitivity components from each discipline of the coupled system. Numerical results verify accuracy of the FUN3D/DYMORE system by conducting simulations for a benchmark rotorcraft test model and comparing solutions with established analyses and experimental data. Complex-variable implementation of sensitivity analysis of DYMORE and the coupled FUN3D/DYMORE system is verified by comparing with real-valued analysis and sensitivities. Correctness of adjoint formulations for FUN3D/DYMORE interfaces is verified by comparing adjoint-based and complex-variable sensitivities. Finally, sensitivities of the lift and drag functions obtained by complex-variable FUN3D/DYMORE simulations are compared with sensitivities computed by the multidisciplinary sensitivity analysis, which couples adjoint-based flow and grid sensitivities of FUN3D and FUN3D/DYMORE interfaces with complex-variable sensitivities of DYMORE structural responses.

Seismic Imaging of VTI, HTI and TTI based on Adjoint Methods

NASA Astrophysics Data System (ADS)

Rusmanugroho, H.; Tromp, J.

2014-12-01

Recent studies show that isotropic seismic imaging based on adjoint method reduces low-frequency artifact caused by diving waves, which commonly occur in two-wave wave-equation migration, such as Reverse Time Migration (RTM). Here, we derive new expressions of sensitivity kernels for Vertical Transverse Isotropy (VTI) using the Thomsen parameters (ɛ, δ, γ) plus the P-, and S-wave speeds (α, β) as well as via the Chen & Tromp (GJI 2005) parameters (A, C, N, L, F). For Horizontal Transverse Isotropy (HTI), these parameters depend on an azimuthal angle φ, where the tilt angle θ is equivalent to 90°, and for Tilted Transverse Isotropy (TTI), these parameters depend on both the azimuth and tilt angles. We calculate sensitivity kernels for each of these two approaches. Individual kernels ("images") are numerically constructed based on the interaction between the regular and adjoint wavefields in smoothed models which are in practice estimated through Full-Waveform Inversion (FWI). The final image is obtained as a result of summing all shots, which are well distributed to sample the target model properly. The impedance kernel, which is a sum of sensitivity kernels of density and the Thomsen or Chen & Tromp parameters, looks crisp and promising for seismic imaging. The other kernels suffer from low-frequency artifacts, similar to traditional seismic imaging conditions. However, all sensitivity kernels are important for estimating the gradient of the misfit function, which, in combination with a standard gradient-based inversion algorithm, is used to minimize the objective function in FWI.

Adjoint tomography of Empirical Green's functions from ambient noise in Southern California

NASA Astrophysics Data System (ADS)

Wang, K.; Liu, Q.; Yang, Y.; Basini, P.; Tape, C.

2017-12-01

We construct a new shear-wave velocity (Vsv) model in Southern California by adjoint tomography of Rayleigh-wave Empirical Green's functions at 5-50 s period from Z-Z component ambient noise cross-correlations. The initial model of our adjoint tomography is the isotropic Vs model M16 from Tape et al. [2010], which is generated by three-component body and surface waves at 2-30 s period from local earthquake data. Synthetic Green's functions (SGFs) from M16 show a good agreement with the Empirical Green's functions (EGFs) from ambient noise at 5-50 s and 10-50 s period bands, but have an average 1.75 s advance in time at 20-50 s. By minimizing the traveltime differences between the EGFs and SGFs using gradient-based algorithm, the initial model is refined and improved and the total misfits is reduced from the initial 1.75s to its convergent point of 0.33 s after five iterations. The final Vsv model fits EGF waveforms better than the initial model at all the three frequency bands with smaller misfit distributions. Our new Vsv model reveals some new features in the mid- and lower-crust, mainly including: (1) the mean speed of lower crust is slowed down by about 5%; (2) In the Los Angeles Basin and its Northern area, the speed is higher than the initial model throughout the crust; (3) beneath the westernmost Peninsular Range Batholith (PRB) and Sierra Nevada Batholith (SNB), we observe high shear velocities in the lower crust; (4) a shallow high-velocity zone in the mid-crust are observed beneath Salton Trough Basin. Our model also shows refined lateral velocity gradient across PRB, SNB, San Andreas Fault (SAF), which helps to understand the west-east compositional boundary in PRB, SNB, and the dip angle and the depth extent of SAF. Our study demonstrates the feasibility of adjoint tomography of ambient noise data in southern California, which is an important complement to earthquake data. The numerical solver used in adjoint tomography can provide more accurate structure sensitivity kernels than analytical methods used in traditional ambient noise tomography.

2D Inviscid and Viscous Inverse Design Using Continuous Adjoint and Lax-Wendroff Formulation

NASA Astrophysics Data System (ADS)

Proctor, Camron Lisle

The continuous adjoint (CA) technique for optimization and/or inverse-design of aerodynamic components has seen nearly 30 years of documented success in academia. The benefits of using CA versus a direct sensitivity analysis are shown repeatedly in the literature. However, the use of CA in industry is relatively unheard-of. The sparseness of industry contributions to the field may be attributed to the tediousness of the derivation and/or to the difficulties in implementation due to the lack of well-documented adjoint numerical methods. The focus of this work has been to thoroughly document the techniques required to build a two-dimensional CA inverse-design tool. To this end, this work begins with a short background on computational fluid dynamics (CFD) and the use of optimization tools in conjunction with CFD tools to solve aerodynamic optimization problems. A thorough derivation of the continuous adjoint equations and the accompanying gradient calculations for inviscid and viscous constraining equations follows the introduction. Next, the numerical techniques used for solving the partial differential equations (PDEs) governing the flow equations and the adjoint equations are described. Numerical techniques for the supplementary equations are discussed briefly. Subsequently, a verification of the efficacy of the inverse design tool, for the inviscid adjoint equations as well as possible numerical implementation pitfalls are discussed. The NACA0012 airfoil is used as an initial airfoil and surface pressure distribution and the NACA16009 is used as the desired pressure and vice versa. Using a Savitsky-Golay gradient filter, convergence (defined as a cost function<1E-5) is reached in approximately 220 design iteration using 121 design variables. The inverse-design using inviscid adjoint equations results are followed by the discussion of the viscous inverse design results and techniques used to further the convergence of the optimizer. The relationship between limiting step-size and convergence in a line-search optimization is shown to slightly decrease the final cost function at significant computational cost. A gradient damping technique is presented and shown to increase the convergence rate for the optimization in viscous problems, at a negligible increase in computational cost, but is insufficient to converge the solution. Systematically including adjacent surface vertices in the perturbation of a design variable, also a surface vertex, is shown to affect the convergence capability of the viscous optimizer. Finally, a comparison of using inviscid adjoint equations, as opposed to viscous adjoint equations, on viscous flow is presented, and the inviscid adjoint paired with viscous flow is found to reduce the cost function further than the viscous adjoint for the presented problem.

Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation

NASA Technical Reports Server (NTRS)

Park, Michael A.

2002-01-01

Engineering computational fluid dynamics (CFD) analysis and design applications focus on output functions (e.g., lift, drag). Errors in these output functions are generally unknown and conservatively accurate solutions may be computed. Computable error estimates can offer the possibility to minimize computational work for a prescribed error tolerance. Such an estimate can be computed by solving the flow equations and the linear adjoint problem for the functional of interest. The computational mesh can be modified to minimize the uncertainty of a computed error estimate. This robust mesh-adaptation procedure automatically terminates when the simulation is within a user specified error tolerance. This procedure for estimating and adapting to error in a functional is demonstrated for three-dimensional Euler problems. An adaptive mesh procedure that links to a Computer Aided Design (CAD) surface representation is demonstrated for wing, wing-body, and extruded high lift airfoil configurations. The error estimation and adaptation procedure yielded corrected functions that are as accurate as functions calculated on uniformly refined grids with ten times as many grid points.

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

DOE PAGES

Jakeman, J. D.; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this papermore » we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

Crustal wavespeed structure of North Texas and Oklahoma based on ambient noise cross-correlation functions and adjoint tomography

NASA Astrophysics Data System (ADS)

Zhu, Hejun

2018-04-01

Recently, seismologists observed increasing seismicity in North Texas and Oklahoma. Based on seismic observations and other geophysical measurements, numerous studies suggested links between the increasing seismicity and wastewater injection during unconventional oil and gas exploration. To better monitor seismic events and investigate their triggering mechanisms, we need an accurate 3D crustal wavespeed model for the study region. Considering the uneven distribution of earthquakes in this area, seismic tomography with local earthquake records have difficulties achieving even illumination. To overcome this limitation, in this study, ambient noise cross-correlation functions are used to constrain subsurface variations in wavespeeds. I use adjoint tomography to iteratively fit frequency-dependent phase differences between observed and predicted band-limited Green's functions. The spectral-element method is used to numerically calculate the band-limited Green's functions and the adjoint method is used to calculate misfit gradients with respect to wavespeeds. Twenty five preconditioned conjugate gradient iterations are used to update model parameters and minimize data misfits. Features in the new crustal model TO25 correlates well with geological provinces in the study region, including the Llano uplift, the Anadarko basin and the Ouachita orogenic front, etc. In addition, there are relatively good correlations between seismic results with gravity and magnetic observations. This new crustal model can be used to better constrain earthquake source parameters in North Texas and Oklahoma, such as epicenter location as well as moment tensor solutions, which are important for investigating triggering mechanisms between these induced earthquakes and unconventional oil and gas exploration activities.

Unsteady Adjoint Approach for Design Optimization of Flapping Airfoils

NASA Technical Reports Server (NTRS)

Lee, Byung Joon; Liou, Meng-Sing

2012-01-01

This paper describes the work for optimizing the propulsive efficiency of flapping airfoils, i.e., improving the thrust under constraining aerodynamic work during the flapping flights by changing their shape and trajectory of motion with the unsteady discrete adjoint approach. For unsteady problems, it is essential to properly resolving time scales of motion under consideration and it must be compatible with the objective sought after. We include both the instantaneous and time-averaged (periodic) formulations in this study. For the design optimization with shape parameters or motion parameters, the time-averaged objective function is found to be more useful, while the instantaneous one is more suitable for flow control. The instantaneous objective function is operationally straightforward. On the other hand, the time-averaged objective function requires additional steps in the adjoint approach; the unsteady discrete adjoint equations for a periodic flow must be reformulated and the corresponding system of equations solved iteratively. We compare the design results from shape and trajectory optimizations and investigate the physical relevance of design variables to the flapping motion at on- and off-design conditions.

Development and Applications of the FV3 GEOS-5 Adjoint Modeling System

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kim, Jong G.; Lin, Shian-Jiann; Errico, Ron; Gelaro, Ron; Kent, James; Coy, Larry; Doyle, Jim; Goldstein, Alex

2017-01-01

GMAO has developed a highly sophisticated adjoint modeling system based on the most recent version of the finite volume cubed sphere (FV3) dynamical core. This provides a mechanism for investigating sensitivity to initial conditions and examining observation impacts. It also allows for the computation of singular vectors and for the implementation of hybrid 4DVAR. In this work we will present the scientific assessment of the new adjoint system and show results from a number of research application of the adjoint system.

Adjoint Sensitivity Analysis of Orbital Mechanics: Application to Computations of Observables' Partials with Respect to Harmonics of the Planetary Gravity Fields

NASA Technical Reports Server (NTRS)

Ustinov, Eugene A.; Sunseri, Richard F.

2005-01-01

An approach is presented to the inversion of gravity fields based on evaluation of partials of observables with respect to gravity harmonics using the solution of adjoint problem of orbital dynamics of the spacecraft. Corresponding adjoint operator is derived directly from the linear operator of the linearized forward problem of orbital dynamics. The resulting adjoint problem is similar to the forward problem and can be solved by the same methods. For given highest degree N of gravity harmonics desired, this method involves integration of N adjoint solutions as compared to integration of N2 partials of the forward solution with respect to gravity harmonics in the conventional approach. Thus, for higher resolution gravity models, this approach becomes increasingly more effective in terms of computer resources as compared to the approach based on the solution of the forward problem of orbital dynamics.

Assessing the Impact of Observations on Numerical Weather Forecasts Using the Adjoint Method

NASA Technical Reports Server (NTRS)

Gelaro, Ronald

2012-01-01

The adjoint of a data assimilation system provides a flexible and efficient tool for estimating observation impacts on short-range weather forecasts. The impacts of any or all observations can be estimated simultaneously based on a single execution of the adjoint system. The results can be easily aggregated according to data type, location, channel, etc., making this technique especially attractive for examining the impacts of new hyper-spectral satellite instruments and for conducting regular, even near-real time, monitoring of the entire observing system. This talk provides a general overview of the adjoint method, including the theoretical basis and practical implementation of the technique. Results are presented from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. When performed in conjunction with standard observing system experiments (OSEs), the adjoint results reveal both redundancies and dependencies between observing system impacts as observations are added or removed from the assimilation system. Understanding these dependencies may be important for optimizing the use of the current observational network and defining requirements for future observing systems

Bose-Fermi degeneracies in large N adjoint QCD

DOE PAGES

Basar, Gokce; Cherman, Aleksey; McGady, David

2015-07-06

Here, we analyze the large N limit of adjoint QCD, an SU( N) gauge theory with N f flavors of massless adjoint Majorana fermions, compactified on S 3 × S 1. We focus on the weakly-coupled confining small- S 3 regime. If the fermions are given periodic boundary conditions on S 1, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition function. These cancellations follow a pattern previously seen in the context of misaligned supersymmetry, and lead to the absence of Hagedorn instabilities for any S 1 size L, even though the bosonicmore » and fermionic densities of states both have Hagedorn growth. Adjoint QCD stays in the confining phase for any L ~ N 0, explaining how it is able to enjoy large N volume independence for any L. The large N boson-fermion cancellations take place in a setting where adjoint QCD is manifestly non-supersymmetric at any finite N, and are consistent with the recent conjecture that adjoint QCD has emergent fermionic symmetries in the large N limit.« less

Development of CO2 inversion system based on the adjoint of the global coupled transport model

NASA Astrophysics Data System (ADS)

Belikov, Dmitry; Maksyutov, Shamil; Chevallier, Frederic; Kaminski, Thomas; Ganshin, Alexander; Blessing, Simon

2014-05-01

We present the development of an inverse modeling system employing an adjoint of the global coupled transport model consisting of the National Institute for Environmental Studies (NIES) Eulerian transport model (TM) and the Lagrangian plume diffusion model (LPDM) FLEXPART. NIES TM is a three-dimensional atmospheric transport model, which solves the continuity equation for a number of atmospheric tracers on a grid spanning the entire globe. Spatial discretization is based on a reduced latitude-longitude grid and a hybrid sigma-isentropic coordinate in the vertical. NIES TM uses a horizontal resolution of 2.5°×2.5°. However, to resolve synoptic-scale tracer distributions and to have the ability to optimize fluxes at resolutions of 0.5° and higher we coupled NIES TM with the Lagrangian model FLEXPART. The Lagrangian component of the forward and adjoint models uses precalculated responses of the observed concentration to the surface fluxes and 3-D concentrations field simulated with the FLEXPART model. NIES TM and FLEXPART are driven by JRA-25/JCDAS reanalysis dataset. Construction of the adjoint of the Lagrangian part is less complicated, as LPDMs calculate the sensitivity of measurements to the surrounding emissions field by tracking a large number of "particles" backwards in time. Developing of the adjoint to Eulerian part was performed with automatic differentiation tool the Transformation of Algorithms in Fortran (TAF) software (http://www.FastOpt.com). This method leads to the discrete adjoint of NIES TM. The main advantage of the discrete adjoint is that the resulting gradients of the numerical cost function are exact, even for nonlinear algorithms. The overall advantages of our method are that: 1. No code modification of Lagrangian model is required, making it applicable to combination of global NIES TM and any Lagrangian model; 2. Once run, the Lagrangian output can be applied to any chemically neutral gas; 3. High-resolution results can be obtained over limited regions close to the monitoring sites (using the LPDM part), and at coarse resolution for the rest of the globe (using the Eulerian part), minimizing aggregation errors and computation cost. The adjoint of the coupled high-resolution Eulerian-Lagrangian model will be incorporated into the PYVAR CO2 variational inverse system (Chevallier et al., 2005). Chevallier, F., Fisher, M., Peylin, P., Serrar, S., Bousquet, P., Bréon, F.-M., Chédin, A., and Ciais, P.: Inferring CO2 sources and sinks from satellite observations: method and application to TOVS data, J. Geophys. Res., 110, D24309, doi:10.1029/2005JD006390, 2005.

Direct Linearization and Adjoint Approaches to Evaluation of Atmospheric Weighting Functions and Surface Partial Derivatives: General Principles, Synergy and Areas of Application

NASA Technical Reports Server (NTRS)

Ustino, Eugene A.

2006-01-01

This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches

Seismic tomography of the southern California crust based on spectral-element and adjoint methods

NASA Astrophysics Data System (ADS)

Tape, Carl; Liu, Qinya; Maggi, Alessia; Tromp, Jeroen

2010-01-01

We iteratively improve a 3-D tomographic model of the southern California crust using numerical simulations of seismic wave propagation based on a spectral-element method (SEM) in combination with an adjoint method. The initial 3-D model is provided by the Southern California Earthquake Center. The data set comprises three-component seismic waveforms (i.e. both body and surface waves), filtered over the period range 2-30 s, from 143 local earthquakes recorded by a network of 203 stations. Time windows for measurements are automatically selected by the FLEXWIN algorithm. The misfit function in the tomographic inversion is based on frequency-dependent multitaper traveltime differences. The gradient of the misfit function and related finite-frequency sensitivity kernels for each earthquake are computed using an adjoint technique. The kernels are combined using a source subspace projection method to compute a model update at each iteration of a gradient-based minimization algorithm. The inversion involved 16 iterations, which required 6800 wavefield simulations. The new crustal model, m16, is described in terms of independent shear (VS) and bulk-sound (VB) wave speed variations. It exhibits strong heterogeneity, including local changes of +/-30 per cent with respect to the initial 3-D model. The model reveals several features that relate to geological observations, such as sedimentary basins, exhumed batholiths, and contrasting lithologies across faults. The quality of the new model is validated by quantifying waveform misfits of full-length seismograms from 91 earthquakes that were not used in the tomographic inversion. The new model provides more accurate synthetic seismograms that will benefit seismic hazard assessment.

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jakeman, J.D., E-mail: jdjakem@sandia.gov; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchicalmore » surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

Optical properties reconstruction using the adjoint method based on the radiative transfer equation

NASA Astrophysics Data System (ADS)

Addoum, Ahmad; Farges, Olivier; Asllanaj, Fatmir

2018-01-01

An efficient algorithm is proposed to reconstruct the spatial distribution of optical properties in heterogeneous media like biological tissues. The light transport through such media is accurately described by the radiative transfer equation in the frequency-domain. The adjoint method is used to efficiently compute the objective function gradient with respect to optical parameters. Numerical tests show that the algorithm is accurate and robust to retrieve simultaneously the absorption μa and scattering μs coefficients for lowly and highly absorbing medium. Moreover, the simultaneous reconstruction of μs and the anisotropy factor g of the Henyey-Greenstein phase function is achieved with a reasonable accuracy. The main novelty in this work is the reconstruction of g which might open the possibility to image this parameter in tissues as an additional contrast agent in optical tomography.

An Efficient Radial Basis Function Mesh Deformation Scheme within an Adjoint-Based Aerodynamic Optimization Framework

NASA Astrophysics Data System (ADS)

Poirier, Vincent

Mesh deformation schemes play an important role in numerical aerodynamic optimization. As the aerodynamic shape changes, the computational mesh must adapt to conform to the deformed geometry. In this work, an extension to an existing fast and robust Radial Basis Function (RBF) mesh movement scheme is presented. Using a reduced set of surface points to define the mesh deformation increases the efficiency of the RBF method; however, at the cost of introducing errors into the parameterization by not recovering the exact displacement of all surface points. A secondary mesh movement is implemented, within an adjoint-based optimization framework, to eliminate these errors. The proposed scheme is tested within a 3D Euler flow by reducing the pressure drag while maintaining lift of a wing-body configured Boeing-747 and an Onera-M6 wing. As well, an inverse pressure design is executed on the Onera-M6 wing and an inverse span loading case is presented for a wing-body configured DLR-F6 aircraft.

Skyshine analysis using energy and angular dependent dose-contribution fluxes obtained from air-over-ground adjoint calculation.

PubMed

Uematsu, Mikio; Kurosawa, Masahiko

2005-01-01

A generalised and convenient skyshine dose analysis method has been developed based on forward-adjoint folding technique. In the method, the air penetration data were prepared by performing an adjoint DOT3.5 calculation with cylindrical air-over-ground geometry having an adjoint point source (importance of unit flux to dose rate at detection point) in the centre. The accuracy of the present method was certified by comparing with DOT3.5 forward calculation. The adjoint flux data can be used as generalised radiation skyshine data for all sorts of nuclear facilities. Moreover, the present method supplies plenty of energy-angular dependent contribution flux data, which will be useful for detailed shielding design of facilities.

Discrete Adjoint-Based Design for Unsteady Turbulent Flows On Dynamic Overset Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Diskin, Boris

2012-01-01

A discrete adjoint-based design methodology for unsteady turbulent flows on three-dimensional dynamic overset unstructured grids is formulated, implemented, and verified. The methodology supports both compressible and incompressible flows and is amenable to massively parallel computing environments. The approach provides a general framework for performing highly efficient and discretely consistent sensitivity analysis for problems involving arbitrary combinations of overset unstructured grids which may be static, undergoing rigid or deforming motions, or any combination thereof. General parent-child motions are also accommodated, and the accuracy of the implementation is established using an independent verification based on a complex-variable approach. The methodology is used to demonstrate aerodynamic optimizations of a wind turbine geometry, a biologically-inspired flapping wing, and a complex helicopter configuration subject to trimming constraints. The objective function for each problem is successfully reduced and all specified constraints are satisfied.

Seismic Full Waveform Modeling & Imaging in Attenuating Media

NASA Astrophysics Data System (ADS)

Guo, Peng

Seismic attenuation strongly affects seismic waveforms by amplitude loss and velocity dispersion. Without proper inclusion of Q parameters, errors can be introduced for seismic full waveform modeling and imaging. Three different (Carcione's, Robertsson's, and the generalized Robertsson's) isotropic viscoelastic wave equations based on the generalized standard linear solid (GSLS) are evaluated. The second-order displacement equations are derived, and used to demonstrate that, with the same stress relaxation times, these viscoelastic formulations are equivalent. By introducing separate memory variables for P and S relaxation functions, Robertsson's formulation is generalized to allow different P and S wave stress relaxation times, which improves the physical consistency of the Qp and Qs modelled in the seismograms.The three formulations have comparable computational cost. 3D seismic finite-difference forward modeling is applied to anisotropic viscoelastic media. The viscoelastic T-matrix (a dynamic effective medium theory) relates frequency-dependent anisotropic attenuation and velocity to reservoir properties in fractured HTI media, based on the meso-scale fluid flow attenuation mechanism. The seismic signatures resulting from changing viscoelastic reservoir properties are easily visible. Analysis of 3D viscoelastic seismograms suggests that anisotropic attenuation is a potential tool for reservoir characterization. To compensate the Q effects during reverse-time migration (RTM) in viscoacoustic and viscoelastic media, amplitudes need to be compensated during wave propagation; the propagation velocity of the Q-compensated wavefield needs to be the same as in the attenuating wavefield, to restore the phase information. Both amplitude and phase can be compensated when the velocity dispersion and the amplitude loss are decoupled. For wave equations based on the GSLS, because Q effects are coupled in the memory variables, Q-compensated wavefield propagates faster than the attenuating wavefield, and introduce unwanted phase shift. Numerical examples show that there are phase (depth) shifts in the Q-compensated RTM images from the GSLS equation. An adjoint-based least-squares reverse-time migration is proposed for viscoelastic media (Q-LSRTM), to compensate the attenuation losses in P and S images. The viscoelastic adjoint operator, and the P and S modulus perturbation imaging conditions are derived using the adjoint-state method and an augmented Lagrangian functional. Q-LSRTM solves the viscoelastic linearized modeling operator for synthetic data, and the adjoint operator is used for back propagating the data residual. Q-LSRTM is capable of iteratively updating the P and S modulus perturbations,in the direction of minimizing data residuals, and attenuation loss is iteratively compensated. A novel Q compensation approach is developed for adjoint seismic imaging by pseudodifferential scaling. With a correct Q model included in the migration algorithm, propagation effects, including the Q effects, can be compensated with the application of the inverse Hessian to the RTM image. Pseudodifferential scaling is used to efficiently approximate the action of the inverse Hessian. Numerical examples indicate that the adjoint RTM images with pseudodifferential scaling approximate the true model perturbation, and can be used as well-conditioned gradients for least-squares imaging.

An Adjoint-Based Approach to Study a Flexible Flapping Wing in Pitching-Rolling Motion

NASA Astrophysics Data System (ADS)

Jia, Kun; Wei, Mingjun; Xu, Min; Li, Chengyu; Dong, Haibo

2017-11-01

Flapping-wing aerodynamics, with advantages in agility, efficiency, and hovering capability, has been the choice of many flyers in nature. However, the study of bio-inspired flapping-wing propulsion is often hindered by the problem's large control space with different wing kinematics and deformation. The adjoint-based approach reduces largely the computational cost to a feasible level by solving an inverse problem. Facing the complication from moving boundaries, non-cylindrical calculus provides an easy extension of traditional adjoint-based approach to handle the optimization involving moving boundaries. The improved adjoint method with non-cylindrical calculus for boundary treatment is first applied on a rigid pitching-rolling plate, then extended to a flexible one with active deformation to further increase its propulsion efficiency. The comparison of flow dynamics with the initial and optimal kinematics and deformation provides a unique opportunity to understand the flapping-wing mechanism. Supported by AFOSR and ARL.

Towards adjoint-based inversion of time-dependent mantle convection with nonlinear viscosity

NASA Astrophysics Data System (ADS)

Li, Dunzhu; Gurnis, Michael; Stadler, Georg

2017-04-01

We develop and study an adjoint-based inversion method for the simultaneous recovery of initial temperature conditions and viscosity parameters in time-dependent mantle convection from the current mantle temperature and historic plate motion. Based on a realistic rheological model with temperature-dependent and strain-rate-dependent viscosity, we formulate the inversion as a PDE-constrained optimization problem. The objective functional includes the misfit of surface velocity (plate motion) history, the misfit of the current mantle temperature, and a regularization for the uncertain initial condition. The gradient of this functional with respect to the initial temperature and the uncertain viscosity parameters is computed by solving the adjoint of the mantle convection equations. This gradient is used in a pre-conditioned quasi-Newton minimization algorithm. We study the prospects and limitations of the inversion, as well as the computational performance of the method using two synthetic problems, a sinking cylinder and a realistic subduction model. The subduction model is characterized by the migration of a ridge toward a trench whereby both plate motions and subduction evolve. The results demonstrate: (1) for known viscosity parameters, the initial temperature can be well recovered, as in previous initial condition-only inversions where the effective viscosity was given; (2) for known initial temperature, viscosity parameters can be recovered accurately, despite the existence of trade-offs due to ill-conditioning; (3) for the joint inversion of initial condition and viscosity parameters, initial condition and effective viscosity can be reasonably recovered, but the high dimension of the parameter space and the resulting ill-posedness may limit recovery of viscosity parameters.

Adjoint Tomography of the Southern California Crust (Invited) (Invited)

NASA Astrophysics Data System (ADS)

Tape, C.; Liu, Q.; Maggi, A.; Tromp, J.

2009-12-01

We iteratively improve a three-dimensional tomographic model of the southern California crust using numerical simulations of seismic wave propagation based on a spectral-element method (SEM) in combination with an adjoint method. The initial 3D model is provided by the Southern California Earthquake Center. The dataset comprises three-component seismic waveforms (i.e. both body and surface waves), filtered over the period range 2-30 s, from 143 local earthquakes recorded by a network of 203 stations. Time windows for measurements are automatically selected by the FLEXWIN algorithm. The misfit function in the tomographic inversion is based on frequency-dependent multitaper traveltime differences. The gradient of the misfit function and related finite-frequency sensitivity kernels for each earthquake are computed using an adjoint technique. The kernels are combined using a source subspace projection method to compute a model update at each iteration of a gradient-based minimization algorithm. The inversion involved 16 iterations, which required 6800 wavefield simulations and a total of 0.8 million CPU hours. The new crustal model, m16, is described in terms of independent shear (Vs) and bulk-sound (Vb) wavespeed variations. It exhibits strong heterogeneity, including local changes of ±30% with respect to the initial 3D model. The model reveals several features that relate to geologic observations, such as sedimentary basins, exhumed batholiths, and contrasting lithologies across faults. The quality of the new model is validated by quantifying waveform misfits of full-length seismograms from 91 earthquakes that were not used in the tomographic inversion. The new model provides more accurate synthetic seismograms that will benefit seismic hazard assessment.

The Tangent Linear and Adjoint of the FV3 Dynamical Core: Development and Applications

NASA Technical Reports Server (NTRS)

Holdaway, Daniel

2018-01-01

GMAO (NASA's Global Modeling and Assimilation Office) has developed a highly sophisticated adjoint modeling system based on the most recent version of the finite volume cubed sphere (FV3) dynamical core. This provides a mechanism for investigating sensitivity to initial conditions and examining observation impacts. It also allows for the computation of singular vectors and for the implementation of hybrid 4DVAR (4-Dimensional Variational Assimilation). In this work we will present the scientific assessment of the new adjoint system and show results from a number of research application of the adjoint system.

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation.

PubMed

Marcotte, Christopher D; Grigoriev, Roman O

2016-09-01

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation

NASA Astrophysics Data System (ADS)

Marcotte, Christopher D.; Grigoriev, Roman O.

2016-09-01

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

Adjoint tomography of Europe

NASA Astrophysics Data System (ADS)

Zhu, H.; Bozdag, E.; Peter, D. B.; Tromp, J.

2010-12-01

We use spectral-element and adjoint methods to image crustal and upper mantle heterogeneity in Europe. The study area involves the convergent boundaries of the Eurasian, African and Arabian plates and the divergent boundary between the Eurasian and North American plates, making the tectonic structure of this region complex. Our goal is to iteratively fit observed seismograms and improve crustal and upper mantle images by taking advantage of 3D forward and inverse modeling techniques. We use data from 200 earthquakes with magnitudes between 5 and 6 recorded by 262 stations provided by ORFEUS. Crustal model Crust2.0 combined with mantle model S362ANI comprise the initial 3D model. Before the iterative adjoint inversion, we determine earthquake source parameters in the initial 3D model by using 3D Green functions and their Fréchet derivatives with respect to the source parameters (i.e., centroid moment tensor and location). The updated catalog is used in the subsequent structural inversion. Since we concentrate on upper mantle structures which involve anisotropy, transversely isotropic (frequency-dependent) traveltime sensitivity kernels are used in the iterative inversion. Taking advantage of the adjoint method, we use as many measurements as can obtain based on comparisons between observed and synthetic seismograms. FLEXWIN (Maggi et al., 2009) is used to automatically select measurement windows which are analyzed based on a multitaper technique. The bandpass ranges from 15 second to 150 second. Long-period surface waves and short-period body waves are combined in source relocations and structural inversions. A statistical assessments of traveltime anomalies and logarithmic waveform differences is used to characterize the inverted sources and structure.

Optimization of wind plant layouts using an adjoint approach

DOE PAGES

King, Ryan N.; Dykes, Katherine; Graf, Peter; ...

2017-03-10

Using adjoint optimization and three-dimensional steady-state Reynolds-averaged Navier–Stokes (RANS) simulations, we present a new gradient-based approach for optimally siting wind turbines within utility-scale wind plants. By solving the adjoint equations of the flow model, the gradients needed for optimization are found at a cost that is independent of the number of control variables, thereby permitting optimization of large wind plants with many turbine locations. Moreover, compared to the common approach of superimposing prescribed wake deficits onto linearized flow models, the computational efficiency of the adjoint approach allows the use of higher-fidelity RANS flow models which can capture nonlinear turbulent flowmore » physics within a wind plant. The steady-state RANS flow model is implemented in the Python finite-element package FEniCS and the derivation and solution of the discrete adjoint equations are automated within the dolfin-adjoint framework. Gradient-based optimization of wind turbine locations is demonstrated for idealized test cases that reveal new optimization heuristics such as rotational symmetry, local speedups, and nonlinear wake curvature effects. Layout optimization is also demonstrated on more complex wind rose shapes, including a full annual energy production (AEP) layout optimization over 36 inflow directions and 5 wind speed bins.« less

Optimization of wind plant layouts using an adjoint approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

King, Ryan N.; Dykes, Katherine; Graf, Peter

Using adjoint optimization and three-dimensional steady-state Reynolds-averaged Navier–Stokes (RANS) simulations, we present a new gradient-based approach for optimally siting wind turbines within utility-scale wind plants. By solving the adjoint equations of the flow model, the gradients needed for optimization are found at a cost that is independent of the number of control variables, thereby permitting optimization of large wind plants with many turbine locations. Moreover, compared to the common approach of superimposing prescribed wake deficits onto linearized flow models, the computational efficiency of the adjoint approach allows the use of higher-fidelity RANS flow models which can capture nonlinear turbulent flowmore » physics within a wind plant. The steady-state RANS flow model is implemented in the Python finite-element package FEniCS and the derivation and solution of the discrete adjoint equations are automated within the dolfin-adjoint framework. Gradient-based optimization of wind turbine locations is demonstrated for idealized test cases that reveal new optimization heuristics such as rotational symmetry, local speedups, and nonlinear wake curvature effects. Layout optimization is also demonstrated on more complex wind rose shapes, including a full annual energy production (AEP) layout optimization over 36 inflow directions and 5 wind speed bins.« less

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis,Michael J.

2006-01-01

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology

NASA Technical Reports Server (NTRS)

Rallabhandi, Siriam K.; Diskin, Boris; Nielsen, Eric J.

2012-01-01

This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.

Using Adjoint Methods to Improve 3-D Velocity Models of Southern California

NASA Astrophysics Data System (ADS)

Liu, Q.; Tape, C.; Maggi, A.; Tromp, J.

2006-12-01

We use adjoint methods popular in climate and ocean dynamics to calculate Fréchet derivatives for tomographic inversions in southern California. The Fréchet derivative of an objective function χ(m), where m denotes the Earth model, may be written in the generic form δχ=int Km(x) δln m(x) d3x, where δln m=δ m/m denotes the relative model perturbation. For illustrative purposes, we construct the 3-D finite-frequency banana-doughnut kernel Km, corresponding to the misfit of a single traveltime measurement, by simultaneously computing the 'adjoint' wave field s† forward in time and reconstructing the regular wave field s backward in time. The adjoint wave field is produced by using the time-reversed velocity at the receiver as a fictitious source, while the regular wave field is reconstructed on the fly by propagating the last frame of the wave field saved by a previous forward simulation backward in time. The approach is based upon the spectral-element method, and only two simulations are needed to produce density, shear-wave, and compressional-wave sensitivity kernels. This method is applied to the SCEC southern California velocity model. Various density, shear-wave, and compressional-wave sensitivity kernels are presented for different phases in the seismograms. We also generate 'event' kernels for Pnl, S and surface waves, which are the Fréchet kernels of misfit functions that measure the P, S or surface wave traveltime residuals at all the receivers simultaneously for one particular event. Effectively, an event kernel is a sum of weighted Fréchet kernels, with weights determined by the associated traveltime anomalies. By the nature of the 3-D simulation, every event kernel is also computed based upon just two simulations, i.e., its construction costs the same amount of computation time as an individual banana-doughnut kernel. One can think of the sum of the event kernels for all available earthquakes, called the 'misfit' kernel, as a graphical representation of the gradient of the misfit function. With the capability of computing both the value of the misfit function and its gradient, which assimilates the traveltime anomalies, we are ready to use a non-linear conjugate gradient algorithm to iteratively improve velocity models of southern California.

A comparison of discrete versus continuous adjoint states to invert groundwater flow in heterogeneous dual porosity systems

NASA Astrophysics Data System (ADS)

Delay, Frederick; Badri, Hamid; Fahs, Marwan; Ackerer, Philippe

2017-12-01

Dual porosity models become increasingly used for simulating groundwater flow at the large scale in fractured porous media. In this context, model inversions with the aim of retrieving the system heterogeneity are frequently faced with huge parameterizations for which descent methods of inversion with the assistance of adjoint state calculations are well suited. We compare the performance of discrete and continuous forms of adjoint states associated with the flow equations in a dual porosity system. The discrete form inherits from previous works by some of the authors, as the continuous form is completely new and here fully differentiated for handling all types of model parameters. Adjoint states assist descent methods by calculating the gradient components of the objective function, these being a key to good convergence of inverse solutions. Our comparison on the basis of synthetic exercises show that both discrete and continuous adjoint states can provide very similar solutions close to reference. For highly heterogeneous systems, the calculation grid of the continuous form cannot be too coarse, otherwise the method may show lack of convergence. This notwithstanding, the continuous adjoint state is the most versatile form as its non-intrusive character allows for plugging an inversion toolbox quasi-independent from the code employed for solving the forward problem.

Full moment tensor and source location inversion based on full waveform adjoint method

NASA Astrophysics Data System (ADS)

Morency, C.

2012-12-01

The development of high-performance computing and numerical techniques enabled global and regional tomography to reach high levels of precision, and seismic adjoint tomography has become a state-of-the-art tomographic technique. The method was successfully used for crustal tomography of Southern California (Tape et al., 2009) and Europe (Zhu et al., 2012). Here, I will focus on the determination of source parameters (full moment tensor and location) based on the same approach (Kim et al, 2011). The method relies on full wave simulations and takes advantage of the misfit between observed and synthetic seismograms. An adjoint wavefield is calculated by back-propagating the difference between observed and synthetics from the receivers to the source. The interaction between this adjoint wavefield and the regular forward wavefield helps define Frechet derivatives of the source parameters, that is, the sensitivity of the misfit with respect to the source parameters. Source parameters are then recovered by minimizing the misfit based on a conjugate gradient algorithm using the Frechet derivatives. First, I will demonstrate the method on synthetic cases before tackling events recorded at the Geysers. The velocity model used at the Geysers is based on the USGS 3D velocity model. Waveform datasets come from the Northern California Earthquake Data Center. Finally, I will discuss strategies to ultimately use this method to characterize smaller events for microseismic and induced seismicity monitoring. References: - Tape, C., Q. Liu, A. Maggi, and J. Tromp, 2009, Adjoint tomography of the Southern California crust: Science, 325, 988992. - Zhu, H., Bozdag, E., Peter, D., and Tromp, J., 2012, Structure of the European upper mantle revealed by adjoint method: Nature Geoscience, 5, 493-498. - Kim, Y., Q. Liu, and J. Tromp, 2011, Adjoint centroid-moment tensor inversions: Geophys. J. Int., 186, 264278. Prepared by LLNL under Contract DE-AC52-07NA27344.

Preliminary Results from the Application of Automated Adjoint Code Generation to CFL3D

NASA Technical Reports Server (NTRS)

Carle, Alan; Fagan, Mike; Green, Lawrence L.

1998-01-01

This report describes preliminary results obtained using an automated adjoint code generator for Fortran to augment a widely-used computational fluid dynamics flow solver to compute derivatives. These preliminary results with this augmented code suggest that, even in its infancy, the automated adjoint code generator can accurately and efficiently deliver derivatives for use in transonic Euler-based aerodynamic shape optimization problems with hundreds to thousands of independent design variables.

Covering Resilience: A Recent Development for Binomial Checkpointing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walther, Andrea; Narayanan, Sri Hari Krishna

In terms of computing time, adjoint methods offer a very attractive alternative to compute gradient information, required, e.g., for optimization purposes. However, together with this very favorable temporal complexity result comes a memory requirement that is in essence proportional with the operation count of the underlying function, e.g., if algorithmic differentiation is used to provide the adjoints. For this reason, checkpointing approaches in many variants have become popular. This paper analyzes an extension of the so-called binomial approach to cover also possible failures of the computing systems. Such a measure of precaution is of special interest for massive parallel simulationsmore » and adjoint calculations where the mean time between failure of the large scale computing system is smaller than the time needed to complete the calculation of the adjoint information. We describe the extensions of standard checkpointing approaches required for such resilience, provide a corresponding implementation and discuss first numerical results.« less

GPU-accelerated adjoint algorithmic differentiation

NASA Astrophysics Data System (ADS)

Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe

2016-03-01

Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the ;tape;. Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography.

GPU-Accelerated Adjoint Algorithmic Differentiation.

PubMed

Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe

2016-03-01

Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the "tape". Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography.

GPU-Accelerated Adjoint Algorithmic Differentiation

PubMed Central

Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe

2015-01-01

Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the “tape”. Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography. PMID:26941443

Mitigation of Engine Inlet Distortion Through Adjoint-Based Design

NASA Technical Reports Server (NTRS)

Ordaz, Irian; Rallabhandi, Sriram; Nielsen, Eric J.; Diskin, Boris

2017-01-01

The adjoint-based design capability in FUN3D is extended to allow efficient gradient- based optimization and design of concepts with highly integrated aero-propulsive systems. A circumferential distortion calculation, along with the derivatives needed to perform adjoint-based design, have been implemented in FUN3D. This newly implemented distortion calculation can be used not only for design but also to drive the existing mesh adaptation process and reduce the error associated with the fan distortion calculation. The design capability is demonstrated by the shape optimization of an in-house aircraft concept equipped with an aft fuselage propulsor. The optimization objective is the minimization of flow distortion at the aerodynamic interface plane of this aft fuselage propulsor.

Equilibrium sensitivities of the Greenland ice sheet inferred from the adjoint of the three- dimensional thermo-mechanical model SICOPOLIS

NASA Astrophysics Data System (ADS)

Heimbach, P.; Bugnion, V.

2008-12-01

We present a new and original approach to understanding the sensitivity of the Greenland ice sheet to key model parameters and environmental conditions. At the heart of this approach is the use of an adjoint ice sheet model. MacAyeal (1992) introduced adjoints in the context of applying control theory to estimate basal sliding parameters (basal shear stress, basal friction) of an ice stream model which minimize a least-squares model vs. observation misfit. Since then, this method has become widespread to fit ice stream models to the increasing number and diversity of satellite observations, and to estimate uncertain model parameters. However, no attempt has been made to extend this method to comprehensive ice sheet models. Here, we present a first step toward moving beyond limiting the use of control theory to ice stream models. We have generated an adjoint of the three-dimensional thermo-mechanical ice sheet model SICOPOLIS of Greve (1997). The adjoint was generated using the automatic differentiation (AD) tool TAF. TAF generates exact source code representing the tangent linear and adjoint model of the parent model provided. Model sensitivities are given by the partial derivatives of a scalar-valued model diagnostic or "cost function" with respect to the controls, and can be efficiently calculated via the adjoint. An effort to generate an efficient adjoint with the newly developed open-source AD tool OpenAD is also under way. To gain insight into the adjoint solutions, we explore various cost functions, such as local and domain-integrated ice temperature, total ice volume or the velocity of ice at the margins of the ice sheet. Elements of our control space include initial cold ice temperatures, surface mass balance, as well as parameters such as appear in Glen's flow law, or in the surface degree-day or basal sliding parameterizations. Sensitivity maps provide a comprehensive view, and allow a quantification of where and to which variables the ice sheet model is most sensitive to. The model used in the present study includes simplifications in the model physics, parameterizations which rely on uncertain empirical constants, and is unable to capture fast ice streams. Nevertheless, as a proof-of-concept, this method can readily be extended to incorporate higher-order physics or parameterizations (or be applied to other models). It also opens the door to ice sheet state estimation: using the model's physics jointly with field and satellite observations to estimate a best estimate of the state of the ice sheets.

The Prediction of Broadband Shock-Associated Noise Including Propagation Effects

NASA Technical Reports Server (NTRS)

Miller, Steven; Morris, Philip J.

2011-01-01

An acoustic analogy is developed based on the Euler equations for broadband shock- associated noise (BBSAN) that directly incorporates the vector Green's function of the linearized Euler equations and a steady Reynolds-Averaged Navier-Stokes solution (SRANS) as the mean flow. The vector Green's function allows the BBSAN propagation through the jet shear layer to be determined. The large-scale coherent turbulence is modeled by two-point second order velocity cross-correlations. Turbulent length and time scales are related to the turbulent kinetic energy and dissipation. An adjoint vector Green's function solver is implemented to determine the vector Green's function based on a locally parallel mean flow at streamwise locations of the SRANS solution. However, the developed acoustic analogy could easily be based on any adjoint vector Green's function solver, such as one that makes no assumptions about the mean flow. The newly developed acoustic analogy can be simplified to one that uses the Green's function associated with the Helmholtz equation, which is consistent with the formulation of Morris and Miller (AIAAJ 2010). A large number of predictions are generated using three different nozzles over a wide range of fully expanded Mach numbers and jet stagnation temperatures. These predictions are compared with experimental data from multiple jet noise labs. In addition, two models for the so-called 'fine-scale' mixing noise are included in the comparisons. Improved BBSAN predictions are obtained relative to other models that do not include the propagation effects, especially in the upstream direction of the jet.

An adjoint method for gradient-based optimization of stellarator coil shapes

NASA Astrophysics Data System (ADS)

Paul, E. J.; Landreman, M.; Bader, A.; Dorland, W.

2018-07-01

We present a method for stellarator coil design via gradient-based optimization of the coil-winding surface. The REGCOIL (Landreman 2017 Nucl. Fusion 57 046003) approach is used to obtain the coil shapes on the winding surface using a continuous current potential. We apply the adjoint method to calculate derivatives of the objective function, allowing for efficient computation of analytic gradients while eliminating the numerical noise of approximate derivatives. We are able to improve engineering properties of the coils by targeting the root-mean-squared current density in the objective function. We obtain winding surfaces for W7-X and HSX which simultaneously decrease the normal magnetic field on the plasma surface and increase the surface-averaged distance between the coils and the plasma in comparison with the actual winding surfaces. The coils computed on the optimized surfaces feature a smaller toroidal extent and curvature and increased inter-coil spacing. A technique for computation of the local sensitivity of figures of merit to normal displacements of the winding surface is presented, with potential applications for understanding engineering tolerances.

Adjoint-based sensitivity analysis of low-order thermoacoustic networks using a wave-based approach

NASA Astrophysics Data System (ADS)

Aguilar, José G.; Magri, Luca; Juniper, Matthew P.

2017-07-01

Strict pollutant emission regulations are pushing gas turbine manufacturers to develop devices that operate in lean conditions, with the downside that combustion instabilities are more likely to occur. Methods to predict and control unstable modes inside combustion chambers have been developed in the last decades but, in some cases, they are computationally expensive. Sensitivity analysis aided by adjoint methods provides valuable sensitivity information at a low computational cost. This paper introduces adjoint methods and their application in wave-based low order network models, which are used as industrial tools, to predict and control thermoacoustic oscillations. Two thermoacoustic models of interest are analyzed. First, in the zero Mach number limit, a nonlinear eigenvalue problem is derived, and continuous and discrete adjoint methods are used to obtain the sensitivities of the system to small modifications. Sensitivities to base-state modification and feedback devices are presented. Second, a more general case with non-zero Mach number, a moving flame front and choked outlet, is presented. The influence of the entropy waves on the computed sensitivities is shown.

Adjoint Fokker-Planck equation and runaway electron dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Chang; Brennan, Dylan P.; Bhattacharjee, Amitava

2016-01-15

The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay timemore » in experiments. A new result from this work is that the decay rate of high energy electrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.« less

Development of the WRF-CO2 4D-Var assimilation system v1.0

NASA Astrophysics Data System (ADS)

Zheng, Tao; French, Nancy H. F.; Baxter, Martin

2018-05-01

Regional atmospheric CO2 inversions commonly use Lagrangian particle trajectory model simulations to calculate the required influence function, which quantifies the sensitivity of a receptor to flux sources. In this paper, an adjoint-based four-dimensional variational (4D-Var) assimilation system, WRF-CO2 4D-Var, is developed to provide an alternative approach. This system is developed based on the Weather Research and Forecasting (WRF) modeling system, including the system coupled to chemistry (WRF-Chem), with tangent linear and adjoint codes (WRFPLUS), and with data assimilation (WRFDA), all in version 3.6. In WRF-CO2 4D-Var, CO2 is modeled as a tracer and its feedback to meteorology is ignored. This configuration allows most WRF physical parameterizations to be used in the assimilation system without incurring a large amount of code development. WRF-CO2 4D-Var solves for the optimized CO2 flux scaling factors in a Bayesian framework. Two variational optimization schemes are implemented for the system: the first uses the limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization algorithm (L-BFGS-B) and the second uses the Lanczos conjugate gradient (CG) in an incremental approach. WRFPLUS forward, tangent linear, and adjoint models are modified to include the physical and dynamical processes involved in the atmospheric transport of CO2. The system is tested by simulations over a domain covering the continental United States at 48 km × 48 km grid spacing. The accuracy of the tangent linear and adjoint models is assessed by comparing against finite difference sensitivity. The system's effectiveness for CO2 inverse modeling is tested using pseudo-observation data. The results of the sensitivity and inverse modeling tests demonstrate the potential usefulness of WRF-CO2 4D-Var for regional CO2 inversions.

Adjoint-Based Uncertainty Quantification with MCNP

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seifried, Jeffrey E.

2011-09-01

This work serves to quantify the instantaneous uncertainties in neutron transport simulations born from nuclear data and statistical counting uncertainties. Perturbation and adjoint theories are used to derive implicit sensitivity expressions. These expressions are transformed into forms that are convenient for construction with MCNP6, creating the ability to perform adjoint-based uncertainty quantification with MCNP6. These new tools are exercised on the depleted-uranium hybrid LIFE blanket, quantifying its sensitivities and uncertainties to important figures of merit. Overall, these uncertainty estimates are small (< 2%). Having quantified the sensitivities and uncertainties, physical understanding of the system is gained and some confidence inmore » the simulation is acquired.« less

Transient sensitivities of sea ice export through the Canadian Arctic Archipelago inferred from a coupled ocean/sea-ice adjoint model

NASA Astrophysics Data System (ADS)

Heimbach, P.; Losch, M.; Menemenlis, D.; Campin, J.; Hill, C.

2008-12-01

The sensitivity of sea-ice export through the Canadian Arctic Archipelago (CAA), measured in terms of its solid freshwater export through Lancaster Sound, to changes in various elements of the ocean and sea-ice state, and to elements of the atmospheric forcing fields through time and space is assessed by means of a coupled ocean/sea-ice adjoint model. The adjoint model furnishes full spatial sensitivity maps (also known as Lagrange multipliers) of the export metric to a variety of model variables at any chosen point in time, providing the unique capability to quantify major drivers of sea-ice export variability. The underlying model is the MIT ocean general circulation model (MITgcm), which is coupled to a Hibler-type dynamic/thermodynamic sea-ice model. The configuration is based on the Arctic face of the ECCO3 high-resolution cubed-sphere model, but coarsened to 36-km horizontal grid spacing. The adjoint of the coupled system has been derived by means of automatic differentiation using the software tool TAF. Finite perturbation simulations are performed to check the information provided by the adjoint. The sea-ice model's performance in the presence of narrow straits is assessed with different sea-ice lateral boundary conditions. The adjoint sensitivity clearly exposes the role of the model trajectory and the transient nature of the problem. The complex interplay between forcing, dynamics, and boundary condition is demonstrated in the comparison between the different calculations. The study is a step towards fully coupled adjoint-based ocean/sea-ice state estimation at basin to global scales as part of the ECCO efforts.

Global Seismic Imaging Based on Adjoint Tomography

NASA Astrophysics Data System (ADS)

Bozdag, E.; Lefebvre, M.; Lei, W.; Peter, D. B.; Smith, J. A.; Zhu, H.; Komatitsch, D.; Tromp, J.

2013-12-01

Our aim is to perform adjoint tomography at the scale of globe to image the entire planet. We have started elastic inversions with a global data set of 253 CMT earthquakes with moment magnitudes in the range 5.8 ≤ Mw ≤ 7 and used GSN stations as well as some local networks such as USArray, European stations, etc. Using an iterative pre-conditioned conjugate gradient scheme, we initially set the aim to obtain a global crustal and mantle model with confined transverse isotropy in the upper mantle. Global adjoint tomography has so far remained a challenge mainly due to computational limitations. Recent improvements in our 3D solvers (e.g., a GPU version) and access to high-performance computational centers (e.g., ORNL's Cray XK7 "Titan" system) now enable us to perform iterations with higher-resolution (T > 9 s) and longer-duration (200 min) simulations to accommodate high-frequency body waves and major-arc surface waves, respectively, which help improve data coverage. The remaining challenge is the heavy I/O traffic caused by the numerous files generated during the forward/adjoint simulations and the pre- and post-processing stages of our workflow. We improve the global adjoint tomography workflow by adopting the ADIOS file format for our seismic data as well as models, kernels, etc., to improve efficiency on high-performance clusters. Our ultimate aim is to use data from all available networks and earthquakes within the magnitude range of our interest (5.5 ≤ Mw ≤ 7) which requires a solid framework to manage big data in our global adjoint tomography workflow. We discuss the current status and future of global adjoint tomography based on our initial results as well as practical issues such as handling big data in inversions and on high-performance computing systems.

Adjoint Sensitivity Method to Determine Optimal Set of Stations for Tsunami Source Inversion

NASA Astrophysics Data System (ADS)

Gusman, A. R.; Hossen, M. J.; Cummins, P. R.; Satake, K.

2017-12-01

We applied the adjoint sensitivity technique in tsunami science for the first time to determine an optimal set of stations for a tsunami source inversion. The adjoint sensitivity (AS) method has been used in numerical weather prediction to find optimal locations for adaptive observations. We implemented this technique to Green's Function based Time Reverse Imaging (GFTRI), which is recently used in tsunami source inversion in order to reconstruct the initial sea surface displacement, known as tsunami source model. This method has the same source representation as the traditional least square (LSQ) source inversion method where a tsunami source is represented by dividing the source region into a regular grid of "point" sources. For each of these, Green's function (GF) is computed using a basis function for initial sea surface displacement whose amplitude is concentrated near the grid point. We applied the AS method to the 2009 Samoa earthquake tsunami that occurred on 29 September 2009 in the southwest Pacific, near the Tonga trench. Many studies show that this earthquake is a doublet associated with both normal faulting in the outer-rise region and thrust faulting in the subduction interface. To estimate the tsunami source model for this complex event, we initially considered 11 observations consisting of 5 tide gauges and 6 DART bouys. After implementing AS method, we found the optimal set of observations consisting with 8 stations. Inversion with this optimal set provides better result in terms of waveform fitting and source model that shows both sub-events associated with normal and thrust faulting.

An adjoint-based simultaneous estimation method of the asthenosphere's viscosity and afterslip using a fast and scalable finite-element adjoint solver

NASA Astrophysics Data System (ADS)

Agata, Ryoichiro; Ichimura, Tsuyoshi; Hori, Takane; Hirahara, Kazuro; Hashimoto, Chihiro; Hori, Muneo

2018-04-01

The simultaneous estimation of the asthenosphere's viscosity and coseismic slip/afterslip is expected to improve largely the consistency of the estimation results to observation data of crustal deformation collected in widely spread observation points, compared to estimations of slips only. Such an estimate can be formulated as a non-linear inverse problem of material properties of viscosity and input force that is equivalent to fault slips based on large-scale finite-element (FE) modeling of crustal deformation, in which the degree of freedom is in the order of 109. We formulated and developed a computationally efficient adjoint-based estimation method for this inverse problem, together with a fast and scalable FE solver for the associated forward and adjoint problems. In a numerical experiment that imitates the 2011 Tohoku-Oki earthquake, the advantage of the proposed method is confirmed by comparing the estimated results with those obtained using simplified estimation methods. The computational cost required for the optimization shows that the proposed method enabled the targeted estimation to be completed with moderate amount of computational resources.

Azimuthally Anisotropic Global Adjoint Tomography

NASA Astrophysics Data System (ADS)

Bozdag, E.; Orsvuran, R.; Lefebvre, M. P.; Lei, W.; Peter, D. B.; Ruan, Y.; Smith, J. A.; Komatitsch, D.; Tromp, J.

2017-12-01

Earth's upper mantle shows significant evidence of anisotropy as a result of its composition and deformation. After the first-generation global adjoint tomography model, GLAD-M15 (Bozdag et al. 2016), which has transverse isotropy confined to upper mantle, we continue our iterations including surface-wave azimuthal anisotropy with an emphasis on the upper mantle. We are focusing on four elastic parameters that surface waves are known to be most sensitive to, namely, vertically and horizontally polarized shear waves and the density-normalised anisotropic parameters Gc' & Gs'. As part of the current anisotropic inversions, which will lead to our "second-generation" global adjoint tomography model, we have started exploring new misfits based on a double-difference approach (Yuan et al. 2016). We define our misfit function in terms of double-difference multitaper measurements, where each waveform is normalized by its number of pairs in the period ranges 45-100 s & 90-250 s. New measurements result in better balanced gradients while extracting more information underneath clusters of stations, such as USArray. Our initial results reveals multi-scale anisotorpic signals depending on ray (kernel) coverage close to continental-scale resolution in areas with dense coverage, consistent with previous studies.

Analysis of Seasonal Chlorophyll-a Using An Adjoint Three-Dimensional Ocean Carbon Cycle Model

NASA Astrophysics Data System (ADS)

Tjiputra, J.; Winguth, A.; Polzin, D.

2004-12-01

The misfit between numerical ocean model and observations can be reduced using data assimilation. This can be achieved by optimizing the model parameter values using adjoint model. The adjoint model minimizes the model-data misfit by estimating the sensitivity or gradient of the cost function with respect to initial condition, boundary condition, or parameters. The adjoint technique was used to assimilate seasonal chlorophyll-a data from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) satellite to a marine biogeochemical model HAMOCC5.1. An Identical Twin Experiment (ITE) was conducted to test the robustness of the model and the non-linearity level of the forward model. The ITE experiment successfully recovered most of the perturbed parameter to their initial values, and identified the most sensitive ecosystem parameters, which contribute significantly to model-data bias. The regional assimilations of SeaWiFS chlorophyll-a data into the model were able to reduce the model-data misfit (i.e. the cost function) significantly. The cost function reduction mostly occurred in the high latitudes (e.g. the model-data misfit in the northern region during summer season was reduced by 54%). On the other hand, the equatorial regions appear to be relatively stable with no strong reduction in cost function. The optimized parameter set is used to forecast the carbon fluxes between marine ecosystem compartments (e.g. Phytoplankton, Zooplankton, Nutrients, Particulate Organic Carbon, and Dissolved Organic Carbon). The a posteriori model run using the regional best-fit parameterization yields approximately 36 PgC/yr of global net primary productions in the euphotic zone.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

Fully automatic adjoints: a robust and efficient mechanism for generating adjoint ocean models

NASA Astrophysics Data System (ADS)

Ham, D. A.; Farrell, P. E.; Funke, S. W.; Rognes, M. E.

2012-04-01

The problem of generating and maintaining adjoint models is sufficiently difficult that typically only the most advanced and well-resourced community ocean models achieve it. There are two current technologies which each suffer from their own limitations. Algorithmic differentiation, also called automatic differentiation, is employed by models such as the MITGCM [2] and the Alfred Wegener Institute model FESOM [3]. This technique is very difficult to apply to existing code, and requires a major initial investment to prepare the code for automatic adjoint generation. AD tools may also have difficulty with code employing modern software constructs such as derived data types. An alternative is to formulate the adjoint differential equation and to discretise this separately. This approach, known as the continuous adjoint and employed in ROMS [4], has the disadvantage that two different model code bases must be maintained and manually kept synchronised as the model develops. The discretisation of the continuous adjoint is not automatically consistent with that of the forward model, producing an additional source of error. The alternative presented here is to formulate the flow model in the high level language UFL (Unified Form Language) and to automatically generate the model using the software of the FEniCS project. In this approach it is the high level code specification which is differentiated, a task very similar to the formulation of the continuous adjoint [5]. However since the forward and adjoint models are generated automatically, the difficulty of maintaining them vanishes and the software engineering process is therefore robust. The scheduling and execution of the adjoint model, including the application of an appropriate checkpointing strategy is managed by libadjoint [1]. In contrast to the conventional algorithmic differentiation description of a model as a series of primitive mathematical operations, libadjoint employs a new abstraction of the simulation process as a sequence of discrete equations which are assembled and solved. It is the coupling of the respective abstractions employed by libadjoint and the FEniCS project which produces the adjoint model automatically, without further intervention from the model developer. This presentation will demonstrate this new technology through linear and non-linear shallow water test cases. The exceptionally simple model syntax will be highlighted and the correctness of the resulting adjoint simulations will be demonstrated using rigorous convergence tests.

Extending the Binomial Checkpointing Technique for Resilience

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walther, Andrea; Narayanan, Sri Hari Krishna

In terms of computing time, adjoint methods offer a very attractive alternative to compute gradient information, re- quired, e.g., for optimization purposes. However, together with this very favorable temporal complexity result comes a memory requirement that is in essence proportional with the operation count of the underlying function, e.g., if algo- rithmic differentiation is used to provide the adjoints. For this reason, checkpointing approaches in many variants have become popular. This paper analyzes an extension of the so-called binomial approach to cover also possible failures of the computing systems. Such a measure of precaution is of special interest for massivemore » parallel simulations and adjoint calculations where the mean time between failure of the large scale computing system is smaller than the time needed to complete the calculation of the adjoint information. We de- scribe the extensions of standard checkpointing approaches required for such resilience, provide a corresponding imple- mentation and discuss numerical results.« less

A hybrid (Monte Carlo/deterministic) approach for multi-dimensional radiation transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bal, Guillaume, E-mail: gb2030@columbia.edu; Davis, Anthony B., E-mail: Anthony.B.Davis@jpl.nasa.gov; Kavli Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, CA 93106-4030

2011-08-20

Highlights: {yields} We introduce a variance reduction scheme for Monte Carlo (MC) transport. {yields} The primary application is atmospheric remote sensing. {yields} The technique first solves the adjoint problem using a deterministic solver. {yields} Next, the adjoint solution is used as an importance function for the MC solver. {yields} The adjoint problem is solved quickly since it ignores the volume. - Abstract: A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with solar illumination, scattering and absorbing 2D atmosphere, a textured reflecting mountain, and a small detector located in the sky (mounted on a satellite or amore » airplane). It uses a deterministic approximation of an adjoint transport solution to reduce variance, computed quickly by ignoring atmospheric interactions. This allows significant variance and computational cost reductions when the atmospheric scattering and absorption coefficient are small. When combined with an atmospheric photon-redirection scheme, significant variance reduction (equivalently acceleration) is achieved in the presence of atmospheric interactions.« less

Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time

NASA Technical Reports Server (NTRS)

Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)

1999-01-01

A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

Neural network training by integration of adjoint systems of equations forward in time

NASA Technical Reports Server (NTRS)

Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)

1992-01-01

A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically, it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved, but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. The trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

Adjoint-Based Sensitivity and Uncertainty Analysis for Density and Composition: A User’s Guide

DOE PAGES

Favorite, Jeffrey A.; Perko, Zoltan; Kiedrowski, Brian C.; ...

2017-03-01

The ability to perform sensitivity analyses using adjoint-based first-order sensitivity theory has existed for decades. This paper provides guidance on how adjoint sensitivity methods can be used to predict the effect of material density and composition uncertainties in critical experiments, including when these uncertain parameters are correlated or constrained. Two widely used Monte Carlo codes, MCNP6 (Ref. 2) and SCALE 6.2 (Ref. 3), are both capable of computing isotopic density sensitivities in continuous energy and angle. Additionally, Perkó et al. have shown how individual isotope density sensitivities, easily computed using adjoint methods, can be combined to compute constrained first-order sensitivitiesmore » that may be used in the uncertainty analysis. This paper provides details on how the codes are used to compute first-order sensitivities and how the sensitivities are used in an uncertainty analysis. Constrained first-order sensitivities are computed in a simple example problem.« less

Adjoint Sensitivity Analysis for Scale-Resolving Turbulent Flow Solvers

NASA Astrophysics Data System (ADS)

Blonigan, Patrick; Garai, Anirban; Diosady, Laslo; Murman, Scott

2017-11-01

Adjoint-based sensitivity analysis methods are powerful design tools for engineers who use computational fluid dynamics. In recent years, these engineers have started to use scale-resolving simulations like large-eddy simulations (LES) and direct numerical simulations (DNS), which resolve more scales in complex flows with unsteady separation and jets than the widely-used Reynolds-averaged Navier-Stokes (RANS) methods. However, the conventional adjoint method computes large, unusable sensitivities for scale-resolving simulations, which unlike RANS simulations exhibit the chaotic dynamics inherent in turbulent flows. Sensitivity analysis based on least-squares shadowing (LSS) avoids the issues encountered by conventional adjoint methods, but has a high computational cost even for relatively small simulations. The following talk discusses a more computationally efficient formulation of LSS, ``non-intrusive'' LSS, and its application to turbulent flows simulated with a discontinuous-Galkerin spectral-element-method LES/DNS solver. Results are presented for the minimal flow unit, a turbulent channel flow with a limited streamwise and spanwise domain.

Adjoint-based constant-mass partial derivatives

DOE PAGES

Favorite, Jeffrey A.

2017-09-01

In transport theory, adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to surface locations (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. This study derives the constant-mass partial derivative of a response with respect to an internal interface location or the outer system boundary and the constant-mass partial derivative of a response with respect to the mass density of a region. Numerical results are given for a multiregion two-dimensional (r-z) cylinder for three very different responses: the uncollided gamma-ray flux at an external detector point, k effmore » of the system, and the total neutron leakage. Finally, results from the derived formulas compare extremely well with direct perturbation calculations.« less

On the symmetry of the boundary conditions of the volume potential

NASA Astrophysics Data System (ADS)

Kal'menov, Tynysbek Sh.; Arepova, Gaukhar; Suragan, Durvudkhan

2017-09-01

It is well known that the volume potential determines the mass or the charge distributed over the domain with density f. The volume potential is extensively used in function theory and embedding theorems. It is also well known that the volume potential gives a solution to an inhomogeneous equation. And it generates a linear self-adjoint operator. It is known that self-adjoint differential operators are generated by boundary conditions. In our previous papers for an arbitrary domain a boundary condition on the volume potential is given. In the past, it was not possible to prove the self-adjointness of these obtained boundary conditions. In the present paper, we prove the symmetry of boundary condition for the volume potential.

Toward regional-scale adjoint tomography in the deep earth

NASA Astrophysics Data System (ADS)

Masson, Y.; Romanowicz, B. A.

2013-12-01

Thanks to the development of efficient numerical computation methods, such as the Spectral Element Method (SEM) and to the increasing power of computer clusters, it is now possible to obtain regional-scale images of the Earth's interior using adjoint-tomography (e.g. Tape, C., et al., 2009). As for now, these tomographic models are limited to the upper layers of the earth, i.e., they provide us with high-resolution images of the crust and the upper part of the mantle. Given the gigantic amount of calculation it represents, obtaing similar models at the global scale (i.e. images of the entire Earth) seems out of reach at the moment. Furthermore, it's likely that the first generation of such global adjoint tomographic models will have a resolution significantly smaller than the current regional models. In order to image regions of interests in the deep Earth, such as plumes, slabs or large low shear velocity provinces (LLSVPs), while keeping the computation tractable, we are developing new tools that will allow us to perform regional-scale adjoint-tomography at arbitrary depths. In a recent study (Masson et al., 2013), we showed that a numerical equivalent of the time reversal mirrors used in experimental acoustics permits to confine the wave propagation computations (i.e. using SEM simulations) inside the region to be imaged. With this ability to limit wave propagation modeling inside a region of interest, obtaining the adjoint sensitivity kernels needed for tomographic imaging is only two steps further. First, the local wavefield modeling needs to be coupled with field extrapolation techniques in order to obtain synthetic seismograms at the surface of the earth. These seismograms will account for the 3D structure inside the region of interest in a quasi-exact manner. We will present preliminary results where the field-extrapolation is performed using Green's function computed in a 1D Earth model thanks to the Direct Solution Method (DSM). Once synthetic seismograms can be obtained, it is possible to evaluate the misfit between observed and computed seismograms. The second step will then be to extrapolate the misfit function back into the SEM region in order to compute local adjoint sensitivity kernels. When available, these kernels will allow us to perform regional-scale adjoint tomography at arbitrary locations inside the earth. Masson Y., Cupillard P., Capdeville Y., & Romanowicz B., 2013. On the numerical implementation of time-reversal mirrors for tomographic imaging, Journal of Geophysical Research (under review). Tape, C., et al. (2009). "Adjoint tomography of the southern California crust." Science 325(5943): 988-992.

High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices

NASA Astrophysics Data System (ADS)

Dunham, Benjamin Z.

This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions--most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series--without changing data-type or modifying code line by line; this allows differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed "stencils," each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the "forward mode" is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of N--i.e., O(1)--the N x N Hessian can be found in O(N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive--e.g., a N x N x N rank-three tensor can be found in O(N2). Alternatively, a Hessian-vector product can be found in O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step differentiation (CD) technique is also shown to be capable of finding the Hessian-vector product. All variants are implemented on a stochastic diffusion problem and compared in-depth with various cost and accuracy metrics.

Comparing mass balance and adjoint methods for inverse modeling of nitrogen dioxide columns for global nitrogen oxide emissions

NASA Astrophysics Data System (ADS)

Cooper, Matthew; Martin, Randall V.; Padmanabhan, Akhila; Henze, Daven K.

2017-04-01

Satellite observations offer information applicable to top-down constraints on emission inventories through inverse modeling. Here we compare two methods of inverse modeling for emissions of nitrogen oxides (NOx) from nitrogen dioxide (NO2) columns using the GEOS-Chem chemical transport model and its adjoint. We treat the adjoint-based 4D-Var modeling approach for estimating top-down emissions as a benchmark against which to evaluate variations on the mass balance method. We use synthetic NO2 columns generated from known NOx emissions to serve as "truth." We find that error in mass balance inversions can be reduced by up to a factor of 2 with an iterative process that uses finite difference calculations of the local sensitivity of NO2 columns to a change in emissions. In a simplified experiment to recover local emission perturbations, horizontal smearing effects due to NOx transport are better resolved by the adjoint approach than by mass balance. For more complex emission changes, or at finer resolution, the iterative finite difference mass balance and adjoint methods produce similar global top-down inventories when inverting hourly synthetic observations, both reducing the a priori error by factors of 3-4. Inversions of simulated satellite observations from low Earth and geostationary orbits also indicate that both the mass balance and adjoint inversions produce similar results, reducing a priori error by a factor of 3. As the iterative finite difference mass balance method provides similar accuracy as the adjoint method, it offers the prospect of accurately estimating top-down NOx emissions using models that do not have an adjoint.

Relating health and climate impacts to grid-scale emissions using adjoint sensitivity modeling for the Climate and Clean Air Coalition

NASA Astrophysics Data System (ADS)

Henze, D. K.; Lacey, F.; Seltzer, M.; Vallack, H.; Kuylenstierna, J.; Bowman, K. W.; Anenberg, S.; Sasser, E.; Lee, C. J.; Martin, R.

2013-12-01

The Climate and Clean Air Coalition (CCAC) was initiated in 2012 to develop, understand and promote measures to reduce short lived climate forcers such as aerosol, ozone and methane. The Coalition now includes over 30 nations, and as a service to these nations is committed to providing a decision support toolkit that allows member nations to explore the benefits of a range of emissions mitigation measures in terms of the combined impacts on air quality and climate and so help in the development of their National Action Plans. Here we will present recent modeling work to support the development of the CCAC National Action Plans toolkit. Adjoint sensitivity analysis is presented as a means of efficiently relating air quality, climate and crop impacts back to changes in emissions from each species, sector and location at the grid-scale resolution of typical global air quality model applications. The GEOS-Chem adjoint model is used to estimate the damages per ton of emissions of PM2.5 related mortality, the impacts of ozone precursors on crops and ozone-related health effects, and the combined impacts of these species on regional surface temperature changes. We show how the benefits-per-emission vary spatially as a function of the surrounding environment, and how this impacts the overall benefit of sector-specific control strategies. We present initial findings for Bangladesh, as well as Mexico, Ghana and Colombia, some of the first countries to join the CCAC, and discuss general issues related to adjoint-based metrics for quantifying air quality and climate co-benefits.

An adjoint-based sensitivity analysis of thermoacoustic network models

NASA Astrophysics Data System (ADS)

Sogaro, Francesca; Morgans, Aimee; Schmid, Peter

2017-11-01

Thermoacoustic instability is a phenomenon that occurs in numerous combustion systems, from rockets to land-based gas turbines. The acoustic oscillations of these systems are of significant importance as they can result in severe vibrations, thrust oscillations, thermal stresses and mechanical loads that lead to fatigue or even failure. In this work we use a low-order network model representation of a combustor system where linear acoustics are solved together with the appropriate boundary conditions, area change jump conditions, acoustic dampers and an appropriate flame transfer function. Special emphasis is directed towards the interaction between acoustically driven instabilities and flame-intrinsic modes. Adjoint methods are used to perform a sensitivity analysis of the spectral properties of the system to changes in the parameters involved. An exchange of modal identity between acoustic and intrinsic modes will be demonstrated and analyzed. The results provide insight into the interplay between various mode types and build a quantitative foundation for the design of combustors.

Numerical Computation of Sensitivities and the Adjoint Approach

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael

1997-01-01

We discuss the numerical computation of sensitivities via the adjoint approach in optimization problems governed by differential equations. We focus on the adjoint problem in its weak form. We show how one can avoid some of the problems with the adjoint approach, such as deriving suitable boundary conditions for the adjoint equation. We discuss the convergence of numerical approximations of the costate computed via the weak form of the adjoint problem and show the significance for the discrete adjoint problem.

Accelerated gradient based diffuse optical tomographic image reconstruction.

PubMed

Biswas, Samir Kumar; Rajan, K; Vasu, R M

2011-01-01

Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data.

Adjoint Methods for Adjusting Three-Dimensional Atmosphere and Surface Properties to Fit Multi-Angle Multi-Pixel Polarimetric Measurements

NASA Technical Reports Server (NTRS)

Martin, William G.; Cairns, Brian; Bal, Guillaume

2014-01-01

This paper derives an efficient procedure for using the three-dimensional (3D) vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties and improve their fit with multi-angle/multi-pixel radiometric and polarimetric measurements of scattered sunlight. The proposed adjoint method uses the 3D VRTE to compute the measurement misfit function and the adjoint 3D VRTE to compute its gradient with respect to all unknown parameters. In the remote sensing problems of interest, the scalar-valued misfit function quantifies agreement with data as a function of atmosphere and surface properties, and its gradient guides the search through this parameter space. Remote sensing of the atmosphere and surface in a three-dimensional region may require thousands of unknown parameters and millions of data points. Many approaches would require calls to the 3D VRTE solver in proportion to the number of unknown parameters or measurements. To avoid this issue of scale, we focus on computing the gradient of the misfit function as an alternative to the Jacobian of the measurement operator. The resulting adjoint method provides a way to adjust 3D atmosphere and surface properties with only two calls to the 3D VRTE solver for each spectral channel, regardless of the number of retrieval parameters, measurement view angles or pixels. This gives a procedure for adjusting atmosphere and surface parameters that will scale to the large problems of 3D remote sensing. For certain types of multi-angle/multi-pixel polarimetric measurements, this encourages the development of a new class of three-dimensional retrieval algorithms with more flexible parametrizations of spatial heterogeneity, less reliance on data screening procedures, and improved coverage in terms of the resolved physical processes in the Earth?s atmosphere.

Adjoint Sensitivity Analyses Of Sand And Dust Storms In East Asia

NASA Astrophysics Data System (ADS)

Kay, J.; Kim, H.

2008-12-01

Sand and Dust Storm (SDS) in East Asia, so called Asian dust, is a seasonal meteorological phenomenon. Mostly in spring, dust particles blown into atmosphere in the arid area over northern China desert and Manchuria are transported to East Asia by prevailing flows. Three SDS events in East Asia from 2005 to 2008 are chosen to investigate how sensitive the SDS forecasts to the initial condition uncertainties and thence to suggest the sensitive regions for adaptive observations of the SDS events. Adaptive observations are additional observations in sensitive regions where the observations may have the most impact on the forecast by decreasing the forecast error. Three SDS events are chosen to represent different transport passes from the dust source regions to the Korean peninsula. To investigate the sensitivities to the initial condition, adjoint sensitivities that calculate gradient of the forecast aspect (i.e., response function) with respect to the initial condition are used. The forecast aspects relevant to the SDS transport are forecast error of the surface pressure, surface pressure perturbation, and steering vector of winds in the lower troposphere. Because the surface low pressure system usually plays an important role for SDS transport, the forecast error of the surface pressure and the surface pressure perturbation are chosen as the response function of the adjoint calculation. Another response function relevant to SDS transport is the steering flow over the downstream region (i.e., Korean peninsula) because direction and intensity of the prevailing winds usually determine the intensity and occurrence of the SDS events at the destination. The results show that the sensitive regions for the forecast error of the surface pressure and surface pressure perturbation are initially located in the vicinity of the trough and then propagate eastward as the low system moves eastward. The vertical structures of the adjoint sensitivities are upshear tilted structures, which are typical structures of extratropical cyclones. The adjoint sensitivities for lower tropospheric steering flow are also located near the trough, which confirms that the accurate forecast on the location and movement of the trough is essential to have better forecasts of Asian dust events. More comprehensive results and discussions of the adjoint sensitivity analyses for Asian dust events will be presented in the meeting.

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Park, Michael A.

2006-01-01

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Park, Michael A.

2005-01-01

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Spectral-element simulations of wave propagation in complex exploration-industry models: Imaging and adjoint tomography

NASA Astrophysics Data System (ADS)

Luo, Y.; Nissen-Meyer, T.; Morency, C.; Tromp, J.

2008-12-01

Seismic imaging in the exploration industry is often based upon ray-theoretical migration techniques (e.g., Kirchhoff) or other ideas which neglect some fraction of the seismic wavefield (e.g., wavefield continuation for acoustic-wave first arrivals) in the inversion process. In a companion paper we discuss the possibility of solving the full physical forward problem (i.e., including visco- and poroelastic, anisotropic media) using the spectral-element method. With such a tool at hand, we can readily apply the adjoint method to tomographic inversions, i.e., iteratively improving an initial 3D background model to fit the data. In the context of this inversion process, we draw connections between kernels in adjoint tomography and basic imaging principles in migration. We show that the images obtained by migration are nothing but particular kinds of adjoint kernels (mainly density kernels). Migration is basically a first step in the iterative inversion process of adjoint tomography. We apply the approach to basic 2D problems involving layered structures, overthrusting faults, topography, salt domes, and poroelastic regions.

Introduction to Adjoint Models

NASA Technical Reports Server (NTRS)

Errico, Ronald M.

2015-01-01

In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.

Optimization of Regional Geodynamic Models for Mantle Dynamics

NASA Astrophysics Data System (ADS)

Knepley, M.; Isaac, T.; Jadamec, M. A.

2016-12-01

The SubductionGenerator program is used to construct high resolution, 3D regional thermal structures for mantle convection simulations using a variety of data sources, including sea floor ages and geographically referenced 3D slab locations based on seismic observations. The initial bulk temperature field is constructed using a half-space cooling model or plate cooling model, and related smoothing functions based on a diffusion length-scale analysis. In this work, we seek to improve the 3D thermal model and test different model geometries and dynamically driven flow fields using constraints from observed seismic velocities and plate motions. Through a formal adjoint analysis, we construct the primal-dual version of the multi-objective PDE-constrained optimization problem for the plate motions and seismic misfit. We have efficient, scalable preconditioners for both the forward and adjoint problems based upon a block preconditioning strategy, and a simple gradient update is used to improve the control residual. The full optimal control problem is formulated on a nested hierarchy of grids, allowing a nonlinear multigrid method to accelerate the solution.

Application of variational principles and adjoint integrating factors for constructing numerical GFD models

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

2015-04-01

The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each direction on a time step. In each direction, they have tridiagonal structure. They are solved by the sweep method. An important advantage of the discrete-analytical schemes is that the values of derivatives at the boundaries of finite volume are calculated together with the values of the unknown functions. This technique is particularly attractive for problems with dominant convection, as it does not require artificial monotonization and limiters. The same idea of integrating factors is applied in temporal dimension to the stiff systems of equations describing chemical transformation models [2]. The proposed method is applicable for the problems involving convection-diffusion-reaction operators. The work has been partially supported by the Presidium of RAS under Program 43, and by the RFBR grants 14-01-00125 and 14-01-31482. References: 1. V.V. Penenko, E.A. Tsvetova, A.V. Penenko. Variational approach and Euler's integrating factors for environmental studies// Computers and Mathematics with Applications, (2014) V.67, Issue 12, P. 2240-2256. 2. V.V.Penenko, E.A.Tsvetova. Variational methods of constructing monotone approximations for atmospheric chemistry models // Numerical analysis and applications, 2013, V. 6, Issue 3, pp 210-220.

[Purifying process of gynostemma pentaphyllum saponins based on "adjoint marker" online control technology and identification of their compositions by UPLC-QTOF-MS].

PubMed

Fan, Dong-Dong; Kuang, Yan-Hui; Dong, Li-Hua; Ye, Xiao; Chen, Liang-Mian; Zhang, Dong; Ma, Zhen-Shan; Wang, Jin-Yu; Zhu, Jing-Jing; Wang, Zhi-Min; Wang, De-Qin; Li, Chu-Yuan

2017-04-01

To optimize the purification process of gynostemma pentaphyllum saponins (GPS) based on "adjoint marker" online control technology with GPS as the testing index. UPLC-QTOF-MS technology was used for qualitative analysis. "Adjoint marker" online control results showed that the end point of load sample was that the UV absorbance of effluent liquid was equal to half of that of load sample solution, and the absorbance was basically stable when the end point was stable. In UPLC-QTOF-MS qualitative analysis, 16 saponins were identified from GPS, including 13 known gynostemma saponins and 3 new saponins. This optimized method was proved to be simple, scientific, reasonable, easy for online determination, real-time record, and can be better applied to the mass production and automation of production. The results of qualitative analysis indicated that the "adjoint marker" online control technology can well retain main efficacy components of medicinal materials, and provide analysis tools for the process control and quality traceability. Copyright© by the Chinese Pharmaceutical Association.

Greenland Regional and Ice Sheet-wide Geometry Sensitivity to Boundary and Initial conditions

NASA Astrophysics Data System (ADS)

Logan, L. C.; Narayanan, S. H. K.; Greve, R.; Heimbach, P.

2017-12-01

Ice sheet and glacier model outputs require inputs from uncertainly known initial and boundary conditions, and other parameters. Conservation and constitutive equations formalize the relationship between model inputs and outputs, and the sensitivity of model-derived quantities of interest (e.g., ice sheet volume above floatation) to model variables can be obtained via the adjoint model of an ice sheet. We show how one particular ice sheet model, SICOPOLIS (SImulation COde for POLythermal Ice Sheets), depends on these inputs through comprehensive adjoint-based sensitivity analyses. SICOPOLIS discretizes the shallow-ice and shallow-shelf approximations for ice flow, and is well-suited for paleo-studies of Greenland and Antarctica, among other computational domains. The adjoint model of SICOPOLIS was developed via algorithmic differentiation, facilitated by the source transformation tool OpenAD (developed at Argonne National Lab). While model sensitivity to various inputs can be computed by costly methods involving input perturbation simulations, the time-dependent adjoint model of SICOPOLIS delivers model sensitivities to initial and boundary conditions throughout time at lower cost. Here, we explore both the sensitivities of the Greenland Ice Sheet's entire and regional volumes to: initial ice thickness, precipitation, basal sliding, and geothermal flux over the Holocene epoch. Sensitivity studies such as described here are now accessible to the modeling community, based on the latest version of SICOPOLIS that has been adapted for OpenAD to generate correct and efficient adjoint code.

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

NASA Technical Reports Server (NTRS)

Reuther, James; Jameson, Antony; Alonso, Juan Jose; Rimlinger, Mark J.; Saunders, David

1997-01-01

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

Supersonic wing and wing-body shape optimization using an adjoint formulation

NASA Technical Reports Server (NTRS)

Reuther, James; Jameson, Antony

1995-01-01

This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design of supersonic configurations. The work represents an extension of our earlier research in which control theory is used to devise a design procedure that significantly reduces the computational cost by employing an adjoint equation. In previous studies it was shown that control theory could be used toeviseransonic design methods for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. The method has also been implemented for both transonic potential flows and transonic flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can treat more general configurations. Here results are presented for three-dimensional design cases subject to supersonic flows governed by the Euler equation.

Adjoint-Based Sensitivity Kernels for Glacial Isostatic Adjustment in a Laterally Varying Earth

NASA Astrophysics Data System (ADS)

Crawford, O.; Al-Attar, D.; Tromp, J.; Mitrovica, J. X.; Austermann, J.; Lau, H. C. P.

2017-12-01

We consider a new approach to both the forward and inverse problems in glacial isostatic adjustment. We present a method for forward modelling GIA in compressible and laterally heterogeneous earth models with a variety of linear and non-linear rheologies. Instead of using the so-called sea level equation, which must be solved iteratively, the forward theory we present consists of a number of coupled evolution equations that can be straightforwardly numerically integrated. We also apply the adjoint method to the inverse problem in order to calculate the derivatives of measurements of GIA with respect to the viscosity structure of the Earth. Such derivatives quantify the sensitivity of the measurements to the model. The adjoint method enables efficient calculation of continuous and laterally varying derivatives, allowing us to calculate the sensitivity of measurements of glacial isostatic adjustment to the Earth's three-dimensional viscosity structure. The derivatives have a number of applications within the inverse method. Firstly, they can be used within a gradient-based optimisation method to find a model which minimises some data misfit function. The derivatives can also be used to quantify the uncertainty in such a model and hence to provide understanding of which parts of the model are well constrained. Finally, they enable construction of measurements which provide sensitivity to a particular part of the model space. We illustrate both the forward and inverse aspects with numerical examples in a spherically symmetric earth model.

Gradient-based Optimization for Poroelastic and Viscoelastic MR Elastography

PubMed Central

Tan, Likun; McGarry, Matthew D.J.; Van Houten, Elijah E.W.; Ji, Ming; Solamen, Ligin; Weaver, John B.

2017-01-01

We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized ‘adjoint method’ based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradient- and Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation. PMID:27608454

Advances in Global Full Waveform Inversion

NASA Astrophysics Data System (ADS)

Tromp, J.; Bozdag, E.; Lei, W.; Ruan, Y.; Lefebvre, M. P.; Modrak, R. T.; Orsvuran, R.; Smith, J. A.; Komatitsch, D.; Peter, D. B.

2017-12-01

Information about Earth's interior comes from seismograms recorded at its surface. Seismic imaging based on spectral-element and adjoint methods has enabled assimilation of this information for the construction of 3D (an)elastic Earth models. These methods account for the physics of wave excitation and propagation by numerically solving the equations of motion, and require the execution of complex computational procedures that challenge the most advanced high-performance computing systems. Current research is petascale; future research will require exascale capabilities. The inverse problem consists of reconstructing the characteristics of the medium from -often noisy- observations. A nonlinear functional is minimized, which involves both the misfit to the measurements and a Tikhonov-type regularization term to tackle inherent ill-posedness. Achieving scalability for the inversion process on tens of thousands of multicore processors is a task that offers many research challenges. We initiated global "adjoint tomography" using 253 earthquakes and produced the first-generation model named GLAD-M15, with a transversely isotropic model parameterization. We are currently running iterations for a second-generation anisotropic model based on the same 253 events. In parallel, we continue iterations for a transversely isotropic model with a larger dataset of 1,040 events to determine higher-resolution plume and slab images. A significant part of our research has focused on eliminating I/O bottlenecks in the adjoint tomography workflow. This has led to the development of a new Adaptable Seismic Data Format based on HDF5, and post-processing tools based on the ADIOS library developed by Oak Ridge National Laboratory. We use the Ensemble Toolkit for workflow stabilization & management to automate the workflow with minimal human interaction.

An Efficient Method Coupling Kernel Principal Component Analysis with Adjoint-Based Optimal Control and Its Goal-Oriented Extensions

NASA Astrophysics Data System (ADS)

Thimmisetty, C.; Talbot, C.; Tong, C. H.; Chen, X.

2016-12-01

The representativeness of available data poses a significant fundamental challenge to the quantification of uncertainty in geophysical systems. Furthermore, the successful application of machine learning methods to geophysical problems involving data assimilation is inherently constrained by the extent to which obtainable data represent the problem considered. We show how the adjoint method, coupled with optimization based on methods of machine learning, can facilitate the minimization of an objective function defined on a space of significantly reduced dimension. By considering uncertain parameters as constituting a stochastic process, the Karhunen-Loeve expansion and its nonlinear extensions furnish an optimal basis with respect to which optimization using L-BFGS can be carried out. In particular, we demonstrate that kernel PCA can be coupled with adjoint-based optimal control methods to successfully determine the distribution of material parameter values for problems in the context of channelized deformable media governed by the equations of linear elasticity. Since certain subsets of the original data are characterized by different features, the convergence rate of the method in part depends on, and may be limited by, the observations used to furnish the kernel principal component basis. By determining appropriate weights for realizations of the stochastic random field, then, one may accelerate the convergence of the method. To this end, we present a formulation of Weighted PCA combined with a gradient-based means using automatic differentiation to iteratively re-weight observations concurrent with the determination of an optimal reduced set control variables in the feature space. We demonstrate how improvements in the accuracy and computational efficiency of the weighted linear method can be achieved over existing unweighted kernel methods, and discuss nonlinear extensions of the algorithm.

Double-Difference Global Adjoint Tomography

NASA Astrophysics Data System (ADS)

Orsvuran, R.; Bozdag, E.; Lei, W.; Tromp, J.

2017-12-01

The adjoint method allows us to incorporate full waveform simulations in inverse problems. Misfit functions play an important role in extracting the relevant information from seismic waveforms. In this study, our goal is to apply the Double-Difference (DD) methodology proposed by Yuan et al. (2016) to global adjoint tomography. Dense seismic networks, such as USArray, lead to higher-resolution seismic images underneath continents. However, the imbalanced distribution of stations and sources poses challenges in global ray coverage. We adapt double-difference multitaper measurements to global adjoint tomography. We normalize each DD measurement by its number of pairs, and if a measurement has no pair, as may frequently happen for data recorded at oceanic stations, classical multitaper measurements are used. As a result, the differential measurements and pair-wise weighting strategy help balance uneven global kernel coverage. Our initial experiments with minor- and major-arc surface waves show promising results, revealing more pronounced structure near dense networks while reducing the prominence of paths towards cluster of stations. We have started using this new measurement in global adjoint inversions, addressing azimuthal anisotropy in upper mantle. Meanwhile, we are working on combining the double-difference approach with instantaneous phase measurements to emphasize contributions of scattered waves in global inversions and extending it to body waves. We will present our results and discuss challenges and future directions in the context of global tomographic inversions.

Comparison of the Adjoint and Adjoint-Free 4dVar Assimilation of the Hydrographic and Velocity Observations in the Adriatic Sea

DTIC Science & Technology

2015-11-10

of the ensemble method o the estimation of sensitivities was demonstrated in meteorological Ancell and Hakim, 2007 ; Torn and Hakim, 2008) and...to predetermined low- dimensional subspaces spanned either by the reduced-order approx- imations of the model Green’s functions ( Stammer and Wunsch...2005; Qui et al., 2007 ; Hoteit, 2008). In fact, the 4dEnVar technique pursues a similar, but more general approach, pa- rameterizing the search

Lossy Wavefield Compression for Full-Waveform Inversion

NASA Astrophysics Data System (ADS)

Boehm, C.; Fichtner, A.; de la Puente, J.; Hanzich, M.

2015-12-01

We present lossy compression techniques, tailored to the inexact computation of sensitivity kernels, that significantly reduce the memory requirements of adjoint-based minimization schemes. Adjoint methods are a powerful tool to solve tomography problems in full-waveform inversion (FWI). Yet they face the challenge of massive memory requirements caused by the opposite directions of forward and adjoint simulations and the necessity to access both wavefields simultaneously during the computation of the sensitivity kernel. Thus, storage, I/O operations, and memory bandwidth become key topics in FWI. In this talk, we present strategies for the temporal and spatial compression of the forward wavefield. This comprises re-interpolation with coarse time steps and an adaptive polynomial degree of the spectral element shape functions. In addition, we predict the projection errors on a hierarchy of grids and re-quantize the residuals with an adaptive floating-point accuracy to improve the approximation. Furthermore, we use the first arrivals of adjoint waves to identify "shadow zones" that do not contribute to the sensitivity kernel at all. Updating and storing the wavefield within these shadow zones is skipped, which reduces memory requirements and computational costs at the same time. Compared to check-pointing, our approach has only a negligible computational overhead, utilizing the fact that a sufficiently accurate sensitivity kernel does not require a fully resolved forward wavefield. Furthermore, we use adaptive compression thresholds during the FWI iterations to ensure convergence. Numerical experiments on the reservoir scale and for the Western Mediterranean prove the high potential of this approach with an effective compression factor of 500-1000. Furthermore, it is computationally cheap and easy to integrate in both, finite-differences and finite-element wave propagation codes.

Airfoil optimization for unsteady flows with application to high-lift noise reduction

NASA Astrophysics Data System (ADS)

Rumpfkeil, Markus Peer

The use of steady-state aerodynamic optimization methods in the computational fluid dynamic (CFD) community is fairly well established. In particular, the use of adjoint methods has proven to be very beneficial because their cost is independent of the number of design variables. The application of numerical optimization to airframe-generated noise, however, has not received as much attention, but with the significant quieting of modern engines, airframe noise now competes with engine noise. Optimal control techniques for unsteady flows are needed in order to be able to reduce airframe-generated noise. In this thesis, a general framework is formulated to calculate the gradient of a cost function in a nonlinear unsteady flow environment via the discrete adjoint method. The unsteady optimization algorithm developed in this work utilizes a Newton-Krylov approach since the gradient-based optimizer uses the quasi-Newton method BFGS, Newton's method is applied to the nonlinear flow problem, GMRES is used to solve the resulting linear problem inexactly, and last but not least the linear adjoint problem is solved using Bi-CGSTAB. The flow is governed by the unsteady two-dimensional compressible Navier-Stokes equations in conjunction with a one-equation turbulence model, which are discretized using structured grids and a finite difference approach. The effectiveness of the unsteady optimization algorithm is demonstrated by applying it to several problems of interest including shocktubes, pulses in converging-diverging nozzles, rotating cylinders, transonic buffeting, and an unsteady trailing-edge flow. In order to address radiated far-field noise, an acoustic wave propagation program based on the Ffowcs Williams and Hawkings (FW-H) formulation is implemented and validated. The general framework is then used to derive the adjoint equations for a novel hybrid URANS/FW-H optimization algorithm in order to be able to optimize the shape of airfoils based on their calculated far-field pressure fluctuations. Validation and application results for this novel hybrid URANS/FW-H optimization algorithm show that it is possible to optimize the shape of an airfoil in an unsteady flow environment to minimize its radiated far-field noise while maintaining good aerodynamic performance.

Adjoint affine fusion and tadpoles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Urichuk, Andrew, E-mail: andrew.urichuk@uleth.ca; Walton, Mark A., E-mail: walton@uleth.ca; International School for Advanced Studies

2016-06-15

We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are writtenmore » for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.« less

Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver

NASA Astrophysics Data System (ADS)

Paige, Cody

The use of adjoint methods is common in computational fluid dynamics to reduce the cost of the sensitivity analysis in an optimization cycle. The forward mode ADjoint is a combination of an adjoint sensitivity analysis method with a forward mode automatic differentiation (AD) and is a modification of the reverse mode ADjoint method proposed by Mader et al.[1]. A colouring acceleration technique is presented to reduce the computational cost increase associated with forward mode AD. The forward mode AD facilitates the implementation of the laminar Navier-Stokes (NS) equations. The forward mode ADjoint method is applied to a three-dimensional computational fluid dynamics solver. The resulting Euler and viscous ADjoint sensitivities are compared to the reverse mode Euler ADjoint derivatives and a complex-step method to demonstrate the reduced computational cost and accuracy. Both comparisons demonstrate the benefits of the colouring method and the practicality of using a forward mode AD. [1] Mader, C.A., Martins, J.R.R.A., Alonso, J.J., and van der Weide, E. (2008) ADjoint: An approach for the rapid development of discrete adjoint solvers. AIAA Journal, 46(4):863-873. doi:10.2514/1.29123.

Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method

NASA Technical Reports Server (NTRS)

Grossman, Bernard

1999-01-01

The technical details are summarized below: Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. . An efficient surface parameterization based on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing.

Discrete adjoint of fractional step Navier-Stokes solver in generalized coordinates

NASA Astrophysics Data System (ADS)

Wang, Mengze; Mons, Vincent; Zaki, Tamer

2017-11-01

Optimization and control in transitional and turbulent flows require evaluation of gradients of the flow state with respect to the problem parameters. Using adjoint approaches, these high-dimensional gradients can be evaluated with a similar computational cost as the forward Navier-Stokes simulations. The adjoint algorithm can be obtained by discretizing the continuous adjoint Navier-Stokes equations or by deriving the adjoint to the discretized Navier-Stokes equations directly. The latter algorithm is necessary when the forward-adjoint relations must be satisfied to machine precision. In this work, our forward model is the fractional step solution to the Navier-Stokes equations in generalized coordinates, proposed by Rosenfeld, Kwak & Vinokur. We derive the corresponding discrete adjoint equations. We also demonstrate the accuracy of the combined forward-adjoint model, and its application to unsteady wall-bounded flows. This work has been partially funded by the Office of Naval Research (Grant N00014-16-1-2542).

Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peplow, Douglas E.; Mosher, Scott W; Evans, Thomas M

2012-08-01

For challenging radiation transport problems, hybrid methods combine the accuracy of Monte Carlo methods with the global information present in deterministic methods. One of the most successful hybrid methods is CADIS Consistent Adjoint Driven Importance Sampling. This method uses a deterministic adjoint solution to construct a biased source distribution and consistent weight windows to optimize a specific tally in a Monte Carlo calculation. The method has been implemented into transport codes using just the spatial and energy information from the deterministic adjoint and has been used in many applications to compute tallies with much higher figures-of-merit than analog calculations. CADISmore » also outperforms user-supplied importance values, which usually take long periods of user time to develop. This work extends CADIS to develop weight windows that are a function of the position, energy, and direction of the Monte Carlo particle. Two types of consistent source biasing are presented: one method that biases the source in space and energy while preserving the original directional distribution and one method that biases the source in space, energy, and direction. Seven simple example problems are presented which compare the use of the standard space/energy CADIS with the new space/energy/angle treatments.« less

Multi-point Adjoint-Based Design of Tilt-Rotors in a Noninertial Reference Frame

NASA Technical Reports Server (NTRS)

Jones, William T.; Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Acree, Cecil W.

2014-01-01

Optimization of tilt-rotor systems requires the consideration of performance at multiple design points. In the current study, an adjoint-based optimization of a tilt-rotor blade is considered. The optimization seeks to simultaneously maximize the rotorcraft figure of merit in hover and the propulsive efficiency in airplane-mode for a tilt-rotor system. The design is subject to minimum thrust constraints imposed at each design point. The rotor flowfields at each design point are cast as steady-state problems in a noninertial reference frame. Geometric design variables used in the study to control blade shape include: thickness, camber, twist, and taper represented by as many as 123 separate design variables. Performance weighting of each operational mode is considered in the formulation of the composite objective function, and a build up of increasing geometric degrees of freedom is used to isolate the impact of selected design variables. In all cases considered, the resulting designs successfully increase both the hover figure of merit and the airplane-mode propulsive efficiency for a rotor designed with classical techniques.

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-04-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Time-domain least-squares migration using the Gaussian beam summation method

NASA Astrophysics Data System (ADS)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-07-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modelling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modelling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a pre-conditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Seismic imaging: From classical to adjoint tomography

NASA Astrophysics Data System (ADS)

Liu, Q.; Gu, Y. J.

2012-09-01

Seismic tomography has been a vital tool in probing the Earth's internal structure and enhancing our knowledge of dynamical processes in the Earth's crust and mantle. While various tomographic techniques differ in data types utilized (e.g., body vs. surface waves), data sensitivity (ray vs. finite-frequency approximations), and choices of model parameterization and regularization, most global mantle tomographic models agree well at long wavelengths, owing to the presence and typical dimensions of cold subducted oceanic lithospheres and hot, ascending mantle plumes (e.g., in central Pacific and Africa). Structures at relatively small length scales remain controversial, though, as will be discussed in this paper, they are becoming increasingly resolvable with the fast expanding global and regional seismic networks and improved forward modeling and inversion techniques. This review paper aims to provide an overview of classical tomography methods, key debates pertaining to the resolution of mantle tomographic models, as well as to highlight recent theoretical and computational advances in forward-modeling methods that spearheaded the developments in accurate computation of sensitivity kernels and adjoint tomography. The first part of the paper is devoted to traditional traveltime and waveform tomography. While these approaches established a firm foundation for global and regional seismic tomography, data coverage and the use of approximate sensitivity kernels remained as key limiting factors in the resolution of the targeted structures. In comparison to classical tomography, adjoint tomography takes advantage of full 3D numerical simulations in forward modeling and, in many ways, revolutionizes the seismic imaging of heterogeneous structures with strong velocity contrasts. For this reason, this review provides details of the implementation, resolution and potential challenges of adjoint tomography. Further discussions of techniques that are presently popular in seismic array analysis, such as noise correlation functions, receiver functions, inverse scattering imaging, and the adaptation of adjoint tomography to these different datasets highlight the promising future of seismic tomography.

Optical solitons, nonlinear self-adjointness and conservation laws for the cubic nonlinear Shrödinger's equation with repulsive delta potential

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi

2017-11-01

In this paper, the complex envelope function ansatz method is used to acquire the optical solitons to the cubic nonlinear Shrödinger's equation with repulsive delta potential (δ-NLSE). The method reveals dark and bright optical solitons. The necessary constraint conditions which guarantee the existence of the solitons are also presented. We studied the δ-NLSE by analyzing a system of partial differential equations (PDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system and prove that the system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conserved vectors for the system using the general Cls theorem presented by Ibragimov. Some interesting figures for the acquired solutions are also presented.

Reduction by symmetries in singular quantum-mechanical problems: General scheme and application to Aharonov-Bohm model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smirnov, A. G., E-mail: smirnov@lpi.ru

2015-12-15

We develop a general technique for finding self-adjoint extensions of a symmetric operator that respects a given set of its symmetries. Problems of this type naturally arise when considering two- and three-dimensional Schrödinger operators with singular potentials. The approach is based on constructing a unitary transformation diagonalizing the symmetries and reducing the initial operator to the direct integral of a suitable family of partial operators. We prove that symmetry preserving self-adjoint extensions of the initial operator are in a one-to-one correspondence with measurable families of self-adjoint extensions of partial operators obtained by reduction. The general scheme is applied to themore » three-dimensional Aharonov-Bohm Hamiltonian describing the electron in the magnetic field of an infinitely thin solenoid. We construct all self-adjoint extensions of this Hamiltonian, invariant under translations along the solenoid and rotations around it, and explicitly find their eigenfunction expansions.« less

An adjoint-based framework for maximizing mixing in binary fluids

NASA Astrophysics Data System (ADS)

Eggl, Maximilian; Schmid, Peter

2017-11-01

Mixing in the inertial, but laminar parameter regime is a common application in a wide range of industries. Enhancing the efficiency of mixing processes thus has a fundamental effect on product quality, material homogeneity and, last but not least, production costs. In this project, we address mixing efficiency in the above mentioned regime (Reynolds number Re = 1000 , Peclet number Pe = 1000) by developing and demonstrating an algorithm based on nonlinear adjoint looping that minimizes the variance of a passive scalar field which models our binary Newtonian fluids. The numerical method is based on the FLUSI code (Engels et al. 2016), a Fourier pseudo-spectral code, which we modified and augmented by scalar transport and adjoint equations. Mixing is accomplished by moving stirrers which are numerically modeled using a penalization approach. In our two-dimensional simulations we consider rotating circular and elliptic stirrers and extract optimal mixing strategies from the iterative scheme. The case of optimizing shape and rotational speed of the stirrers will be demonstrated.

FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

NASA Astrophysics Data System (ADS)

Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

2010-11-01

In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

Data-based adjoint and H2 optimal control of the Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Banks, Michael; Bodony, Daniel

2017-11-01

Equation-free, reduced-order methods of control are desirable when the governing system of interest is of very high dimension or the control is to be applied to a physical experiment. Two-phase flow optimal control problems, our target application, fit these criteria. Dynamic Mode Decomposition (DMD) is a data-driven method for model reduction that can be used to resolve the dynamics of very high dimensional systems and project the dynamics onto a smaller, more manageable basis. We evaluate the effectiveness of DMD-based forward and adjoint operator estimation when applied to H2 optimal control approaches applied to the linear and nonlinear Ginzburg-Landau equation. Perspectives on applying the data-driven adjoint to two phase flow control will be given. Office of Naval Research (ONR) as part of the Multidisciplinary University Research Initiatives (MURI) Program, under Grant Number N00014-16-1-2617.

A Computational Study of Shear Layer Receptivity

NASA Astrophysics Data System (ADS)

Barone, Matthew; Lele, Sanjiva

2002-11-01

The receptivity of two-dimensional, compressible shear layers to local and external excitation sources is examined using a computational approach. The family of base flows considered consists of a laminar supersonic stream separated from nearly quiescent fluid by a thin, rigid splitter plate with a rounded trailing edge. The linearized Euler and linearized Navier-Stokes equations are solved numerically in the frequency domain. The flow solver is based on a high order finite difference scheme, coupled with an overset mesh technique developed for computational aeroacoustics applications. Solutions are obtained for acoustic plane wave forcing near the most unstable shear layer frequency, and are compared to the existing low frequency theory. An adjoint formulation to the present problem is developed, and adjoint equation calculations are performed using the same numerical methods as for the regular equation sets. Solutions to the adjoint equations are used to shed light on the mechanisms which control the receptivity of finite-width compressible shear layers.

Electrical Resistivity Tomography using a finite element based BFGS algorithm with algebraic multigrid preconditioning

NASA Astrophysics Data System (ADS)

Codd, A. L.; Gross, L.

2018-03-01

We present a new inversion method for Electrical Resistivity Tomography which, in contrast to established approaches, minimizes the cost function prior to finite element discretization for the unknown electric conductivity and electric potential. Minimization is performed with the Broyden-Fletcher-Goldfarb-Shanno method (BFGS) in an appropriate function space. BFGS is self-preconditioning and avoids construction of the dense Hessian which is the major obstacle to solving large 3-D problems using parallel computers. In addition to the forward problem predicting the measurement from the injected current, the so-called adjoint problem also needs to be solved. For this problem a virtual current is injected through the measurement electrodes and an adjoint electric potential is obtained. The magnitude of the injected virtual current is equal to the misfit at the measurement electrodes. This new approach has the advantage that the solution process of the optimization problem remains independent to the meshes used for discretization and allows for mesh adaptation during inversion. Computation time is reduced by using superposition of pole loads for the forward and adjoint problems. A smoothed aggregation algebraic multigrid (AMG) preconditioned conjugate gradient is applied to construct the potentials for a given electric conductivity estimate and for constructing a first level BFGS preconditioner. Through the additional reuse of AMG operators and coarse grid solvers inversion time for large 3-D problems can be reduced further. We apply our new inversion method to synthetic survey data created by the resistivity profile representing the characteristics of subsurface fluid injection. We further test it on data obtained from a 2-D surface electrode survey on Heron Island, a small tropical island off the east coast of central Queensland, Australia.

Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations

NASA Astrophysics Data System (ADS)

He, Wei

2015-02-01

The Gauge/Bethe correspondence relates Omega-deformed N = 2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory with an adjoint matter, or with 4 fundamental matters, the potential of corresponding quantum model is the elliptic function. If the mass of matter takes special value then the potential is an elliptic solution of KdV hierarchy. We show that the deformed prepotential of gauge theory can be obtained from the average densities of conserved charges of the classical KdV solution, the UV gauge coupling dependence is assembled into the Eisenstein series. The gauge theory with adjoint mass is taken as the example.

A new approach for developing adjoint models

NASA Astrophysics Data System (ADS)

Farrell, P. E.; Funke, S. W.

2011-12-01

Many data assimilation algorithms rely on the availability of gradients of misfit functionals, which can be efficiently computed with adjoint models. However, the development of an adjoint model for a complex geophysical code is generally very difficult. Algorithmic differentiation (AD, also called automatic differentiation) offers one strategy for simplifying this task: it takes the abstraction that a model is a sequence of primitive instructions, each of which may be differentiated in turn. While extremely successful, this low-level abstraction runs into time-consuming difficulties when applied to the whole codebase of a model, such as differentiating through linear solves, model I/O, calls to external libraries, language features that are unsupported by the AD tool, and the use of multiple programming languages. While these difficulties can be overcome, it requires a large amount of technical expertise and an intimate familiarity with both the AD tool and the model. An alternative to applying the AD tool to the whole codebase is to assemble the discrete adjoint equations and use these to compute the necessary gradients. With this approach, the AD tool must be applied to the nonlinear assembly operators, which are typically small, self-contained units of the codebase. The disadvantage of this approach is that the assembly of the discrete adjoint equations is still very difficult to perform correctly, especially for complex multiphysics models that perform temporal integration; as it stands, this approach is as difficult and time-consuming as applying AD to the whole model. In this work, we have developed a library which greatly simplifies and automates the alternate approach of assembling the discrete adjoint equations. We propose a complementary, higher-level abstraction to that of AD: that a model is a sequence of linear solves. The developer annotates model source code with library calls that build a 'tape' of the operators involved and their dependencies, and supplies callbacks to compute the action of these operators. The library, called libadjoint, is then capable of symbolically manipulating the forward annotation to automatically assemble the adjoint equations. Libadjoint is open source, and is explicitly designed to be bolted-on to an existing discrete model. It can be applied to any discretisation, steady or time-dependent problems, and both linear and nonlinear systems. Using libadjoint has several advantages. It requires the application of an AD tool only to small pieces of code, making the use of AD far more tractable. As libadjoint derives the adjoint equations, the expertise required to develop an adjoint model is greatly diminished. One major advantage of this approach is that the model developer is freed from implementing complex checkpointing strategies for the adjoint model: libadjoint has sufficient information about the forward model to re-play the entire forward solve when necessary, and thus the checkpointing algorithm can be implemented entirely within the library itself. Examples are shown using the Fluidity/ICOM framework, a complex ocean model under development at Imperial College London.

Minimization of model representativity errors in identification of point source emission from atmospheric concentration measurements

NASA Astrophysics Data System (ADS)

Sharan, Maithili; Singh, Amit Kumar; Singh, Sarvesh Kumar

2017-11-01

Estimation of an unknown atmospheric release from a finite set of concentration measurements is considered an ill-posed inverse problem. Besides ill-posedness, the estimation process is influenced by the instrumental errors in the measured concentrations and model representativity errors. The study highlights the effect of minimizing model representativity errors on the source estimation. This is described in an adjoint modelling framework and followed in three steps. First, an estimation of point source parameters (location and intensity) is carried out using an inversion technique. Second, a linear regression relationship is established between the measured concentrations and corresponding predicted using the retrieved source parameters. Third, this relationship is utilized to modify the adjoint functions. Further, source estimation is carried out using these modified adjoint functions to analyse the effect of such modifications. The process is tested for two well known inversion techniques, called renormalization and least-square. The proposed methodology and inversion techniques are evaluated for a real scenario by using concentrations measurements from the Idaho diffusion experiment in low wind stable conditions. With both the inversion techniques, a significant improvement is observed in the retrieval of source estimation after minimizing the representativity errors.

A New Method for Computing Three-Dimensional Capture Fraction in Heterogeneous Regional Systems using the MODFLOW Adjoint Code

NASA Astrophysics Data System (ADS)

Clemo, T. M.; Ramarao, B.; Kelly, V. A.; Lavenue, M.

2011-12-01

Capture is a measure of the impact of groundwater pumping upon groundwater and surface water systems. The computation of capture through analytical or numerical methods has been the subject of articles in the literature for several decades (Bredehoeft et al., 1982). Most recently Leake et al. (2010) described a systematic way to produce capture maps in three-dimensional systems using a numerical perturbation approach in which capture from streams was computed using unit rate pumping at many locations within a MODFLOW model. The Leake et al. (2010) method advances the current state of computing capture. A limitation stems from the computational demand required by the perturbation approach wherein days or weeks of computational time might be required to obtain a robust measure of capture. In this paper, we present an efficient method to compute capture in three-dimensional systems based upon adjoint states. The efficiency of the adjoint method will enable uncertainty analysis to be conducted on capture calculations. The USGS and INTERA have collaborated to extend the MODFLOW Adjoint code (Clemo, 2007) to include stream-aquifer interaction and have applied it to one of the examples used in Leake et al. (2010), the San Pedro Basin MODFLOW model. With five layers and 140,800 grid blocks per layer, the San Pedro Basin model, provided an ideal example data set to compare the capture computed from the perturbation and the adjoint methods. The capture fraction map produced from the perturbation method for the San Pedro Basin model required significant computational time to compute and therefore the locations for the pumping wells were limited to 1530 locations in layer 4. The 1530 direct simulations of capture require approximately 76 CPU hours. Had capture been simulated in each grid block in each layer, as is done in the adjoint method, the CPU time would have been on the order of 4 years. The MODFLOW-Adjoint produced the capture fraction map of the San Pedro Basin model at 704,000 grid blocks (140,800 grid blocks x 5 layers) in just 6 minutes. The capture fraction maps from the perturbation and adjoint methods agree closely. The results of this study indicate that the adjoint capture method and its associated computational efficiency will enable scientists and engineers facing water resource management decisions to evaluate the sensitivity and uncertainty of impacts to regional water resource systems as part of groundwater supply strategies. Bredehoeft, J.D., S.S. Papadopulos, and H.H. Cooper Jr, Groundwater: The water budget myth. In Scientific Basis of Water-Resources Management, ed. National Research Council (U.S.), Geophysical Study Committee, 51-57. Washington D.C.: National Academy Press, 1982. Clemo, Tom, MODFLOW-2005 Ground-Water Model-Users Guide to Adjoint State based Sensitivity Process (ADJ), BSU CGISS 07-01, Center for the Geophysical Investigation of the Shallow Subsurface, Boise State University, 2007. Leake, S.A., H.W. Reeves, and J.E. Dickinson, A New Capture Fraction Method to Map How Pumpage Affects Surface Water Flow, Ground Water, 48(5), 670-700, 2010.

New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks.

PubMed

Bouchard, M

2001-01-01

In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

Adjoint Inversion for Extended Earthquake Source Kinematics From Very Dense Strong Motion Data

NASA Astrophysics Data System (ADS)

Ampuero, J. P.; Somala, S.; Lapusta, N.

2010-12-01

Addressing key open questions about earthquake dynamics requires a radical improvement of the robustness and resolution of seismic observations of large earthquakes. Proposals for a new generation of earthquake observation systems include the deployment of “community seismic networks” of low-cost accelerometers in urban areas and the extraction of strong ground motions from high-rate optical images of the Earth's surface recorded by a large space telescope in geostationary orbit. Both systems could deliver strong motion data with a spatial density orders of magnitude higher than current seismic networks. In particular, a “space seismometer” could sample the seismic wave field at a spatio-temporal resolution of 100 m, 1 Hz over areas several 100 km wide with an amplitude resolution of few cm/s in ground velocity. The amount of data to process would be immensely larger than what current extended source inversion algorithms can handle, which hampers the quantitative assessment of the cost-benefit trade-offs that can guide the practical design of the proposed earthquake observation systems. We report here on the development of a scalable source imaging technique based on iterative adjoint inversion and its application to the proof-of-concept of a space seismometer. We generated synthetic ground motions for M7 earthquake rupture scenarios based on dynamic rupture simulations on a vertical strike-slip fault embedded in an elastic half-space. A range of scenarios include increasing levels of complexity and interesting features such as supershear rupture speed. The resulting ground shaking is then processed accordingly to what would be captured by an optical satellite. Based on the resulting data, we perform source inversion by an adjoint/time-reversal method. The gradient of a cost function quantifying the waveform misfit between data and synthetics is efficiently obtained by applying the time-reversed ground velocity residuals as surface force sources, back-propagating onto the locked fault plane through a seismic wave simulation and recording the fault shear stress, which is the adjoint field of the fault slip-rate. Restricting the procedure to a single iteration is known as imaging. The source reconstructed by imaging reproduces the original forward model quite well in the shallow part of the fault. However, the deeper part of the earthquake source is not well reproduced, due to the lack of data on the side and bottom boundaries of our computational domain. To resolve this issue, we are implementing the complete iterative procedure and we will report on the convergence aspects of the adjoint iterations. Our current work is also directed towards addressing the lack of data on other boundaries of our domain and improving the source reconstruction by including teleseismic data for those boundaries and non-negativity constraints on the dominant slip-rate component.

Sensitivity kernels for viscoelastic loading based on adjoint methods

NASA Astrophysics Data System (ADS)

Al-Attar, David; Tromp, Jeroen

2014-01-01

Observations of glacial isostatic adjustment (GIA) allow for inferences to be made about mantle viscosity, ice sheet history and other related parameters. Typically, this inverse problem can be formulated as minimizing the misfit between the given observations and a corresponding set of synthetic data. When the number of parameters is large, solution of such optimization problems can be computationally challenging. A practical, albeit non-ideal, solution is to use gradient-based optimization. Although the gradient of the misfit required in such methods could be calculated approximately using finite differences, the necessary computation time grows linearly with the number of model parameters, and so this is often infeasible. A far better approach is to apply the `adjoint method', which allows the exact gradient to be calculated from a single solution of the forward problem, along with one solution of the associated adjoint problem. As a first step towards applying the adjoint method to the GIA inverse problem, we consider its application to a simpler viscoelastic loading problem in which gravitationally self-consistent ocean loading is neglected. The earth model considered is non-rotating, self-gravitating, compressible, hydrostatically pre-stressed, laterally heterogeneous and possesses a Maxwell solid rheology. We determine adjoint equations and Fréchet kernels for this problem based on a Lagrange multiplier method. Given an objective functional J defined in terms of the surface deformation fields, we show that its first-order perturbation can be written δ J = int _{MS}K_{η }δ ln η dV +int _{t0}^{t1}int _{partial M}K_{dot{σ }} δ dot{σ } dS dt, where δ ln η = δη/η denotes relative viscosity variations in solid regions MS, dV is the volume element, δ dot{σ } is the perturbation to the time derivative of the surface load which is defined on the earth model's surface ∂M and for times [t0, t1] and dS is the surface element on ∂M. The `viscosity kernel' Kη determines the linearized sensitivity of J to viscosity perturbations defined with respect to a laterally heterogeneous reference earth model, while the `rate-of-loading kernel' K_{dot{σ }} determines the sensitivity to variations in the time derivative of the surface load. By restricting attention to spherically symmetric viscosity perturbations, we also obtain a `radial viscosity kernel' overline{K}_{η } such that the associated contribution to δJ can be written int _{IS}overline{K}_{η }δ ln η dr, where IS denotes the subset of radii lying in solid regions. In order to illustrate this theory, we describe its numerical implementation in the case of a spherically symmetric earth model using a 1-D spectral element method, and calculate sensitivity kernels for a range of realistic observables.

Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems With Switching [Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems

DOE PAGES

Zhang, Hong; Abhyankar, Shrirang; Constantinescu, Emil; ...

2017-01-24

Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this paper, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating sensitivities of larger systems and is consistent, within machine precision, with the function whosemore » sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as dc exciters, by deriving and implementing the adjoint jump conditions that arise from state-dependent and time-dependent switchings. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach. In conclusion, this paper focuses primarily on the power system dynamics, but the approach is general and can be applied to hybrid dynamical systems in a broader range of fields.« less

Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems With Switching [Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hong; Abhyankar, Shrirang; Constantinescu, Emil

Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this paper, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating sensitivities of larger systems and is consistent, within machine precision, with the function whosemore » sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as dc exciters, by deriving and implementing the adjoint jump conditions that arise from state-dependent and time-dependent switchings. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach. In conclusion, this paper focuses primarily on the power system dynamics, but the approach is general and can be applied to hybrid dynamical systems in a broader range of fields.« less

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andrade, F.M., E-mail: fmandrade@uepg.br; Silva, E.O., E-mail: edilbertoo@gmail.com; Pereira, M., E-mail: marciano@uepg.br

2013-12-15

In this work the bound state and scattering problems for a spin- 1/2 particle undergone to an Aharonov–Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a δ-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and S matrix are determined in terms of the self-adjoint extension parameter, which is explicitly determinedmore » in terms of the parameters of the problem. The relation between the bound state and zero modes and the failure of helicity conservation in the scattering problem and its relation with the gyromagnetic ratio g are discussed. Also, as an application, we consider the spin- 1/2 Aharonov–Bohm problem in conical space plus a two-dimensional isotropic harmonic oscillator. -- Highlights: •Planar dynamics of a spin- 1/2 neutral particle. •Bound state for Aharonov–Bohm systems. •Aharonov–Bohm scattering. •Helicity nonconservation. •Determination of the self-adjoint extension parameter.« less

An integrand reconstruction method for three-loop amplitudes

NASA Astrophysics Data System (ADS)

Badger, Simon; Frellesvig, Hjalte; Zhang, Yang

2012-08-01

We consider the maximal cut of a three-loop four point function with massless kinematics. By applying Gröbner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an arbitrary triple-box configuration via generalized unitarity cuts. As an example we present analytic results for the three loop triple-box contribution to gluon-gluon scattering in Yang-Mills with adjoint fermions and scalars in terms of three master integrals.

A New Class of Highly Accurate Differentiation Schemes Based on the Prolate Spheroidal Wave Functions

DTIC Science & Technology

2011-04-07

predictor - corrector scheme. Such an approach for the solution of time-dependent PDEs, which is some- times referred to as the “method of lines,” is studied...particular, λj = i j |λj |. We define the self -adjoint operator Qc : L 2([−1, 1]) → L2([−1, 1]) by the formula Qc(φ) = 1 π ∫ 1 −1 sin( c (x− t)) x− t φ...Gaussian quadratures for bandlimited functions is to use the Newton-type nonlinear optimization algorithm of [14]. Specifically, for bandlimit c and

An Adjoint-Based Analysis of the Sampling Footprints of Tall Tower, Aircraft and Potential Future Lidar Observations of CO2

NASA Technical Reports Server (NTRS)

Andrews, Arlyn; Kawa, Randy; Zhu, Zhengxin; Burris, John; Abshire, Jim

2004-01-01

A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future CO2 levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an 'inverse problem', where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from longterm surface and aircraft monitoring stations with data from intensive field campaigns and with proposed future satellite observations. We have recently developed an adjoint for the GSFC 3-D Parameterized Chemistry and Transport Model (PCTM). Here, we will present results from a PCTM Adjoint study comparing the sampling footprints of tall tower, aircraft and potential future lidar observations of CO2. The vertical resolution and extent of the profiles and the observation frequency will be considered for several sites in North America.

Unsteady adjoint for large eddy simulation of a coupled turbine stator-rotor system

NASA Astrophysics Data System (ADS)

Talnikar, Chaitanya; Wang, Qiqi; Laskowski, Gregory

2016-11-01

Unsteady fluid flow simulations like large eddy simulation are crucial in capturing key physics in turbomachinery applications like separation and wake formation in flow over a turbine vane with a downstream blade. To determine how sensitive the design objectives of the coupled system are to control parameters, an unsteady adjoint is needed. It enables the computation of the gradient of an objective with respect to a large number of inputs in a computationally efficient manner. In this paper we present unsteady adjoint solutions for a coupled turbine stator-rotor system. As the transonic fluid flows over the stator vane, the boundary layer transitions to turbulence. The turbulent wake then impinges on the rotor blades, causing early separation. This coupled system exhibits chaotic dynamics which causes conventional adjoint solutions to diverge exponentially, resulting in the corruption of the sensitivities obtained from the adjoint solutions for long-time simulations. In this presentation, adjoint solutions for aerothermal objectives are obtained through a localized adjoint viscosity injection method which aims to stabilize the adjoint solution and maintain accurate sensitivities. Preliminary results obtained from the supercomputer Mira will be shown in the presentation.

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

Adjoint Airfoil Optimization of Darrieus-Type Vertical Axis Wind Turbine

NASA Astrophysics Data System (ADS)

Fuchs, Roman; Nordborg, Henrik

2012-11-01

We present the feasibility of using an adjoint solver to optimize the torque of a Darrieus-type vertical axis wind turbine (VAWT). We start with a 2D cross section of a symmetrical airfoil and restrict us to low solidity ratios to minimize blade vortex interactions. The adjoint solver of the ANSYS FLUENT software package computes the sensitivities of airfoil surface forces based on a steady flow field. Hence, we find the torque of a full revolution using a weighted average of the sensitivities at different wind speeds and angles of attack. The weights are computed analytically, and the range of angles of attack is given by the tip speed ratio. Then the airfoil geometry is evolved, and the proposed methodology is evaluated by transient simulations.

Examination of Observation Impacts derived from OSEs and Adjoint Models

NASA Technical Reports Server (NTRS)

Gelaro, Ronald

2008-01-01

With the adjoint of a data assimilation system, the impact of any or all assimilated observations on measures of forecast skill can be estimated accurately and efficiently. The approach allows aggregation of results in terms of individual data types, channels or locations, all computed simultaneously. In this study, adjoint-based estimates of observation impact are compared with results from standard observing system experiments (OSEs) in the NASA Goddard Earth Observing System Model, Version 5 (GEOS-5) GEOS-5 system. The two approaches are shown to provide unique, but complimentary, information. Used together, they reveal both redundancies and dependencies between observing system impacts as observations are added or removed. Understanding these dependencies poses a major challenge for optimizing the use of the current observational network and defining requirements for future observing systems.

The development of three-dimensional adjoint method for flow control with blowing in convergent-divergent nozzle flows

NASA Astrophysics Data System (ADS)

Sikarwar, Nidhi

The noise produced by the low bypass ratio turbofan engines used to power fighter aircraft is a problem for communities near military bases and for personnel working in close proximity to the aircraft. For example, carrier deck personnel are subject to noise exposure that can result in Noise-Induced Hearing Loss which in-turn results in over a billion dollars of disability payments by the Veterans Administration. Several methods have been proposed to reduce the jet noise at the source. These methods include microjet injection of air or water downstream of the jet exit, chevrons, and corrugated nozzle inserts. The last method involves the insertion of corrugated seals into the diverging section of a military-style convergent-divergent jet nozzle (to replace the existing seals). This has been shown to reduce both the broadband shock-associated noise as well as the mixing noise in the peak noise radiation direction. However, the original inserts were designed to be effective for a take-off condition where the jet is over-expanded. The nozzle performance would be expected to degrade at other conditions, such as in cruise at altitude. A new method has been proposed to achieve the same effects as corrugated seals, but using fluidic inserts. This involves injection of air, at relatively low pressures and total mass flow rates, into the diverging section of the nozzle. These fluidic inserts" deflect the flow in the same way as the mechanical inserts. The fluidic inserts represent an active control method, since the injectors can be modified or turned off depending on the jet operating conditions. Noise reductions in the peak noise direction of 5 to 6 dB have been achieved and broadband shock-associated noise is effectively suppressed. There are multiple parameters to be considered in the design of the fluidic inserts. This includes the number and location of the injectors and the pressures and mass flow rates to be used. These could be optimized on an ad hoc basis with multiple experiments or numerical simulations. Alternatively an inverse design method can be used. An adjoint optimization method can be used to achieve the optimum blowing rate. It is shown that the method works for both geometry optimization and active control of the flow in order to deflect the flow in desirable ways. An adjoint optimization method is described. It is used to determine the blowing distribution in the diverging section of a convergent-divergent nozzle that gives a desired pressure distribution in the nozzle. Both the direct and adjoint problems and their associated boundary conditions are developed. The adjoint method is used to determine the blowing distribution required to minimize the shock strength in the nozzle to achieve a known target pressure and to achieve close to an ideally expanded flow pressure. A multi-block structured solver is developed to calculate the flow solution and associated adjoint variables. Two and three-dimensional calculations are performed for internal and external of the nozzle domains. A two step MacCormack scheme based on predictor- corrector technique is was used for some calculations. The four and five stage Runge-Kutta schemes are also used to artificially march in time. A modified Runge-Kutta scheme is used to accelerate the convergence to a steady state. Second order artificial dissipation has been added to stabilize the calculations. The steepest decent method has been used for the optimization of the blowing velocity after the gradients of the cost function with respect to the blowing velocity are calculated using adjoint method. Several examples are given of the optimization of blowing using the adjoint method.

The Global Modeling and Assimilation Office (GMAO) 4d-Var and its Adjoint-based Tools

NASA Technical Reports Server (NTRS)

Todling, Ricardo; Tremolet, Yannick

2008-01-01

The fifth generation of the Goddard Earth Observing System (GEOS-5) Data Assimilation System (DAS) is a 3d-var system that uses the Grid-point Statistical Interpolation (GSI) system developed in collaboration with NCEP, and a general circulation model developed at Goddard, that includes the finite-volume hydrodynamics of GEOS-4 wrapped in the Earth System Modeling Framework and physical packages tuned to provide a reliable hydrological cycle for the integration of the Modern Era Retrospective-analysis for Research and Applications (MERRA). This MERRA system is essentially complete and the next generation GEOS is under intense development. A prototype next generation system is now complete and has been producing preliminary results. This prototype system replaces the GSI-based Incremental Analysis Update procedure with a GSI-based 4d-var which uses the adjoint of the finite-volume hydrodynamics of GEOS-4 together with a vertical diffusing scheme for simplified physics. As part of this development we have kept the GEOS-5 IAU procedure as an option and have added the capability to experiment with a First Guess at the Appropriate Time (FGAT) procedure, thus allowing for at least three modes of running the data assimilation experiments. The prototype system is a large extension of GEOS-5 as it also includes various adjoint-based tools, namely, a forecast sensitivity tool, a singular vector tool, and an observation impact tool, that combines the model sensitivity tool with a GSI-based adjoint tool. These features bring the global data assimilation effort at Goddard up to date with technologies used in data assimilation systems at major meteorological centers elsewhere. Various aspects of the next generation GEOS will be discussed during the presentation at the Workshop, and preliminary results will illustrate the discussion.

Adjoint-Based Implicit Uncertainty Analysis for Figures of Merit in a Laser Inertial Fusion Engine

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seifried, J E; Fratoni, M; Kramer, K J

A primary purpose of computational models is to inform design decisions and, in order to make those decisions reliably, the confidence in the results of such models must be estimated. Monte Carlo neutron transport models are common tools for reactor designers. These types of models contain several sources of uncertainty that propagate onto the model predictions. Two uncertainties worthy of note are (1) experimental and evaluation uncertainties of nuclear data that inform all neutron transport models and (2) statistical counting precision, which all results of a Monte Carlo codes contain. Adjoint-based implicit uncertainty analyses allow for the consideration of anymore » number of uncertain input quantities and their effects upon the confidence of figures of merit with only a handful of forward and adjoint transport calculations. When considering a rich set of uncertain inputs, adjoint-based methods remain hundreds of times more computationally efficient than Direct Monte-Carlo methods. The LIFE (Laser Inertial Fusion Energy) engine is a concept being developed at Lawrence Livermore National Laboratory. Various options exist for the LIFE blanket, depending on the mission of the design. The depleted uranium hybrid LIFE blanket design strives to close the fission fuel cycle without enrichment or reprocessing, while simultaneously achieving high discharge burnups with reduced proliferation concerns. Neutron transport results that are central to the operation of the design are tritium production for fusion fuel, fission of fissile isotopes for energy multiplication, and production of fissile isotopes for sustained power. In previous work, explicit cross-sectional uncertainty analyses were performed for reaction rates related to the figures of merit for the depleted uranium hybrid LIFE blanket. Counting precision was also quantified for both the figures of merit themselves and the cross-sectional uncertainty estimates to gauge the validity of the analysis. All cross-sectional uncertainties were small (0.1-0.8%), bounded counting uncertainties, and were precise with regard to counting precision. Adjoint/importance distributions were generated for the same reaction rates. The current work leverages those adjoint distributions to transition from explicit sensitivities, in which the neutron flux is constrained, to implicit sensitivities, in which the neutron flux responds to input perturbations. This treatment vastly expands the set of data that contribute to uncertainties to produce larger, more physically accurate uncertainty estimates.« less

Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

NASA Technical Reports Server (NTRS)

Webb, G. M.; Jokipii, J. R.; Morfill, G. E.

1994-01-01

Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of aziuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega(sub 0)(omega(sub 0)/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from monoenergetic and truncated power-law sources. We conclude that it is possible to accelerate particles beyond the knee by galactic rotation, but not in sufficient number to adequately explain the observed spectrum.

Improving the Fit of a Land-Surface Model to Data Using its Adjoint

NASA Astrophysics Data System (ADS)

Raoult, N.; Jupp, T. E.; Cox, P. M.; Luke, C.

2015-12-01

Land-surface models (LSMs) are of growing importance in the world of climate prediction. They are crucial components of larger Earth system models that are aimed at understanding the effects of land surface processes on the global carbon cycle. The Joint UK Land Environment Simulator (JULES) is the land-surface model used by the UK Met Office. It has been automatically differentiated using commercial software from FastOpt, resulting in an analytical gradient, or 'adjoint', of the model. Using this adjoint, the adJULES parameter estimation system has been developed, to search for locally optimum parameter sets by calibrating against observations. adJULES presents an opportunity to confront JULES with many different observations, and make improvements to the model parameterisation. In the newest version of adJULES, multiple sites can be used in the calibration, to giving a generic set of parameters that can be generalised over plant functional types. We present an introduction to the adJULES system and its applications to data from a variety of flux tower sites. We show that calculation of the 2nd derivative of JULES allows us to produce posterior probability density functions of the parameters and how knowledge of parameter values is constrained by observations.

Solid oxide fuel cell simulation and design optimization with numerical adjoint techniques

NASA Astrophysics Data System (ADS)

Elliott, Louie C.

This dissertation reports on the application of numerical optimization techniques as applied to fuel cell simulation and design. Due to the "multi-physics" inherent in a fuel cell, which results in a highly coupled and non-linear behavior, an experimental program to analyze and improve the performance of fuel cells is extremely difficult. This program applies new optimization techniques with computational methods from the field of aerospace engineering to the fuel cell design problem. After an overview of fuel cell history, importance, and classification, a mathematical model of solid oxide fuel cells (SOFC) is presented. The governing equations are discretized and solved with computational fluid dynamics (CFD) techniques including unstructured meshes, non-linear solution methods, numerical derivatives with complex variables, and sensitivity analysis with adjoint methods. Following the validation of the fuel cell model in 2-D and 3-D, the results of the sensitivity analysis are presented. The sensitivity derivative for a cost function with respect to a design variable is found with three increasingly sophisticated techniques: finite difference, direct differentiation, and adjoint. A design cycle is performed using a simple optimization method to improve the value of the implemented cost function. The results from this program could improve fuel cell performance and lessen the world's dependence on fossil fuels.

Advances in Global Adjoint Tomography -- Massive Data Assimilation

NASA Astrophysics Data System (ADS)

Ruan, Y.; Lei, W.; Bozdag, E.; Lefebvre, M. P.; Smith, J. A.; Krischer, L.; Tromp, J.

2015-12-01

Azimuthal anisotropy and anelasticity are key to understanding a myriad of processes in Earth's interior. Resolving these properties requires accurate simulations of seismic wave propagation in complex 3-D Earth models and an iterative inversion strategy. In the wake of successes in regional studies(e.g., Chen et al., 2007; Tape et al., 2009, 2010; Fichtner et al., 2009, 2010; Chen et al.,2010; Zhu et al., 2012, 2013; Chen et al., 2015), we are employing adjoint tomography based on a spectral-element method (Komatitsch & Tromp 1999, 2002) on a global scale using the supercomputer ''Titan'' at Oak Ridge National Laboratory. After 15 iterations, we have obtained a high-resolution transversely isotropic Earth model (M15) using traveltime data from 253 earthquakes. To obtain higher resolution images of the emerging new features and to prepare the inversion for azimuthal anisotropy and anelasticity, we expanded the original dataset with approximately 4,220 additional global earthquakes (Mw5.5-7.0) --occurring between 1995 and 2014-- and downloaded 300-minute-long time series for all available data archived at the IRIS Data Management Center, ORFEUS, and F-net. Ocean Bottom Seismograph data from the last decade are also included to maximize data coverage. In order to handle the huge dataset and solve the I/O bottleneck in global adjoint tomography, we implemented a python-based parallel data processing workflow based on the newly developed Adaptable Seismic Data Format (ASDF). With the help of the data selection tool MUSTANG developed by IRIS, we cleaned our dataset and assembled event-based ASDF files for parallel processing. We have started Centroid Moment Tensors (CMT) inversions for all 4,220 earthquakes with the latest model M15, and selected high-quality data for measurement. We will statistically investigate each channel using synthetic seismograms calculated in M15 for updated CMTs and identify problematic channels. In addition to data screening, we also modified the conventional multi-taper method to obtain better frequency-dependent measurements of surface-wave phase and amplitude anomalies, and therefore more accurate adjoint sources, which are particularly important for anelastic tomography. We present a summary of these data culling and processing procedures for global adjoint tomography.

Universal Racah matrices and adjoint knot polynomials: Arborescent knots

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.

2016-04-01

By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.

Aerodynamic Design on Unstructured Grids for Turbulent Flows

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Bonhaus, Daryl L.

1997-01-01

An aerodynamic design algorithm for turbulent flows using unstructured grids is described. The current approach uses adjoint (costate) variables for obtaining derivatives of the cost function. The solution of the adjoint equations is obtained using an implicit formulation in which the turbulence model is fully coupled with the flow equations when solving for the costate variables. The accuracy of the derivatives is demonstrated by comparison with finite-difference gradients and a few example computations are shown. In addition, a user interface is described which significantly reduces the time required for setting up the design problems. Recommendations on directions of further research into the Navier Stokes design process are made.

Recent Improvements in Aerodynamic Design Optimization on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Anderson, W. Kyle

2000-01-01

Recent improvements in an unstructured-grid method for large-scale aerodynamic design are presented. Previous work had shown such computations to be prohibitively long in a sequential processing environment. Also, robust adjoint solutions and mesh movement procedures were difficult to realize, particularly for viscous flows. To overcome these limiting factors, a set of design codes based on a discrete adjoint method is extended to a multiprocessor environment using a shared memory approach. A nearly linear speedup is demonstrated, and the consistency of the linearizations is shown to remain valid. The full linearization of the residual is used to precondition the adjoint system, and a significantly improved convergence rate is obtained. A new mesh movement algorithm is implemented and several advantages over an existing technique are presented. Several design cases are shown for turbulent flows in two and three dimensions.

Self-adjointness of deformed unbounded operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Much, Albert

2015-09-15

We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.

Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method

NASA Technical Reports Server (NTRS)

Grossman, Bernard

1999-01-01

Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. An efficient surface parameterization based on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing. In order for large scale optimization to become routine, the benefits of parallel architectures should be exploited. Although the flow solver has been parallelized using compiler directives. The parallel efficiency is under 50 percent. Clearly, parallel versions of the codes will have an immediate impact on the ability to design realistic configurations on fine meshes, and this effort is currently underway.

SCIPUFF Tangent-Linear/Adjoint Model for Release Source Location from Observational Data

DTIC Science & Technology

2011-01-18

magnitudes, times? Inverse model based on SCIPUFF (AIMS) 1/17/2011 Aerodyne Research, Inc. W911NF-06-C-0161 5 (1981), Daescu and Carmichael (2003...Defined Choice- Situations” The Journal of the Operational Research Society, Vol. 32, No. 2 (1981) Daescu, D. N., and Carmichael , G. R., “An Adjoint...Intelligence Applications to Environmental Sciences at AMS Annual Meeting, Atlanta, GA, Jan 17-21 (2010 ) N. Platt, S. Warner and S. M. Nunes, ’Plan for

Almost commuting self-adjoint matrices: The real and self-dual cases

NASA Astrophysics Data System (ADS)

Loring, Terry A.; Sørensen, Adam P. W.

2016-08-01

We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover, we prove that the same holds with self-dual in place of symmetric and also for paths of self-adjoint matrices. Since a symmetric, self-adjoint matrix is real, we get a real version of Huaxin Lin’s famous theorem on almost commuting matrices. Similarly, the self-dual case gives a version for matrices over the quaternions. To prove these results, we develop a theory of semiprojectivity for real C*-algebras and also examine various definitions of low-rank for real C*-algebras.

Space-time adaptive solution of inverse problems with the discrete adjoint method

NASA Astrophysics Data System (ADS)

Alexe, Mihai; Sandu, Adrian

2014-08-01

This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The space-time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter-grid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided through a multi-level optimization strategy using discontinuous Galerkin (DG) hp-adaptive discretizations paired with Runge-Kutta (RK) time integration. We extend the concept of dual (adjoint) consistency to space-time RK-DG discretizations, which are then shown to be well suited for the adaptive solution of time-dependent inverse problems. Furthermore, we prove that DG mesh transfer operators on general meshes are also dual consistent. This allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation (AD), potentially speeding up development of large-scale simulation codes. The theoretical analysis is supported by numerical results reported for a two-dimensional non-stationary inverse problem.

Adjoint assimilation of altimetric, surface drifter, and hydrographic data in a quasi-geostrophic model of the Azores Current

NASA Astrophysics Data System (ADS)

Morrow, Rosemary; de Mey, Pierre

1995-12-01

The flow characteristics in the region of the Azores Current are investigated by assimilating TOPEX/POSEIDON and ERS 1 altimeter data into the multilevel Harvard quasigeostrophic (QG) model with open boundaries (Miller et al., 1983) using an adjoint variational scheme (Moore, 1991). The study site lies in the path of the Azores Current, where a branch retroflects to the south in the vicinity of the Madeira Rise. The region was the site of an intensive field program in 1993, SEMAPHORE. We had two main aims in this adjoint assimilation project. The first was to see whether the adjoint method could be applied locally to optimize an initial guess field, derived from the continous assimilation of altimetry data using optimal interpolation (OI). The second aim was to assimilate a variety of different data sets and evaluate their importance in constraining our QG model. The adjoint assimilation of surface data was effective in optimizing the initial conditions from OI. After 20 iterations the cost function was generally reduced by 50-80%, depending on the chosen data constraints. The primary adjustment process was via the barotropic mode. Altimetry proved to be a good constraint on the variable flow field, in particular, for constraining the barotropic field. The excellent data quality of the TOPEX/POSEIDON (T/P) altimeter data provided smooth and reliable forcing; but for our mesoscale study in a region of long decorrelation times O(30 days), the spatial coverage from the combined T/P and ERS 1 data sets was more important for constraining the solution and providing stable flow at all levels. Surface drifters provided an excellent constraint on both the barotropic and baroclinic model fields. More importantly, the drifters provided a reliable measure of the mean field. Hydrographic data were also applied as a constraint; in general, hydrography provided a weak but effective constraint on the vertical Rossby modes in the model. Finally, forecasts run over a 2-month period indicate that the initial conditions optimized by the 20-day adjoint assimilation provide more stable, longer-term forecasts.

Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization.

PubMed

Fujarewicz, Krzysztof; Lakomiec, Krzysztof

2016-12-01

We investigate a spatial model of growth of a tumor and its sensitivity to radiotherapy. It is assumed that the radiation dose may vary in time and space, like in intensity modulated radiotherapy (IMRT). The change of the final state of the tumor depends on local differences in the radiation dose and varies with the time and the place of these local changes. This leads to the concept of a tumor's spatiotemporal sensitivity to radiation, which is a function of time and space. We show how adjoint sensitivity analysis may be applied to calculate the spatiotemporal sensitivity of the finite difference scheme resulting from the partial differential equation describing the tumor growth. We demonstrate results of this approach to the tumor proliferation, invasion and response to radiotherapy (PIRT) model and we compare the accuracy and the computational effort of the method to the simple forward finite difference sensitivity analysis. Furthermore, we use the spatiotemporal sensitivity during the gradient-based optimization of the spatiotemporal radiation protocol and present results for different parameters of the model.

Modeling Sound Propagation Through Non-Axisymmetric Jets

NASA Technical Reports Server (NTRS)

Leib, Stewart J.

2014-01-01

A method for computing the far-field adjoint Green's function of the generalized acoustic analogy equations under a locally parallel mean flow approximation is presented. The method is based on expanding the mean-flow-dependent coefficients in the governing equation and the scalar Green's function in truncated Fourier series in the azimuthal direction and a finite difference approximation in the radial direction in circular cylindrical coordinates. The combined spectral/finite difference method yields a highly banded system of algebraic equations that can be efficiently solved using a standard sparse system solver. The method is applied to test cases, with mean flow specified by analytical functions, corresponding to two noise reduction concepts of current interest: the offset jet and the fluid shield. Sample results for the Green's function are given for these two test cases and recommendations made as to the use of the method as part of a RANS-based jet noise prediction code.

Aerodynamic Shape Optimization of a Dual-Stream Supersonic Plug Nozzle

NASA Technical Reports Server (NTRS)

Heath, Christopher M.; Gray, Justin S.; Park, Michael A.; Nielsen, Eric J.; Carlson, Jan-Renee

2015-01-01

Aerodynamic shape optimization was performed on an isolated axisymmetric plug nozzle sized for a supersonic business jet. The dual-stream concept was tailored to attenuate nearfield pressure disturbances without compromising nozzle performance. Adjoint-based anisotropic mesh refinement was applied to resolve nearfield compression and expansion features in the baseline viscous grid. Deformed versions of the adapted grid were used for subsequent adjoint-driven shape optimization. For design, a nonlinear gradient-based optimizer was coupled to the discrete adjoint formulation of the Reynolds-averaged Navier- Stokes equations. All nozzle surfaces were parameterized using 3rd order B-spline interpolants and perturbed axisymmetrically via free-form deformation. Geometry deformations were performed using 20 design variables shared between the outer cowl, shroud and centerbody nozzle surfaces. Interior volume grid deformation during design was accomplished using linear elastic mesh morphing. The nozzle optimization was performed at a design cruise speed of Mach 1.6, assuming core and bypass pressure ratios of 6.19 and 3.24, respectively. Ambient flight conditions at design were commensurate with 45,000-ft standard day atmosphere.

A POSTERIORI ERROR ANALYSIS OF TWO STAGE COMPUTATION METHODS WITH APPLICATION TO EFFICIENT DISCRETIZATION AND THE PARAREAL ALGORITHM.

PubMed

Chaudhry, Jehanzeb Hameed; Estep, Don; Tavener, Simon; Carey, Varis; Sandelin, Jeff

2016-01-01

We consider numerical methods for initial value problems that employ a two stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, parallel-in-time solution schemes, and efficient solution of adjoint problems for computing a posteriori error estimates. We describe a general formulation of two stage computations then perform a general a posteriori error analysis based on computable residuals and solution of an adjoint problem. The analysis accommodates various variations in the two stage computation and in formulation of the adjoint problems. We apply the analysis to compute "dual-weighted" a posteriori error estimates, to develop novel algorithms for efficient solution that take into account cancellation of error, and to the Parareal Algorithm. We test the various results using several numerical examples.

An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.

2003-01-01

An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.

Novel numerical techniques for magma dynamics

NASA Astrophysics Data System (ADS)

Rhebergen, S.; Katz, R. F.; Wathen, A.; Alisic, L.; Rudge, J. F.; Wells, G.

2013-12-01

We discuss the development of finite element techniques and solvers for magma dynamics computations. These are implemented within the FEniCS framework. This approach allows for user-friendly, expressive, high-level code development, but also provides access to powerful, scalable numerical solvers and a large family of finite element discretisations. With the recent addition of dolfin-adjoint, FeniCS supports automated adjoint and tangent-linear models, enabling the rapid development of Generalised Stability Analysis. The ability to easily scale codes to three dimensions with large meshes, and/or to apply intricate adjoint calculations means that efficiency of the numerical algorithms is vital. We therefore describe our development and analysis of preconditioners designed specifically for finite element discretizations of equations governing magma dynamics. The preconditioners are based on Elman-Silvester-Wathen methods for the Stokes equation, and we extend these to flows with compaction. Our simulations are validated by comparison of results with laboratory experiments on partially molten aggregates.

Tangent Adjoint Methods In a Higher-Order Space-Time Discontinuous-Galerkin Solver For Turbulent Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo; Murman, Scott; Blonigan, Patrick; Garai, Anirban

2017-01-01

Presented space-time adjoint solver for turbulent compressible flows. Confirmed failure of traditional sensitivity methods for chaotic flows. Assessed rate of exponential growth of adjoint for practical 3D turbulent simulation. Demonstrated failure of short-window sensitivity approximations.

Topology optimization of thermal fluid flows with an adjoint Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Dugast, Florian; Favennec, Yann; Josset, Christophe; Fan, Yilin; Luo, Lingai

2018-07-01

This paper presents an adjoint Lattice Boltzmann Method (LBM) coupled with the Level-Set Method (LSM) for topology optimization of thermal fluid flows. The adjoint-state formulation implies discrete velocity directions in order to take into account the LBM boundary conditions. These boundary conditions are introduced at the beginning of the adjoint-state method as the LBM residuals, so that the adjoint-state boundary conditions can appear directly during the adjoint-state equation formulation. The proposed method is tested with 3 numerical examples concerning thermal fluid flows, but with different objectives: minimization of the mean temperature in the domain, maximization of the heat evacuated by the fluid, and maximization of the heat exchange with heated solid parts. This latter example, treated in several articles, is used to validate our method. In these optimization problems, a limitation of the maximal pressure drop and of the porosity (number of fluid elements) is also applied. The obtained results demonstrate that the method is robust and effective for solving topology optimization of thermal fluid flows.

Assessing the Impact of Advanced Satellite Observations in the NASA GEOS-5 Forecast System Using the Adjoint Method

NASA Technical Reports Server (NTRS)

Gelaro, Ron; Liu, Emily; Sienkiewicz, Meta

2011-01-01

The adjoint of a data assimilation system provides a flexible and efficient tool for estimating observation impacts on short-range weather forecasts. The impacts of any or all observations can be estimated simultaneously based on a single execution of the adjoint system. The results can be easily aggregated according to data type, location, channel, etc., making this technique especially attractive for examining the impacts of new hyper-spectral satellite instruments and for conducting regular, even near-real time, monitoring of the entire observing system. In this talk, we present results from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. The tool has been running in various off-line configurations for some time, and is scheduled to run as a regular part of the real-time forecast suite beginning in autumn 20 I O. We focus on the impacts of the newest components of the satellite observing system, including AIRS, IASI and GPS. For AIRS and IASI, it is shown that the vast majority of the channels assimilated have systematic positive impacts (of varying magnitudes), although some channels degrade the forecast. Of the latter, most are moisture-sensitive or near-surface channels. The impact of GPS observations in the southern hemisphere is found to be a considerable overall benefit to the system. In addition, the spatial variability of observation impacts reveals coherent patterns of positive and negative impacts that may point to deficiencies in the use of certain observations over, for example, specific surface types. When performed in conjunction with selected observing system experiments (OSEs), the adjoint results reveal both redundancies and dependencies between observing system impacts as observations are added or removed from the assimilation system. Understanding these dependencies appears to pose a major challenge for optimizing the use of the current observational network and defining requirements for future observing systems.

Improving the Fit of a Land-Surface Model to Data Using its Adjoint

NASA Astrophysics Data System (ADS)

Raoult, Nina; Jupp, Tim; Cox, Peter; Luke, Catherine

2016-04-01

Land-surface models (LSMs) are crucial components of the Earth System Models (ESMs) which are used to make coupled climate-carbon cycle projections for the 21st century. The Joint UK Land Environment Simulator (JULES) is the land-surface model used in the climate and weather forecast models of the UK Met Office. In this study, JULES is automatically differentiated using commercial software from FastOpt, resulting in an analytical gradient, or adjoint, of the model. Using this adjoint, the adJULES parameter estimation system has been developed, to search for locally optimum parameter sets by calibrating against observations. We present an introduction to the adJULES system and demonstrate its ability to improve the model-data fit using eddy covariance measurements of gross primary production (GPP) and latent heat (LE) fluxes. adJULES also has the ability to calibrate over multiple sites simultaneously. This feature is used to define new optimised parameter values for the 5 Plant Functional Types (PFTS) in JULES. The optimised PFT-specific parameters improve the performance of JULES over 90% of the FLUXNET sites used in the study. These reductions in error are shown and compared to reductions found due to site-specific optimisations. Finally, we show that calculation of the 2nd derivative of JULES allows us to produce posterior probability density functions of the parameters and how knowledge of parameter values is constrained by observations.

Quasi-stationary states and fermion pair creation from a vacuum in supercritical Coulomb field

NASA Astrophysics Data System (ADS)

Khalilov, V. R.

2017-12-01

Creation of charged fermion pair from a vacuum in so-called supercritical Coulomb potential is examined for the case when fermions can move only in the same (one) plane. In which case, quantum dynamics of charged massive or massless fermions can be described by the two-dimensional Dirac Hamiltonians with an usual (-a/r) Coulomb potential. These Hamiltonians are singular and require the additional definition in order for them to be treated as self-adjoint quantum-mechanical operators. We construct the self-adjoint two-dimensional Dirac Hamiltonians with a Coulomb potential and determine the quantum-mechanical states for such Hamiltonians in the corresponding Hilbert spaces of square-integrable functions. We determine the scattering amplitude in which the self-adjoint extension parameter is incorporated and then obtain equations implicitly defining possible discrete energy spectra of the self-adjoint Dirac Hamiltonians with a Coulomb potential. It is shown that this quantum system becomes unstable in the presence of a supercritical Coulomb potential which manifests in the appearance of quasi-stationary states in the lower (negative) energy continuum. The energy spectrum of those states is quasi-discrete, consists of broadened levels with widths related to the inverse lifetimes of the quasi-stationary states as well as the probability of creation of charged fermion pair by a supercritical Coulomb field. Explicit analytical expressions for the creation probabilities of charged (massive or massless) fermion pair are obtained in a supercritical Coulomb field.

Improved Adjoint-Operator Learning For A Neural Network

NASA Technical Reports Server (NTRS)

Toomarian, Nikzad; Barhen, Jacob

1995-01-01

Improved method of adjoint-operator learning reduces amount of computation and associated computational memory needed to make electronic neural network learn temporally varying pattern (e.g., to recognize moving object in image) in real time. Method extension of method described in "Adjoint-Operator Learning for a Neural Network" (NPO-18352).

Sensitivities of Greenland ice sheet volume inferred from an ice sheet adjoint model

NASA Astrophysics Data System (ADS)

Heimbach, P.; Bugnion, V.

2009-04-01

We present a new and original approach to understanding the sensitivity of the Greenland ice sheet to key model parameters and environmental conditions. At the heart of this approach is the use of an adjoint ice sheet model. Since its introduction by MacAyeal (1992), the adjoint method has become widespread to fit ice stream models to the increasing number and diversity of satellite observations, and to estimate uncertain model parameters such as basal conditions. However, no attempt has been made to extend this method to comprehensive ice sheet models. As a first step toward the use of adjoints of comprehensive three-dimensional ice sheet models we have generated an adjoint of the ice sheet model SICOPOLIS of Greve (1997). The adjoint was generated by means of the automatic differentiation (AD) tool TAF. The AD tool generates exact source code representing the tangent linear and adjoint model of the nonlinear parent model provided. Model sensitivities are given by the partial derivatives of a scalar-valued model diagnostic with respect to the controls, and can be efficiently calculated via the adjoint. By way of example, we determine the sensitivity of the total Greenland ice volume to various control variables, such as spatial fields of basal flow parameters, surface and basal forcings, and initial conditions. Reliability of the adjoint was tested through finite-difference perturbation calculations for various control variables and perturbation regions. Besides confirming qualitative aspects of ice sheet sensitivities, such as expected regional variations, we detect regions where model sensitivities are seemingly unexpected or counter-intuitive, albeit ``real'' in the sense of actual model behavior. An example is inferred regions where sensitivities of ice sheet volume to basal sliding coefficient are positive, i.e. where a local increase in basal sliding parameter increases the ice sheet volume. Similarly, positive ice temperature sensitivities in certain parts of the ice sheet are found (in most regions it is negativ, i.e. an increase in temperature decreases ice sheet volume), the detection of which seems highly unlikely if only conventional perturbation experiments had been used. An effort to generate an efficient adjoint with the newly developed open-source AD tool OpenAD is also under way. Available adjoint code generation tools now open up a variety of novel model applications, notably with regard to sensitivity and uncertainty analyses and ice sheet state estimation or data assimilation.

Bayesian Inversion of Concentration Data for an Unknown Number of Contaminant Sources

DTIC Science & Technology

2007-06-01

répondre aux urgences et celle de leur gestion rétrospective dirigée contre des incidents ter- roristes comprenant la dissémination secrète d’agent CBR...d’intervention d’urgence avancé pour la prédiction et l’évaluation des risques CBRN en mi- lieu urbain). Cette composante a été incorporée dans le...computationally efficient methodology for de - termination of the likelihood function for the problem, based on an adjoint representation of the source–receptor

Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method

PubMed Central

Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter

2017-01-01

An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated. PMID:28098851

Application of the sequential quadratic programming algorithm for reconstructing the distribution of optical parameters based on the time-domain radiative transfer equation.

PubMed

Qi, Hong; Qiao, Yao-Bin; Ren, Ya-Tao; Shi, Jing-Wen; Zhang, Ze-Yu; Ruan, Li-Ming

2016-10-17

Sequential quadratic programming (SQP) is used as an optimization algorithm to reconstruct the optical parameters based on the time-domain radiative transfer equation (TD-RTE). Numerous time-resolved measurement signals are obtained using the TD-RTE as forward model. For a high computational efficiency, the gradient of objective function is calculated using an adjoint equation technique. SQP algorithm is employed to solve the inverse problem and the regularization term based on the generalized Gaussian Markov random field (GGMRF) model is used to overcome the ill-posed problem. Simulated results show that the proposed reconstruction scheme performs efficiently and accurately.

Skyshine at neutron energies less than or equal to 400 MeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alsmiller, A.G. Jr.; Barish, J.; Childs, R.L.

1980-10-01

The dose equivalent at an air-ground interface as a function of distance from an assumed azimuthally symmetric point source of neutrons can be calculated as a double integral. The integration is over the source strength as a function of energy and polar angle weighted by an importance function that depends on the source variables and on the distance from the source to the filed point. The neutron importance function for a source 15 m above the ground emitting only into the upper hemisphere has been calculated using the two-dimensional discrete ordinates code, DOT, and the first collision source code, GRTUNCL,more » in the adjoint mode. This importance function is presented for neutron energies less than or equal to 400 MeV, for source cosine intervals of 1 to .8, .8 to .6 to .4, .4 to .2 and .2 to 0, and for various distances from the source to the field point. As part of the adjoint calculations a photon importance function is also obtained. This importance function for photon energies less than or equal to 14 MEV and for various source cosine intervals and source-to-field point distances is also presented. These importance functions may be used to obtain skyshine dose equivalent estimates for any known source energy-angle distribution.« less

Adjoint of the global Eulerian-Lagrangian coupled atmospheric transport model (A-GELCA v1.0): development and validation

NASA Astrophysics Data System (ADS)

Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander

2016-02-01

We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated into a variational inversion system designed to optimize surface fluxes of greenhouse gases.

Time domain viscoelastic full waveform inversion

NASA Astrophysics Data System (ADS)

Fabien-Ouellet, Gabriel; Gloaguen, Erwan; Giroux, Bernard

2017-06-01

Viscous attenuation can have a strong impact on seismic wave propagation, but it is rarely taken into account in full waveform inversion (FWI). When viscoelasticity is considered in time domain FWI, the displacement formulation of the wave equation is usually used instead of the popular velocity-stress formulation. However, inversion schemes rely on the adjoint equations, which are quite different for the velocity-stress formulation than for the displacement formulation. In this paper, we apply the adjoint state method to the isotropic viscoelastic wave equation in the velocity-stress formulation based on the generalized standard linear solid rheology. By applying linear transformations to the wave equation before deriving the adjoint state equations, we obtain two symmetric sets of partial differential equations for the forward and adjoint variables. The resulting sets of equations only differ by a sign change and can be solved by the same numerical implementation. We also investigate the crosstalk between parameter classes (velocity and attenuation) of the viscoelastic equation. More specifically, we show that the attenuation levels can be used to recover the quality factors of P and S waves, but that they are very sensitive to velocity errors. Finally, we present a synthetic example of viscoelastic FWI in the context of monitoring CO2 geological sequestration. We show that FWI based on our formulation can indeed recover P- and S-wave velocities and their attenuation levels when attenuation is high enough. Both changes in velocity and attenuation levels recovered with FWI can be used to track the CO2 plume during and after injection. Further studies are required to evaluate the performance of viscoelastic FWI on real data.

A three-dimensional cohesive sediment transport model with data assimilation: Model development, sensitivity analysis and parameter estimation

NASA Astrophysics Data System (ADS)

Wang, Daosheng; Cao, Anzhou; Zhang, Jicai; Fan, Daidu; Liu, Yongzhi; Zhang, Yue

2018-06-01

Based on the theory of inverse problems, a three-dimensional sigma-coordinate cohesive sediment transport model with the adjoint data assimilation is developed. In this model, the physical processes of cohesive sediment transport, including deposition, erosion and advection-diffusion, are parameterized by corresponding model parameters. These parameters are usually poorly known and have traditionally been assigned empirically. By assimilating observations into the model, the model parameters can be estimated using the adjoint method; meanwhile, the data misfit between model results and observations can be decreased. The model developed in this work contains numerous parameters; therefore, it is necessary to investigate the parameter sensitivity of the model, which is assessed by calculating a relative sensitivity function and the gradient of the cost function with respect to each parameter. The results of parameter sensitivity analysis indicate that the model is sensitive to the initial conditions, inflow open boundary conditions, suspended sediment settling velocity and resuspension rate, while the model is insensitive to horizontal and vertical diffusivity coefficients. A detailed explanation of the pattern of sensitivity analysis is also given. In ideal twin experiments, constant parameters are estimated by assimilating 'pseudo' observations. The results show that the sensitive parameters are estimated more easily than the insensitive parameters. The conclusions of this work can provide guidance for the practical applications of this model to simulate sediment transport in the study area.

Fugitive emission source characterization using a gradient-based optimization scheme and scalar transport adjoint

NASA Astrophysics Data System (ADS)

Brereton, Carol A.; Joynes, Ian M.; Campbell, Lucy J.; Johnson, Matthew R.

2018-05-01

Fugitive emissions are important sources of greenhouse gases and lost product in the energy sector that can be difficult to detect, but are often easily mitigated once they are known, located, and quantified. In this paper, a scalar transport adjoint-based optimization method is presented to locate and quantify unknown emission sources from downstream measurements. This emission characterization approach correctly predicted locations to within 5 m and magnitudes to within 13% of experimental release data from Project Prairie Grass. The method was further demonstrated on simulated simultaneous releases in a complex 3-D geometry based on an Alberta gas plant. Reconstructions were performed using both the complex 3-D transient wind field used to generate the simulated release data and using a sequential series of steady-state RANS wind simulations (SSWS) representing 30 s intervals of physical time. Both the detailed transient and the simplified wind field series could be used to correctly locate major sources and predict their emission rates within 10%, while predicting total emission rates from all sources within 24%. This SSWS case would be much easier to implement in a real-world application, and gives rise to the possibility of developing pre-computed databases of both wind and scalar transport adjoints to reduce computational time.

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

DOE PAGES

Finn, John M.

2015-03-01

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a 'special divergence-free' property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. Wemore » also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Ref. [11], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Ref. [35], appears to work very well.« less

Four-Dimensional Data Assimilation Using the Adjoint Method

NASA Astrophysics Data System (ADS)

Bao, Jian-Wen

The calculus of variations is used to confirm that variational four-dimensional data assimilation (FDDA) using the adjoint method can be implemented when the numerical model equations have a finite number of first-order discontinuous points. These points represent the on/off switches associated with physical processes, for which the Jacobian matrix of the model equation does not exist. Numerical evidence suggests that, in some situations when the adjoint method is used for FDDA, the temperature field retrieved using horizontal wind data is numerically not unique. A physical interpretation of this type of non-uniqueness of the retrieval is proposed in terms of energetics. The adjoint equations of a numerical model can also be used for model-parameter estimation. A general computational procedure is developed to determine the size and distribution of any internal model parameter. The procedure is then applied to a one-dimensional shallow -fluid model in the context of analysis-nudging FDDA: the weighting coefficients used by the Newtonian nudging technique are determined. The sensitivity of these nudging coefficients to the optimal objectives and constraints is investigated. Experiments of FDDA using the adjoint method are conducted using the dry version of the hydrostatic Penn State/NCAR mesoscale model (MM4) and its adjoint. The minimization procedure converges and the initialization experiment is successful. Temperature-retrieval experiments involving an assimilation of the horizontal wind are also carried out using the adjoint of MM4.

Receptivity of the compressible mixing layer

NASA Astrophysics Data System (ADS)

Barone, Matthew F.; Lele, Sanjiva K.

2005-09-01

Receptivity of compressible mixing layers to general source distributions is examined by a combined theoretical/computational approach. The properties of solutions to the adjoint Navier Stokes equations are exploited to derive expressions for receptivity in terms of the local value of the adjoint solution. The result is a description of receptivity for arbitrary small-amplitude mass, momentum, and heat sources in the vicinity of a mixing-layer flow, including the edge-scattering effects due to the presence of a splitter plate of finite width. The adjoint solutions are examined in detail for a Mach 1.2 mixing-layer flow. The near field of the adjoint solution reveals regions of relatively high receptivity to direct forcing within the mixing layer, with receptivity to nearby acoustic sources depending on the source type and position. Receptivity ‘nodes’ are present at certain locations near the splitter plate edge where the flow is not sensitive to forcing. The presence of the nodes is explained by interpretation of the adjoint solution as the superposition of incident and scattered fields. The adjoint solution within the boundary layer upstream of the splitter-plate trailing edge reveals a mechanism for transfer of energy from boundary-layer stability modes to Kelvin Helmholtz modes. Extension of the adjoint solution to the far field using a Kirchhoff surface gives the receptivity of the mixing layer to incident sound from distant sources.

A hybrid method for the computation of quasi-3D seismograms.

NASA Astrophysics Data System (ADS)

Masson, Yder; Romanowicz, Barbara

2013-04-01

The development of powerful computer clusters and efficient numerical computation methods, such as the Spectral Element Method (SEM) made possible the computation of seismic wave propagation in a heterogeneous 3D earth. However, the cost of theses computations is still problematic for global scale tomography that requires hundreds of such simulations. Part of the ongoing research effort is dedicated to the development of faster modeling methods based on the spectral element method. Capdeville et al. (2002) proposed to couple SEM simulations with normal modes calculation (C-SEM). Nissen-Meyer et al. (2007) used 2D SEM simulations to compute 3D seismograms in a 1D earth model. Thanks to these developments, and for the first time, Lekic et al. (2011) developed a 3D global model of the upper mantle using SEM simulations. At the local and continental scale, adjoint tomography that is using a lot of SEM simulation can be implemented on current computers (Tape, Liu et al. 2009). Due to their smaller size, these models offer higher resolution. They provide us with images of the crust and the upper part of the mantle. In an attempt to teleport such local adjoint tomographic inversions into the deep earth, we are developing a hybrid method where SEM computation are limited to a region of interest within the earth. That region can have an arbitrary shape and size. Outside this region, the seismic wavefield is extrapolated to obtain synthetic data at the Earth's surface. A key feature of the method is the use of a time reversal mirror to inject the wavefield induced by distant seismic source into the region of interest (Robertsson and Chapman 2000). We compute synthetic seismograms as follow: Inside the region of interest, we are using regional spectral element software RegSEM to compute wave propagation in 3D. Outside this region, the wavefield is extrapolated to the surface by convolution with the Green's functions from the mirror to the seismic stations. For now, these Green's functions are computed using 2D SEM simulation in a 1D Earth model. Such seismograms account for the 3D structure inside the region of interest in a quasi-exact manner. Later we plan to extrapolate the misfit function computed from such seismograms at the stations back into the SEM region in order to compute local adjoint kernels. This opens a new path toward regional adjoint tomography into the deep Earth. Capdeville, Y., et al. (2002). "Coupling the spectral element method with a modal solution for elastic wave propagation in global Earth models." Geophysical Journal International 152(1): 34-67. Lekic, V. and B. Romanowicz (2011). "Inferring upper-mantle structure by full waveform tomography with the spectral element method." Geophysical Journal International 185(2): 799-831. Nissen-Meyer, T., et al. (2007). "A two-dimensional spectral-element method for computing spherical-earth seismograms-I. Moment-tensor source." Geophysical Journal International 168(3): 1067-1092. Robertsson, J. O. A. and C. H. Chapman (2000). "An efficient method for calculating finite-difference seismograms after model alterations." Geophysics 65(3): 907-918. Tape, C., et al. (2009). "Adjoint tomography of the southern California crust." Science 325(5943): 988-992.

Aerosol Polarimetry Sensor (APS): Design Summary, Performance and Potential Modifications

NASA Technical Reports Server (NTRS)

Cairns, Brian

2014-01-01

APS is a mature design that has already been built and has a TRL of 7. Algorithmic and retrieval capabilities continue to improve and make better and more sophisticated used of the data. Adjoint solutions, both in one dimensional and three dimensional are computationally efficient and should be the preferred implementation for the calculation of Jacobians (one dimensional), or cost-function gradients (three dimensional). Adjoint solutions necessarily provide resolution of internal fields and simplify incorporation of active measurements in retrievals, which will be necessary for a future ACE mission. Its best to test these capabilities when you know the answer: OSSEs that are well constrained observationally provide the best place to test future multi-instrument platform capabilities and ensure capabilities will meet scientific needs.

Comparison of Evolutionary (Genetic) Algorithm and Adjoint Methods for Multi-Objective Viscous Airfoil Optimizations

NASA Technical Reports Server (NTRS)

Pulliam, T. H.; Nemec, M.; Holst, T.; Zingg, D. W.; Kwak, Dochan (Technical Monitor)

2002-01-01

A comparison between an Evolutionary Algorithm (EA) and an Adjoint-Gradient (AG) Method applied to a two-dimensional Navier-Stokes code for airfoil design is presented. Both approaches use a common function evaluation code, the steady-state explicit part of the code,ARC2D. The parameterization of the design space is a common B-spline approach for an airfoil surface, which together with a common griding approach, restricts the AG and EA to the same design space. Results are presented for a class of viscous transonic airfoils in which the optimization tradeoff between drag minimization as one objective and lift maximization as another, produces the multi-objective design space. Comparisons are made for efficiency, accuracy and design consistency.

An approach to computing discrete adjoints for MPI-parallelized models applied to Ice Sheet System Model 4.11

NASA Astrophysics Data System (ADS)

Larour, Eric; Utke, Jean; Bovin, Anton; Morlighem, Mathieu; Perez, Gilberto

2016-11-01

Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar, gravity, and altimetry observations mainly). However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient ice-flow models. Here, we look at the computation of adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model (ISSM), written in C++ and designed for parallel execution with MPI. We present the adaptations required in the way the software is designed and written, but also generic adaptations in the tools facilitating the adjoint computations. We concentrate on the use of operator overloading coupled with the AdjoinableMPI library to achieve the adjoint computation of the ISSM. We present a comprehensive approach to (1) carry out type changing through the ISSM, hence facilitating operator overloading, (2) bind to external solvers such as MUMPS and GSL-LU, and (3) handle MPI-based parallelism to scale the capability. We demonstrate the success of the approach by computing sensitivities of hindcast metrics such as the misfit to observed records of surface altimetry on the northeastern Greenland Ice Stream, or the misfit to observed records of surface velocities on Upernavik Glacier, central West Greenland. We also provide metrics for the scalability of the approach, and the expected performance. This approach has the potential to enable a new generation of hindcast-validated projections that make full use of the wealth of datasets currently being collected, or already collected, in Greenland and Antarctica.

An Approach to Computing Discrete Adjoints for MPI-Parallelized Models Applied to the Ice Sheet System Model}

NASA Astrophysics Data System (ADS)

Perez, G. L.; Larour, E. Y.; Morlighem, M.

2016-12-01

Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar and altimetry observations mainly). However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient ice-flow models. Here, we look at the computation of adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model, written in C++ and designed for parallel execution with MPI. We present the adaptations required in the way the software is designed and written but also generic adaptations in the tools facilitating the adjoint computations. We concentrate on the use of operator overloading coupled with the AdjoinableMPI library to achieve the adjoint computation of ISSM. We present a comprehensive approach to 1) carry out type changing through ISSM, hence facilitating operator overloading, 2) bind to external solvers such as MUMPS and GSL-LU and 3) handle MPI-based parallelism to scale the capability. We demonstrate the success of the approach by computing sensitivities of hindcast metrics such as the misfit to observed records of surface altimetry on the North-East Greenland Ice Stream, or the misfit to observed records of surface velocities on Upernavik Glacier, Central West Greenland. We also provide metrics for the scalability of the approach, and the expected performance. This approach has the potential of enabling a new generation of hindcast-validated projections that make full use of the wealth of datasets currently being collected, or alreay collected in Greenland and Antarctica, such as surface altimetry, surface velocities, and/or gravity measurements.

Asynchronous Two-Level Checkpointing Scheme for Large-Scale Adjoints in the Spectral-Element Solver Nek5000

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schanen, Michel; Marin, Oana; Zhang, Hong

Adjoints are an important computational tool for large-scale sensitivity evaluation, uncertainty quantification, and derivative-based optimization. An essential component of their performance is the storage/recomputation balance in which efficient checkpointing methods play a key role. We introduce a novel asynchronous two-level adjoint checkpointing scheme for multistep numerical time discretizations targeted at large-scale numerical simulations. The checkpointing scheme combines bandwidth-limited disk checkpointing and binomial memory checkpointing. Based on assumptions about the target petascale systems, which we later demonstrate to be realistic on the IBM Blue Gene/Q system Mira, we create a model of the expected performance of our checkpointing approach and validatemore » it using the highly scalable Navier-Stokes spectralelement solver Nek5000 on small to moderate subsystems of the Mira supercomputer. In turn, this allows us to predict optimal algorithmic choices when using all of Mira. We also demonstrate that two-level checkpointing is significantly superior to single-level checkpointing when adjoining a large number of time integration steps. To our knowledge, this is the first time two-level checkpointing had been designed, implemented, tuned, and demonstrated on fluid dynamics codes at large scale of 50k+ cores.« less

On the role of self-adjointness in the continuum formulation of topological quantum phases

NASA Astrophysics Data System (ADS)

Tanhayi Ahari, Mostafa; Ortiz, Gerardo; Seradjeh, Babak

2016-11-01

Topological quantum phases of matter are characterized by an intimate relationship between the Hamiltonian dynamics away from the edges and the appearance of bound states localized at the edges of the system. Elucidating this correspondence in the continuum formulation of topological phases, even in the simplest case of a one-dimensional system, touches upon fundamental concepts and methods in quantum mechanics that are not commonly discussed in textbooks, in particular the self-adjoint extensions of a Hermitian operator. We show how such topological bound states can be derived in a prototypical one-dimensional system. Along the way, we provide a pedagogical exposition of the self-adjoint extension method as well as the role of symmetries in correctly formulating the continuum, field-theory description of topological matter with boundaries. Moreover, we show that self-adjoint extensions can be characterized generally in terms of a conserved local current associated with the self-adjoint operator.

Two- and four-dimensional representations of the PT - and CPT -symmetric fermionic algebras

NASA Astrophysics Data System (ADS)

Beygi, Alireza; Klevansky, S. P.; Bender, Carl M.

2018-03-01

Fermionic systems differ from their bosonic counterparts, the main difference with regard to symmetry considerations being that T2=-1 for fermionic systems. In PT -symmetric quantum mechanics an operator has both PT and CPT adjoints. Fermionic operators η , which are quadratically nilpotent (η2=0 ), and algebras with PT and CPT adjoints can be constructed. These algebras obey different anticommutation relations: η ηPT+ηPTη =-1 , where ηPT is the PT adjoint of η , and η ηCPT+ηCPTη =1 , where ηCPT is the CPT adjoint of η . This paper presents matrix representations for the operator η and its PT and CPT adjoints in two and four dimensions. A PT -symmetric second-quantized Hamiltonian modeled on quantum electrodynamics that describes a system of interacting fermions and bosons is constructed within this framework and is solved exactly.

Jointly reconstructing ground motion and resistivity for ERT-based slope stability monitoring

NASA Astrophysics Data System (ADS)

Boyle, Alistair; Wilkinson, Paul B.; Chambers, Jonathan E.; Meldrum, Philip I.; Uhlemann, Sebastian; Adler, Andy

2018-02-01

Electrical resistivity tomography (ERT) is increasingly being used to investigate unstable slopes and monitor the hydrogeological processes within. But movement of electrodes or incorrect placement of electrodes with respect to an assumed model can introduce significant resistivity artefacts into the reconstruction. In this work, we demonstrate a joint resistivity and electrode movement reconstruction algorithm within an iterative Gauss-Newton framework. We apply this to ERT monitoring data from an active slow-moving landslide in the UK. Results show fewer resistivity artefacts and suggest that electrode movement and resistivity can be reconstructed at the same time under certain conditions. A new 2.5-D formulation for the electrode position Jacobian is developed and is shown to give accurate numerical solutions when compared to the adjoint method on 3-D models. On large finite element meshes, the calculation time of the newly developed approach was also proven to be orders of magnitude faster than the 3-D adjoint method and addressed modelling errors in the 2-D perturbation and adjoint electrode position Jacobian.

Simulation and Optimization of an Airfoil with Leading Edge Slat

NASA Astrophysics Data System (ADS)

Schramm, Matthias; Stoevesandt, Bernhard; Peinke, Joachim

2016-09-01

A gradient-based optimization is used in order to improve the shape of a leading edge slat upstream of a DU 91-W2-250 airfoil. The simulations are performed by solving the Reynolds-Averaged Navier-Stokes equations (RANS) using the open source CFD code OpenFOAM. Gradients are computed via the adjoint approach, which is suitable to deal with many design parameters, but keeping the computational costs low. The implementation is verified by comparing the gradients from the adjoint method with gradients obtained by finite differences for a NACA 0012 airfoil. The simulations of the leading edge slat are validated against measurements from the acoustic wind tunnel of Oldenburg University at a Reynolds number of Re = 6 • 105. The shape of the slat is optimized using the adjoint approach resulting in a drag reduction of 2%. Although the optimization is done for Re = 6 • 105, the improvements also hold for a higher Reynolds number of Re = 7.9 • 106, which is more realistic at modern wind turbines.

Geometry of quantum dynamics in infinite-dimensional Hilbert space

NASA Astrophysics Data System (ADS)

Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana

2018-04-01

We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.

Development of WRF-CO2 4DVAR Data Assimilation System

NASA Astrophysics Data System (ADS)

Zheng, T.; French, N. H. F.

2016-12-01

Four dimensional variational (4DVar) assimilation systems have been widely used for CO2 inverse modeling at global scale. At regional scale, however, 4DVar assimilation systems have been lacking. At present, most regional CO2 inverse models use Lagrangian particle backward trajectory tools to compute influence function in an analytical/synthesis framework. To provide a 4DVar based alternative, we developed WRF-CO2 4DVAR based on Weather Research and Forecasting (WRF), its chemistry extension (WRF-Chem), and its data assimilation system (WRFDA/WRFPLUS). Different from WRFDA, WRF-CO2 4DVAR does not optimize meteorology initial condition, instead it solves for the optimized CO2 surface fluxes (sources/sink) constrained by atmospheric CO2 observations. Based on WRFPLUS, we developed tangent linear and adjoint code for CO2 emission, advection, vertical mixing in boundary layer, and convective transport. Furthermore, we implemented an incremental algorithm to solve for optimized CO2 emission scaling factors by iteratively minimizing the cost function in a Bayes framework. The model sensitivity (of atmospheric CO2 with respect to emission scaling factor) calculated by tangent linear and adjoint model agrees well with that calculated by finite difference, indicating the validity of the newly developed code. The effectiveness of WRF-CO2 4DVar for inverse modeling is tested using forward-model generated pseudo-observation data in two experiments: first-guess CO2 fluxes has a 50% overestimation in the first case and 50% underestimation in the second. In both cases, WRF-CO2 4DVar reduces cost function to less than 10-4 of its initial values in less than 20 iterations and successfully recovers the true values of emission scaling factors. We expect future applications of WRF-CO2 4DVar with satellite observations will provide insights for CO2 regional inverse modeling, including the impacts of model transport error in vertical mixing.

Adjoint sensitivity analysis of plasmonic structures using the FDTD method.

PubMed

Zhang, Yu; Ahmed, Osman S; Bakr, Mohamed H

2014-05-15

We present an adjoint variable method for estimating the sensitivities of arbitrary responses with respect to the parameters of dispersive discontinuities in nanoplasmonic devices. Our theory is formulated in terms of the electric field components at the vicinity of perturbed discontinuities. The adjoint sensitivities are computed using at most one extra finite-difference time-domain (FDTD) simulation regardless of the number of parameters. Our approach is illustrated through the sensitivity analysis of an add-drop coupler consisting of a square ring resonator between two parallel waveguides. The computed adjoint sensitivities of the scattering parameters are compared with those obtained using the accurate but computationally expensive central finite difference approach.

Operator pencil passing through a given operator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biggs, A., E-mail: khudian@manchester.ac.uk, E-mail: adam.biggs@student.manchester.ac.uk; Khudaverdian, H. M., E-mail: khudian@manchester.ac.uk, E-mail: adam.biggs@student.manchester.ac.uk

Let Δ be a linear differential operator acting on the space of densities of a given weight λ{sub 0} on a manifold M. One can consider a pencil of operators Π-circumflex(Δ)=(Δ{sub λ}) passing through the operator Δ such that any Δ{sub λ} is a linear differential operator acting on densities of weight λ. This pencil can be identified with a linear differential operator Δ-circumflex acting on the algebra of densities of all weights. The existence of an invariant scalar product in the algebra of densities implies a natural decomposition of operators, i.e., pencils of self-adjoint and anti-self-adjoint operators. We studymore » lifting maps that are on one hand equivariant with respect to divergenceless vector fields, and, on the other hand, with values in self-adjoint or anti-self-adjoint operators. In particular, we analyze the relation between these two concepts, and apply it to the study of diff (M)-equivariant liftings. Finally, we briefly consider the case of liftings equivariant with respect to the algebra of projective transformations and describe all regular self-adjoint and anti-self-adjoint liftings. Our constructions can be considered as a generalisation of equivariant quantisation.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE PAGES

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; ...

2016-07-13

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

NASA Astrophysics Data System (ADS)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar

2016-07-01

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

Observation Impacts for Longer Forecast Lead-Times

NASA Astrophysics Data System (ADS)

Mahajan, R.; Gelaro, R.; Todling, R.

2013-12-01

Observation impact on forecasts evaluated using adjoint-based techniques (e.g. Langland and Baker, 2004) are limited by the validity of the assumptions underlying the forecasting model adjoint. Most applications of this approach have focused on deriving observation impacts on short-range forecasts (e.g. 24-hour) in part to stay well within linearization assumptions. The most widely used measure of observation impact relies on the availability of the analysis for verifying the forecasts. As pointed out by Gelaro et al. (2007), and more recently by Todling (2013), this introduces undesirable correlations in the measure that are likely to affect the resulting assessment of the observing system. Stappers and Barkmeijer (2012) introduced a technique that, in principle, allows extending the validity of tangent linear and corresponding adjoint models to longer lead-times, thereby reducing the correlations in the measures used for observation impact assessments. The methodology provides the means to better represent linearized models by making use of Gaussian quadrature relations to handle various underlying non-linear model trajectories. The formulation is exact for particular bi-linear dynamics; it corresponds to an approximation for general-type nonlinearities and must be tested for large atmospheric models. The present work investigates the approach of Stappers and Barkmeijer (2012)in the context of NASA's Goddard Earth Observing System Version 5 (GEOS-5) atmospheric data assimilation system (ADAS). The goal is to calculate observation impacts in the GEOS-5 ADAS for forecast lead-times of at least 48 hours in order to reduce the potential for undesirable correlations that occur at shorter forecast lead times. References [1]Langland, R. H., and N. L. Baker, 2004: Estimation of observation impact using the NRL atmospheric variational data assimilation adjoint system. Tellus, 56A, 189-201. [2] Gelaro, R., Y. Zhu, and R. M. Errico, 2007: Examination of various-order adjoint-based approximations of observation impact. Meteoroloische Zeitschrift, 16, 685-692. [3]Stappers, R. J. J., and J. Barkmeijer, 2012: Optimal linearization trajectories for tangent linear models. Q. J. R. Meteorol. Soc., 138, 170-184. [4] Todling, R. 2013: Comparing two approaches for assessing observation impact. Mon. Wea. Rev., 141, 1484-1505.

Global adjoint tomography: First-generation model

DOE PAGES

Bozdag, Ebru; Peter, Daniel; Lefebvre, Matthieu; ...

2016-09-22

We present the first-generation global tomographic model constructed based on adjoint tomography, an iterative full-waveform inversion technique. Synthetic seismograms were calculated using GPU-accelerated spectral-element simulations of global seismic wave propagation, accommodating effects due to 3-D anelastic crust & mantle structure, topography & bathymetry, the ocean load, ellipticity, rotation, and self-gravitation. Fréchet derivatives were calculated in 3-D anelastic models based on an adjoint-state method. The simulations were performed on the Cray XK7 named ‘Titan’, a computer with 18 688 GPU accelerators housed at Oak Ridge National Laboratory. The transversely isotropic global model is the result of 15 tomographic iterations, which systematicallymore » reduced differences between observed and simulated three-component seismograms. Our starting model combined 3-D mantle model S362ANI with 3-D crustal model Crust2.0. We simultaneously inverted for structure in the crust and mantle, thereby eliminating the need for widely used ‘crustal corrections’. We used data from 253 earthquakes in the magnitude range 5.8 ≤ M w ≤ 7.0. We started inversions by combining ~30 s body-wave data with ~60 s surface-wave data. The shortest period of the surface waves was gradually decreased, and in the last three iterations we combined ~17 s body waves with ~45 s surface waves. We started using 180 min long seismograms after the 12th iteration and assimilated minor- and major-arc body and surface waves. The 15th iteration model features enhancements of well-known slabs, an enhanced image of the Samoa/Tahiti plume, as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone and Erebus. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the starting model. Point-spread function tests demonstrate that we are approaching the resolution of continental-scale studies in some areas, for example, underneath Yellowstone. Here, this is a consequence of our multiscale smoothing strategy in which we define our smoothing operator as a function of the approximate Hessian kernel, thereby smoothing gradients less wherever we have good ray coverage, such as underneath North America.« less

Global adjoint tomography: First-generation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bozdag, Ebru; Peter, Daniel; Lefebvre, Matthieu

We present the first-generation global tomographic model constructed based on adjoint tomography, an iterative full-waveform inversion technique. Synthetic seismograms were calculated using GPU-accelerated spectral-element simulations of global seismic wave propagation, accommodating effects due to 3-D anelastic crust & mantle structure, topography & bathymetry, the ocean load, ellipticity, rotation, and self-gravitation. Fréchet derivatives were calculated in 3-D anelastic models based on an adjoint-state method. The simulations were performed on the Cray XK7 named ‘Titan’, a computer with 18 688 GPU accelerators housed at Oak Ridge National Laboratory. The transversely isotropic global model is the result of 15 tomographic iterations, which systematicallymore » reduced differences between observed and simulated three-component seismograms. Our starting model combined 3-D mantle model S362ANI with 3-D crustal model Crust2.0. We simultaneously inverted for structure in the crust and mantle, thereby eliminating the need for widely used ‘crustal corrections’. We used data from 253 earthquakes in the magnitude range 5.8 ≤ M w ≤ 7.0. We started inversions by combining ~30 s body-wave data with ~60 s surface-wave data. The shortest period of the surface waves was gradually decreased, and in the last three iterations we combined ~17 s body waves with ~45 s surface waves. We started using 180 min long seismograms after the 12th iteration and assimilated minor- and major-arc body and surface waves. The 15th iteration model features enhancements of well-known slabs, an enhanced image of the Samoa/Tahiti plume, as well as various other plumes and hotspots, such as Caroline, Galapagos, Yellowstone and Erebus. Furthermore, we see clear improvements in slab resolution along the Hellenic and Japan Arcs, as well as subduction along the East of Scotia Plate, which does not exist in the starting model. Point-spread function tests demonstrate that we are approaching the resolution of continental-scale studies in some areas, for example, underneath Yellowstone. Here, this is a consequence of our multiscale smoothing strategy in which we define our smoothing operator as a function of the approximate Hessian kernel, thereby smoothing gradients less wherever we have good ray coverage, such as underneath North America.« less

A practical globalization of one-shot optimization for optimal design of tokamak divertors

NASA Astrophysics Data System (ADS)

Blommaert, Maarten; Dekeyser, Wouter; Baelmans, Martine; Gauger, Nicolas R.; Reiter, Detlev

2017-01-01

In past studies, nested optimization methods were successfully applied to design of the magnetic divertor configuration in nuclear fusion reactors. In this paper, so-called one-shot optimization methods are pursued. Due to convergence issues, a globalization strategy for the one-shot solver is sought. Whereas Griewank introduced a globalization strategy using a doubly augmented Lagrangian function that includes primal and adjoint residuals, its practical usability is limited by the necessity of second order derivatives and expensive line search iterations. In this paper, a practical alternative is offered that avoids these drawbacks by using a regular augmented Lagrangian merit function that penalizes only state residuals. Additionally, robust rank-two Hessian estimation is achieved by adaptation of Powell's damped BFGS update rule. The application of the novel one-shot approach to magnetic divertor design is considered in detail. For this purpose, the approach is adapted to be complementary with practical in parts adjoint sensitivities. Using the globalization strategy, stable convergence of the one-shot approach is achieved.

Complexity of parallel implementation of domain decomposition techniques for elliptic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gropp, W.D.; Keyes, D.E.

1988-03-01

The authors discuss the parallel implementation of preconditioned conjugate gradient (PCG)-based domain decomposition techniques for self-adjoint elliptic partial differential equations in two dimensions on several architectures. The complexity of these methods is described on a variety of message-passing parallel computers as a function of the size of the problem, number of processors and relative communication speeds of the processors. They show that communication startups are very important, and that even the small amount of global communication in these methods can significantly reduce the performance of many message-passing architectures.

Automated variance reduction for MCNP using deterministic methods.

PubMed

Sweezy, J; Brown, F; Booth, T; Chiaramonte, J; Preeg, B

2005-01-01

In order to reduce the user's time and the computer time needed to solve deep penetration problems, an automated variance reduction capability has been developed for the MCNP Monte Carlo transport code. This new variance reduction capability developed for MCNP5 employs the PARTISN multigroup discrete ordinates code to generate mesh-based weight windows. The technique of using deterministic methods to generate importance maps has been widely used to increase the efficiency of deep penetration Monte Carlo calculations. The application of this method in MCNP uses the existing mesh-based weight window feature to translate the MCNP geometry into geometry suitable for PARTISN. The adjoint flux, which is calculated with PARTISN, is used to generate mesh-based weight windows for MCNP. Additionally, the MCNP source energy spectrum can be biased based on the adjoint energy spectrum at the source location. This method can also use angle-dependent weight windows.

Running coupling from gluon and ghost propagators in the Landau gauge: Yang-Mills theories with adjoint fermions

NASA Astrophysics Data System (ADS)

Bergner, Georg; Piemonte, Stefano

2018-04-01

Non-Abelian gauge theories with fermions transforming in the adjoint representation of the gauge group (AdjQCD) are a fundamental ingredient of many models that describe the physics beyond the Standard Model. Two relevant examples are N =1 supersymmetric Yang-Mills (SYM) theory and minimal walking technicolor, which are gauge theories coupled to one adjoint Majorana and two adjoint Dirac fermions, respectively. While confinement is a property of N =1 SYM, minimal walking technicolor is expected to be infrared conformal. We study the propagators of ghost and gluon fields in the Landau gauge to compute the running coupling in the MiniMom scheme. We analyze several different ensembles of lattice Monte Carlo simulations for the SU(2) adjoint QCD with Nf=1 /2 ,1 ,3 /2 , and 2 Dirac fermions. We show how the running of the coupling changes as the number of interacting fermions is increased towards the conformal window.

The continuous adjoint approach to the k-ε turbulence model for shape optimization and optimal active control of turbulent flows

NASA Astrophysics Data System (ADS)

Papoutsis-Kiachagias, E. M.; Zymaris, A. S.; Kavvadias, I. S.; Papadimitriou, D. I.; Giannakoglou, K. C.

2015-03-01

The continuous adjoint to the incompressible Reynolds-averaged Navier-Stokes equations coupled with the low Reynolds number Launder-Sharma k-ε turbulence model is presented. Both shape and active flow control optimization problems in fluid mechanics are considered, aiming at minimum viscous losses. In contrast to the frequently used assumption of frozen turbulence, the adjoint to the turbulence model equations together with appropriate boundary conditions are derived, discretized and solved. This is the first time that the adjoint equations to the Launder-Sharma k-ε model have been derived. Compared to the formulation that neglects turbulence variations, the impact of additional terms and equations is evaluated. Sensitivities computed using direct differentiation and/or finite differences are used for comparative purposes. To demonstrate the need for formulating and solving the adjoint to the turbulence model equations, instead of merely relying upon the 'frozen turbulence assumption', the gain in the optimization turnaround time offered by the proposed method is quantified.

Technical Note: Adjoint formulation of the TOMCAT atmospheric transport scheme in the Eulerian backtracking framework (RETRO-TOM)

NASA Astrophysics Data System (ADS)

Haines, P. E.; Esler, J. G.; Carver, G. D.

2014-06-01

A new methodology for the formulation of an adjoint to the transport component of the chemistry transport model TOMCAT is described and implemented in a new model, RETRO-TOM. The Eulerian backtracking method is used, allowing the forward advection scheme (Prather's second-order moments) to be efficiently exploited in the backward adjoint calculations. Prather's scheme is shown to be time symmetric, suggesting the possibility of high accuracy. To attain this accuracy, however, it is necessary to make a careful treatment of the "density inconsistency" problem inherent to offline transport models. The results are verified using a series of test experiments. These demonstrate the high accuracy of RETRO-TOM when compared with direct forward sensitivity calculations, at least for problems in which flux limiters in the advection scheme are not required. RETRO-TOM therefore combines the flexibility and stability of a "finite difference of adjoint" formulation with the accuracy of an "adjoint of finite difference" formulation.

Technical Note: Adjoint formulation of the TOMCAT atmospheric transport scheme in the Eulerian backtracking framework (RETRO-TOM)

NASA Astrophysics Data System (ADS)

Haines, P. E.; Esler, J. G.; Carver, G. D.

2014-01-01

A new methodology for the formulation of an adjoint to the transport component of the chemistry transport model TOMCAT is described and implemented in a new model RETRO-TOM. The Eulerian backtracking method is used, allowing the forward advection scheme (Prather's second-order moments), to be efficiently exploited in the backward adjoint calculations. Prather's scheme is shown to be time-symmetric suggesting the possibility of high accuracy. To attain this accuracy, however, it is necessary to make a careful treatment of the "density inconsistency" problem inherent to offline transport models. The results are verified using a series of test experiments. These demonstrate the high accuracy of RETRO-TOM when compared with direct forward sensitivity calculations, at least for problems in which flux-limiters in the advection scheme are not required. RETRO-TOM therefore combines the flexibility and stability of a "finite difference of adjoint" formulation with the accuracy of an "adjoint of finite difference" formulation.

Full-Carpet Design of a Low-Boom Demonstrator Concept

NASA Technical Reports Server (NTRS)

Ordaz, Irian; Wintzer, Mathias; Rallabhandi, Sriram K.

2015-01-01

The Cart3D adjoint-based design framework is used to mitigate the undesirable o -track sonic boom properties of a demonstrator concept designed for low-boom directly under the flight path. First, the requirements of a Cart3D design mesh are determined using a high-fidelity mesh adapted to minimize the discretization error of the CFD analysis. Low-boom equivalent area targets are then generated at the under-track and one off-track azimuthal position for the baseline configuration. The under-track target is generated using a trim- feasible low-boom target generation process, ensuring that the final design is not only low-boom, but also trimmed at the specified flight condition. The o -track equivalent area target is generated by minimizing the A-weighted loudness using an efficient adjoint-based approach. The configuration outer mold line is then parameterized and optimized to match the off-body pressure distributions prescribed by the low-boom targets. The numerical optimizer uses design gradients which are calculated using the Cart3D adjoint- based design capability. Optimization constraints are placed on the geometry to satisfy structural feasibility. The low-boom properties of the final design are verified using the adaptive meshing approach. This analysis quantifies the error associated with the CFD mesh that is used for design. Finally, an alternate mesh construction and target positioning approach offering greater computational efficiency is demonstrated and verified.

Advanced Variance Reduction Strategies for Optimizing Mesh Tallies in MAVRIC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peplow, Douglas E.; Blakeman, Edward D; Wagner, John C

2007-01-01

More often than in the past, Monte Carlo methods are being used to compute fluxes or doses over large areas using mesh tallies (a set of region tallies defined on a mesh that overlays the geometry). For problems that demand that the uncertainty in each mesh cell be less than some set maximum, computation time is controlled by the cell with the largest uncertainty. This issue becomes quite troublesome in deep-penetration problems, and advanced variance reduction techniques are required to obtain reasonable uncertainties over large areas. The CADIS (Consistent Adjoint Driven Importance Sampling) methodology has been shown to very efficientlymore » optimize the calculation of a response (flux or dose) for a single point or a small region using weight windows and a biased source based on the adjoint of that response. This has been incorporated into codes such as ADVANTG (based on MCNP) and the new sequence MAVRIC, which will be available in the next release of SCALE. In an effort to compute lower uncertainties everywhere in the problem, Larsen's group has also developed several methods to help distribute particles more evenly, based on forward estimates of flux. This paper focuses on the use of a forward estimate to weight the placement of the source in the adjoint calculation used by CADIS, which we refer to as a forward-weighted CADIS (FW-CADIS).« less

On the theory of self-adjoint extensions of symmetric operators and its applications to quantum physics

NASA Astrophysics Data System (ADS)

Ibort, A.; Pérez-Pardo, J. M.

2015-04-01

This is a series of five lectures around the common subject of the construction of self-adjoint extensions of symmetric operators and its applications to Quantum Physics. We will try to offer a brief account of some recent ideas in the theory of self-adjoint extensions of symmetric operators on Hilbert spaces and their applications to a few specific problems in Quantum Mechanics.

Sensitivity Analysis for Steady State Groundwater Flow Using Adjoint Operators

NASA Astrophysics Data System (ADS)

Sykes, J. F.; Wilson, J. L.; Andrews, R. W.

1985-03-01

Adjoint sensitivity theory is currently being considered as a potential method for calculating the sensitivity of nuclear waste repository performance measures to the parameters of the system. For groundwater flow systems, performance measures of interest include piezometric heads in the vicinity of a waste site, velocities or travel time in aquifers, and mass discharge to biosphere points. The parameters include recharge-discharge rates, prescribed boundary heads or fluxes, formation thicknesses, and hydraulic conductivities. The derivative of a performance measure with respect to the system parameters is usually taken as a measure of sensitivity. To calculate sensitivities, adjoint sensitivity equations are formulated from the equations describing the primary problem. The solution of the primary problem and the adjoint sensitivity problem enables the determination of all of the required derivatives and hence related sensitivity coefficients. In this study, adjoint sensitivity theory is developed for equations of two-dimensional steady state flow in a confined aquifer. Both the primary flow equation and the adjoint sensitivity equation are solved using the Galerkin finite element method. The developed computer code is used to investigate the regional flow parameters of the Leadville Formation of the Paradox Basin in Utah. The results illustrate the sensitivity of calculated local heads to the boundary conditions. Alternatively, local velocity related performance measures are more sensitive to hydraulic conductivities.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Favorite, Jeffrey A.

In transport theory, adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to surface locations (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. This study derives the constant-mass partial derivative of a response with respect to an internal interface location or the outer system boundary and the constant-mass partial derivative of a response with respect to the mass density of a region. Numerical results are given for a multiregion two-dimensional (r-z) cylinder for three very different responses: the uncollided gamma-ray flux at an external detector point, k effmore » of the system, and the total neutron leakage. Finally, results from the derived formulas compare extremely well with direct perturbation calculations.« less

Lessons Learned from Inlet Integration Analysis of NASA's Low Boom Flight Demonstrator

NASA Technical Reports Server (NTRS)

Friedlander, David; Heath, Christopher; Castner, Ray

2017-01-01

In 2016, NASA's Aeronautics Research Mission Directorate announced the New Aviation Horizons Initiative with a goal of designing/building several X-Planes, including a Low Boom Flight Demonstrator (LBFD). That same year, NASA awarded a contract to Lockheed Martin (LM) to advance the LBFD concept through preliminary design. Several configurations of the LBFD aircraft were analyzed by both LM engineers and NASA researchers. This presentation focuses on some of the CFD simulations that were run by NASA Glenn researchers. NASA's FUN3D V13.1 code was used for all adjoint-based grid refinement studies and Spalart-Allmaras turbulence model was used during adaptation. It was found that adjoint-based grid adaptation did not accurately capture inlet performance for high speed top-aft-mounted propulsion.

Regularized wave equation migration for imaging and data reconstruction

NASA Astrophysics Data System (ADS)

Kaplan, Sam T.

The reflection seismic experiment results in a measurement (reflection seismic data) of the seismic wavefield. The linear Born approximation to the seismic wavefield leads to a forward modelling operator that we use to approximate reflection seismic data in terms of a scattering potential. We consider approximations to the scattering potential using two methods: the adjoint of the forward modelling operator (migration), and regularized numerical inversion using the forward and adjoint operators. We implement two parameterizations of the forward modelling and migration operators: source-receiver and shot-profile. For both parameterizations, we find requisite Green's function using the split-step approximation. We first develop the forward modelling operator, and then find the adjoint (migration) operator by recognizing a Fredholm integral equation of the first kind. The resulting numerical system is generally under-determined, requiring prior information to find a solution. In source-receiver migration, the parameterization of the scattering potential is understood using the migration imaging condition, and this encourages us to apply sparse prior models to the scattering potential. To that end, we use both a Cauchy prior and a mixed Cauchy-Gaussian prior, finding better resolved estimates of the scattering potential than are given by the adjoint. In shot-profile migration, the parameterization of the scattering potential has its redundancy in multiple active energy sources (i.e. shots). We find that a smallest model regularized inverse representation of the scattering potential gives a more resolved picture of the earth, as compared to the simpler adjoint representation. The shot-profile parameterization allows us to introduce a joint inversion to further improve the estimate of the scattering potential. Moreover, it allows us to introduce a novel data reconstruction algorithm so that limited data can be interpolated/extrapolated. The linearized operators are expensive, encouraging their parallel implementation. For the source-receiver parameterization of the scattering potential this parallelization is non-trivial. Seismic data is typically corrupted by various types of noise. Sparse coding can be used to suppress noise prior to migration. It is a method that stems from information theory and that we apply to noise suppression in seismic data.

Global Modeling and Data Assimilation. Volume 11; Documentation of the Tangent Linear and Adjoint Models of the Relaxed Arakawa-Schubert Moisture Parameterization of the NASA GEOS-1 GCM; 5.2

NASA Technical Reports Server (NTRS)

Suarez, Max J. (Editor); Yang, Wei-Yu; Todling, Ricardo; Navon, I. Michael

1997-01-01

A detailed description of the development of the tangent linear model (TLM) and its adjoint model of the Relaxed Arakawa-Schubert moisture parameterization package used in the NASA GEOS-1 C-Grid GCM (Version 5.2) is presented. The notational conventions used in the TLM and its adjoint codes are described in detail.

Quantum mechanical reality according to Copenhagen 2.0

NASA Astrophysics Data System (ADS)

Din, Allan M.

2016-05-01

The long-standing conceptual controversies concerning the interpretation of nonrelativistic quantum mechanics are argued, on one hand, to be due to its incompleteness, as affirmed by Einstein. But on the other hand, it appears to be possible to complete it at least partially, as Bohr might have appreciated it, in the framework of its standard mathematical formalism with observables as appropriately defined self-adjoint operators. This completion of quantum mechanics is based on the requirement on laboratory physics to be effectively confined to a bounded space region and on the application of the von Neumann deficiency theorem to properly define a set of self-adjoint extensions of standard observables, e.g. the momenta and the Hamiltonian, in terms of certain isometries on the region boundary. This is formalized mathematically in the setting of a boundary ontology for the so-called Qbox in which the wave function acquires a supplementary dependence on a set of Additional Boundary Variables (ABV). It is argued that a certain geometric subset of the ABV parametrizing Quasi-Periodic Translational Isometries (QPTI) has a particular physical importance by allowing for the definition of an ontic wave function, which has the property of epitomizing the spatial wave function “collapse.” Concomitantly the standard wave function in an unbounded geometry is interpreted as an epistemic wave function, which together with the ontic QPTI wave function gives rise to the notion of two-wave duality, replacing the standard concept of wave-particle duality. More generally, this approach to quantum physics in a bounded geometry provides a novel analytical basis for a better understanding of several conceptual notions of quantum mechanics, including reality, nonlocality, entanglement and Heisenberg’s uncertainty relation. The scope of this analysis may be seen as a foundational update of the multiple versions 1.x of the Copenhagen interpretation of quantum mechanics, which is sufficiently incremental so as to be appropriately characterized as Copenhagen 2.0.

Adjoint-Based Climate Model Tuning: Application to the Planet Simulator

NASA Astrophysics Data System (ADS)

Lyu, Guokun; Köhl, Armin; Matei, Ion; Stammer, Detlef

2018-01-01

The adjoint method is used to calibrate the medium complexity climate model "Planet Simulator" through parameter estimation. Identical twin experiments demonstrate that this method can retrieve default values of the control parameters when using a long assimilation window of the order of 2 months. Chaos synchronization through nudging, required to overcome limits in the temporal assimilation window in the adjoint method, is employed successfully to reach this assimilation window length. When assimilating ERA-Interim reanalysis data, the observations of air temperature and the radiative fluxes are the most important data for adjusting the control parameters. The global mean net longwave fluxes at the surface and at the top of the atmosphere are significantly improved by tuning two model parameters controlling the absorption of clouds and water vapor. The global mean net shortwave radiation at the surface is improved by optimizing three model parameters controlling cloud optical properties. The optimized parameters improve the free model (without nudging terms) simulation in a way similar to that in the assimilation experiments. Results suggest a promising way for tuning uncertain parameters in nonlinear coupled climate models.

Seismic wave-speed structure beneath the metropolitan area of Japan based on adjoint tomography

NASA Astrophysics Data System (ADS)

Miyoshi, T.; Obayashi, M.; Tono, Y.; Tsuboi, S.

2015-12-01

We have obtained a three-dimensional (3D) model of seismic wave-speed structure beneath the metropolitan area of Japan. We applied the spectral-element method (e.g. Komatitsch and Tromp 1999) and adjoint method (Liu and Tromp 2006) to the broadband seismograms in order to infer the 3D model. We used the travel-time tomography result (Matsubara and Obara 2011) as an initial 3D model and used broadband waveforms recorded at the NIED F-net stations. We selected 147 earthquakes with magnitude of larger than 4.5 from the F-net earthquake catalog and used their bandpass filtered seismograms between 5 and 20 second with a high S/N ratio. The 3D model used for the forward and adjoint simulations is represented as a region of approximately 500 by 450 km in horizontal and 120 km in depth. Minimum period of theoretical waveforms was 4.35 second. For the adjoint inversion, we picked up the windows of the body waves from the observed and theoretical seismograms. We used SPECFEM3D_Cartesian code (e.g. Peter et al. 2011) for the forward and adjoint simulations, and their simulations were implemented by K-computer in RIKEN. Each iteration required about 0.1 million CPU hours at least. The model parameters of Vp and Vs were updated by using the steepest descent method. We obtained the fourth iterative model (M04), which reproduced observed waveforms better than the initial model. The shear wave-speed of M04 was significantly smaller than the initial model at any depth. The model of compressional wave-speed was not improved by inversion because of small alpha kernel values. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We thank to the NIED for providing seismological data.

Adjoint-Based Sensitivity Maps for the Nearshore

NASA Astrophysics Data System (ADS)

Orzech, Mark; Veeramony, Jay; Ngodock, Hans

2013-04-01

The wave model SWAN (Booij et al., 1999) solves the spectral action balance equation to produce nearshore wave forecasts and climatologies. It is widely used by the coastal modeling community and is part of a variety of coupled ocean-wave-atmosphere model systems. A variational data assimilation system (Orzech et al., 2013) has recently been developed for SWAN and is presently being transitioned to operational use by the U.S. Naval Oceanographic Office. This system is built around a numerical adjoint to the fully nonlinear, nonstationary SWAN code. When provided with measured or artificial "observed" spectral wave data at a location of interest on a given nearshore bathymetry, the adjoint can compute the degree to which spectral energy levels at other locations are correlated with - or "sensitive" to - variations in the observed spectrum. Adjoint output may be used to construct a sensitivity map for the entire domain, tracking correlations of spectral energy throughout the grid. When access is denied to the actual locations of interest, sensitivity maps can be used to determine optimal alternate locations for data collection by identifying regions of greatest sensitivity in the mapped domain. The present study investigates the properties of adjoint-generated sensitivity maps for nearshore wave spectra. The adjoint and forward SWAN models are first used in an idealized test case at Duck, NC, USA, to demonstrate the system's effectiveness at optimizing forecasts of shallow water wave spectra for an inaccessible surf-zone location. Then a series of simulations is conducted for a variety of different initializing conditions, to examine the effects of seasonal changes in wave climate, errors in bathymetry, and variations in size and shape of the inaccessible region of interest. Model skill is quantified using two methods: (1) a more traditional correlation of observed and modeled spectral statistics such as significant wave height, and (2) a recently developed RMS spectral skill score summed over all frequency-directional bins. The relative advantages and disadvantages of these two methods are considered. References: Booij, N., R.C. Ris, and L.H. Holthuijsen, 1999: A third-generation wave model for coastal regions: 1. Model description and validation. J. Geophys. Res. 104 (C4), 7649-7666. Orzech, M.D., J. Veeramony, and H.E. Ngodock, 2013: A variational assimilation system for nearshore wave modeling. J. Atm. & Oc. Tech., in press.

Sensitivity analysis of discrete structural systems: A survey

NASA Technical Reports Server (NTRS)

Adelman, H. M.; Haftka, R. T.

1984-01-01

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications addressed to structural analysis, but also includes a number of methods developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

DOE Office of Scientific and Technical Information (OSTI.GOV)

Finn, John M., E-mail: finn@lanl.gov

2015-03-15

Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a “special divergence-free” (SDF) property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint.more » We also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volume-preserving flows. We investigate two potential schemes, both based on the general method of Feng and Shang [Numer. Math. 71, 451 (1995)], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Richardson and Finn [Plasma Phys. Controlled Fusion 54, 014004 (2012)], appears to work very well.« less

First- and second-order sensitivity analysis of linear and nonlinear structures

NASA Technical Reports Server (NTRS)

Haftka, R. T.; Mroz, Z.

1986-01-01

This paper employs the principle of virtual work to derive sensitivity derivatives of structural response with respect to stiffness parameters using both direct and adjoint approaches. The computations required are based on additional load conditions characterized by imposed initial strains, body forces, or surface tractions. As such, they are equally applicable to numerical or analytical solution techniques. The relative efficiency of various approaches for calculating first and second derivatives is assessed. It is shown that for the evaluation of second derivatives the most efficient approach is one that makes use of both the first-order sensitivities and adjoint vectors. Two example problems are used for demonstrating the various approaches.

An adjoint-based method for a linear mechanically-coupled tumor model: application to estimate the spatial variation of murine glioma growth based on diffusion weighted magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Feng, Xinzeng; Hormuth, David A.; Yankeelov, Thomas E.

2018-06-01

We present an efficient numerical method to quantify the spatial variation of glioma growth based on subject-specific medical images using a mechanically-coupled tumor model. The method is illustrated in a murine model of glioma in which we consider the tumor as a growing elastic mass that continuously deforms the surrounding healthy-appearing brain tissue. As an inverse parameter identification problem, we quantify the volumetric growth of glioma and the growth component of deformation by fitting the model predicted cell density to the cell density estimated using the diffusion-weighted magnetic resonance imaging data. Numerically, we developed an adjoint-based approach to solve the optimization problem. Results on a set of experimentally measured, in vivo rat glioma data indicate good agreement between the fitted and measured tumor area and suggest a wide variation of in-plane glioma growth with the growth-induced Jacobian ranging from 1.0 to 6.0.

A practical globalization of one-shot optimization for optimal design of tokamak divertors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blommaert, Maarten, E-mail: maarten.blommaert@kuleuven.be; Dekeyser, Wouter; Baelmans, Martine

In past studies, nested optimization methods were successfully applied to design of the magnetic divertor configuration in nuclear fusion reactors. In this paper, so-called one-shot optimization methods are pursued. Due to convergence issues, a globalization strategy for the one-shot solver is sought. Whereas Griewank introduced a globalization strategy using a doubly augmented Lagrangian function that includes primal and adjoint residuals, its practical usability is limited by the necessity of second order derivatives and expensive line search iterations. In this paper, a practical alternative is offered that avoids these drawbacks by using a regular augmented Lagrangian merit function that penalizes onlymore » state residuals. Additionally, robust rank-two Hessian estimation is achieved by adaptation of Powell's damped BFGS update rule. The application of the novel one-shot approach to magnetic divertor design is considered in detail. For this purpose, the approach is adapted to be complementary with practical in parts adjoint sensitivities. Using the globalization strategy, stable convergence of the one-shot approach is achieved.« less

Convergence of Distributed Optimal Controls on the Internal Energy in Mixed Elliptic Problems when the Heat Transfer Coefficient Goes to Infinity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gariboldi, C.; E-mail: cgariboldi@exa.unrc.edu.ar; Tarzia, D.

2003-05-21

We consider a steady-state heat conduction problem P{sub {alpha}} with mixed boundary conditions for the Poisson equation depending on a positive parameter {alpha} , which represents the heat transfer coefficient on a portion {gamma} {sub 1} of the boundary of a given bounded domain in R{sup n} . We formulate distributed optimal control problems over the internal energy g for each {alpha}. We prove that the optimal control g{sub o}p{sub {alpha}} and its corresponding system u{sub go}p{sub {alpha}}{sub {alpha}} and adjoint p{sub go}p{sub {alpha}}{sub {alpha}} states for each {alpha} are strongly convergent to g{sub op},u{sub gop} and p{sub gop} ,more » respectively, in adequate functional spaces. We also prove that these limit functions are respectively the optimal control, and the system and adjoint states corresponding to another distributed optimal control problem for the same Poisson equation with a different boundary condition on the portion {gamma}{sub 1} . We use the fixed point and elliptic variational inequality theories.« less

Seismic structure of the European crust and upper mantle based on adjoint tomography

NASA Astrophysics Data System (ADS)

Zhu, H.; Bozdag, E.; Peter, D.; Tromp, J.

2013-12-01

We present a new crustal and upper mantle model for the European continent and the North Atlantic Ocean, named EU60. It is constructed based on adjoint tomography and involves 3D variations in elastic wavespeeds, anelastic attenuation, and radial/azimuthal anisotropy. Long-wavelength elastic wavespeed structure of EU60 agree with previous body- and surface-wave tomographic models. Some hitherto unidentified features, such as the Adria microplate, naturally emerge from smoothed starting model. Subducting slabs, slab detachment, ancient suture zones, continental rifts and back-arc basins are well resolved in EU60. For anelastic structure, we find an anti-correlation between shear wavespeeds and anelastic attenuation at shallow depths. At greater depths, this anti-correlation becomes relatively weak, in agreement with previous attenuation studies at global scales. Consistent with radial anisotropy in 1D reference models, the European continent is dominated by features with radially anisotropic parameter xi>1, indicating the presence of horizontal flow within the upper mantle. In addition, subduction zones, such as the Apennines and Hellenic arcs, are characterized as vertical flow with xi<1 at depths greater than 150~km. For azimuthal anisotropy, we find that the direction of fast anisotropic axis is well correlated with complicated tectonic evolution in this region, such as extension along the North Atlantic Ridge, trench retreat in the Mediterranean and counter-clockwise rotation of the Anatolian Plate. The ``point spread function'' is used to assess image quality and analyze tradeoff between different model parameters.

Deterministic Local Sensitivity Analysis of Augmented Systems - II: Applications to the QUENCH-04 Experiment Using the RELAP5/MOD3.2 Code System

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ionescu-Bujor, Mihaela; Jin Xuezhou; Cacuci, Dan G.

2005-09-15

The adjoint sensitivity analysis procedure for augmented systems for application to the RELAP5/MOD3.2 code system is illustrated. Specifically, the adjoint sensitivity model corresponding to the heat structure models in RELAP5/MOD3.2 is derived and subsequently augmented to the two-fluid adjoint sensitivity model (ASM-REL/TF). The end product, called ASM-REL/TFH, comprises the complete adjoint sensitivity model for the coupled fluid dynamics/heat structure packages of the large-scale simulation code RELAP5/MOD3.2. The ASM-REL/TFH model is validated by computing sensitivities to the initial conditions for various time-dependent temperatures in the test bundle of the Quench-04 reactor safety experiment. This experiment simulates the reflooding with water ofmore » uncovered, degraded fuel rods, clad with material (Zircaloy-4) that has the same composition and size as that used in typical pressurized water reactors. The most important response for the Quench-04 experiment is the time evolution of the cladding temperature of heated fuel rods. The ASM-REL/TFH model is subsequently used to perform an illustrative sensitivity analysis of this and other time-dependent temperatures within the bundle. The results computed by using the augmented adjoint sensitivity system, ASM-REL/TFH, highlight the reliability, efficiency, and usefulness of the adjoint sensitivity analysis procedure for computing time-dependent sensitivities.« less

Partition function of free conformal fields in 3-plet representation

NASA Astrophysics Data System (ADS)

Beccaria, Matteo; Tseytlin, Arkady A.

2017-05-01

Simplest examples of AdS/CFT duality correspond to free CFTs in d dimensions with fields in vector or adjoint representation of an internal symmetry group dual in the large N limit to a theory of massless or massless plus massive higher spins in AdS d+1. One may also study generalizations when conformal fields belong to higher dimensional representations, i.e. carry more than two internal symmetry indices. Here we consider the case of the 3-fundamental ("3-plet") representation. One motivation is a conjectured connection to multiple M5-brane theory: heuristic arguments suggest that it may be related to an (interacting) CFT of 6d (2,0) tensor multiplets in 3-plet representation of large N symmetry group that has an AdS7 dual. We compute the singlet partition function Z on S 1 × S d-1 for a free field in 3-plet representation of U( N) and analyse its novel large N behaviour. The large N limit of the low temperature expansion of Z which is convergent in the vector and adjoint cases here is only asymptotic, reflecting the much faster growth of the number of singlet operators with dimension, indicating a phase transition at very low temperature. Indeed, while the critical temperatures in the vector ( T c ˜ N γ , γ > 0) and adjoint ( T c ˜ 1) cases are finite, we find that in the 3-plet case T c ˜ (log N)-1, i.e. it approaches zero at large N. We discuss some details of large N solution for the eigenvalue distribution. Similar conclusions apply to higher p-plet representations of U( N) or O( N) and also to the free p-tensor theories invariant under [U( N)] p or [ O( N)] p with p ≥ 3.

FW-CADIS Method for Global and Semi-Global Variance Reduction of Monte Carlo Radiation Transport Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wagner, John C; Peplow, Douglas E.; Mosher, Scott W

2014-01-01

This paper presents a new hybrid (Monte Carlo/deterministic) method for increasing the efficiency of Monte Carlo calculations of distributions, such as flux or dose rate distributions (e.g., mesh tallies), as well as responses at multiple localized detectors and spectra. This method, referred to as Forward-Weighted CADIS (FW-CADIS), is an extension of the Consistent Adjoint Driven Importance Sampling (CADIS) method, which has been used for more than a decade to very effectively improve the efficiency of Monte Carlo calculations of localized quantities, e.g., flux, dose, or reaction rate at a specific location. The basis of this method is the development ofmore » an importance function that represents the importance of particles to the objective of uniform Monte Carlo particle density in the desired tally regions. Implementation of this method utilizes the results from a forward deterministic calculation to develop a forward-weighted source for a deterministic adjoint calculation. The resulting adjoint function is then used to generate consistent space- and energy-dependent source biasing parameters and weight windows that are used in a forward Monte Carlo calculation to obtain more uniform statistical uncertainties in the desired tally regions. The FW-CADIS method has been implemented and demonstrated within the MAVRIC sequence of SCALE and the ADVANTG/MCNP framework. Application of the method to representative, real-world problems, including calculation of dose rate and energy dependent flux throughout the problem space, dose rates in specific areas, and energy spectra at multiple detectors, is presented and discussed. Results of the FW-CADIS method and other recently developed global variance reduction approaches are also compared, and the FW-CADIS method outperformed the other methods in all cases considered.« less

The spectral function of a singular differential operator of order 2m

NASA Astrophysics Data System (ADS)

Kozko, Artem I.; Pechentsov, Alexander S.

2010-12-01

We study the spectral function of a self-adjoint semibounded below differential operator on a Hilbert space L_2 \\lbrack 0,\\infty) and obtain the formulae for the spectral function of the operator (-1)^{m}y^{(2m)}(x) with general boundary conditions at the zero. In particular, for the boundary conditions y(0)=y'(0)=\\dots=y^{(m-1)}(0)=0 we find the explicit form of the spectral function \\Theta_{mB'}(x,x,\\lambda) on the diagonal x=y for \\lambda \\ge 0.

Comparative Study of Three Data Assimilation Methods for Ice Sheet Model Initialisation

NASA Astrophysics Data System (ADS)

Mosbeux, Cyrille; Gillet-Chaulet, Fabien; Gagliardini, Olivier

2015-04-01

The current global warming has direct consequences on ice-sheet mass loss contributing to sea level rise. This loss is generally driven by an acceleration of some coastal outlet glaciers and reproducing these mechanisms is one of the major issues in ice-sheet and ice flow modelling. The construction of an initial state, as close as possible to current observations, is required as a prerequisite before producing any reliable projection of the evolution of ice-sheets. For this step, inverse methods are often used to infer badly known or unknown parameters. For instance, the adjoint inverse method has been implemented and applied with success by different authors in different ice flow models in order to infer the basal drag [ Schafer et al., 2012; Gillet-chauletet al., 2012; Morlighem et al., 2010]. Others data fields, such as ice surface and bedrock topography, are easily measurable with more or less uncertainty but only locally along tracks and interpolated on finer model grid. All these approximations lead to errors on the data elevation model and give rise to an ill-posed problem inducing non-physical anomalies in flux divergence [Seroussi et al, 2011]. A solution to dissipate these divergences of flux is to conduct a surface relaxation step at the expense of the accuracy of the modelled surface [Gillet-Chaulet et al., 2012]. Other solutions, based on the inversion of ice thickness and basal drag were proposed [Perego et al., 2014; Pralong & Gudmundsson, 2011]. In this study, we create a twin experiment to compare three different assimilation algorithms based on inverse methods and nudging to constrain the bedrock friction and the bedrock elevation: (i) cyclic inversion of friction parameter and bedrock topography using adjoint method, (ii) cycles coupling inversion of friction parameter using adjoint method and nudging of bedrock topography, (iii) one step inversion of both parameters with adjoint method. The three methods show a clear improvement in parameters knowledge leading to a significant reduction of flux divergence of the model before forecasting.

Mapping Emissions that Contribute to Air Pollution Using Adjoint Sensitivity Analysis

NASA Astrophysics Data System (ADS)

Bastien, L. A. J.; Mcdonald, B. C.; Brown, N. J.; Harley, R.

2014-12-01

The adjoint of the Community Multiscale Air Quality model (CMAQ) is used to map emissions that contribute to air pollution at receptors of interest. Adjoint tools provide an efficient way to calculate the sensitivity of a model response to a large number of model inputs, a task that would require thousands of simulations using a more traditional forward sensitivity approach. Initial applications of this technique, demonstrated here, are to benzene and directly-emitted diesel particulate matter, for which atmospheric reactions are neglected. Emissions of these pollutants are strongly influenced by light-duty gasoline vehicles and heavy-duty diesel trucks, respectively. We study air quality responses in three receptor areas where populations have been identified as especially susceptible to, and adversely affected by air pollution. Population-weighted air basin-wide responses for each pollutant are also evaluated for the entire San Francisco Bay area. High-resolution (1 km horizontal grid) emission inventories have been developed for on-road motor vehicle emission sources, based on observed traffic count data. Emission estimates represent diurnal, day of week, and seasonal variations of on-road vehicle activity, with separate descriptions for gasoline and diesel sources. Emissions that contribute to air pollution at each receptor have been mapped in space and time using the adjoint method. Effects on air quality of both relative (multiplicative) and absolute (additive) perturbations to underlying emission inventories are analyzed. The contributions of local versus upwind sources to air quality in each receptor area are quantified, and weekday/weekend and seasonal variations in the influence of emissions from upwind areas are investigated. The contribution of local sources to the total air pollution burden within the receptor areas increases from about 40% in the summer to about 50% in the winter due to increased atmospheric stagnation. The effectiveness of control strategies based on region-wide exposure metrics is compared with strategies that focus on improving air quality at specific receptors.

Quantifying co-benefits of source-specific CO2 emission reductions in Canada and the US: An adjoint sensitivity analysis

NASA Astrophysics Data System (ADS)

Zhao, S.; Soltanzadeh, M.; Pappin, A. J.; Hakami, A.; Turner, M. D.; Capps, S.; Henze, D. K.; Percell, P.; Bash, J. O.; Napelenok, S. L.; Pinder, R. W.; Russell, A. G.; Nenes, A.; Baek, J.; Carmichael, G. R.; Stanier, C. O.; Chai, T.; Byun, D.; Fahey, K.; Resler, J.; Mashayekhi, R.

2016-12-01

Scenario-based studies evaluate air quality co-benefits by adopting collective measures introduced under a climate policy scenario cannot distinguish between benefits accrued from CO2 reductions among sources of different types and at different locations. Location and sector dependencies are important factors that can be captured in an adjoint-based analysis of CO2 reduction co-benefits. The present study aims to quantify how the ancillary benefits of reducing criteria co-pollutants vary spatially and by sector. The adjoint of USEPA's CMAQ was applied to quantify the health benefits associated with emission reduction of criteria pollutants (NOX) in on-road mobile, Electric Generation Units (EGUs), and other select sectors on a location-by-location basis across the US and Canada. These health benefits are then converted to CO2 emission reduction co-benefits by accounting for source-specific emission rates of criteria pollutants in comparison to CO2. We integrate the results from the adjoint of CMAQ with emission estimates from 2011 NEI at the county level, and point source data from EPA's Air Markets Program Data and National Pollutant Release Inventory (NPRI) for Canada. Our preliminary results show that the monetized health benefits (due to averted chronic mortality) associated with reductions of 1 ton of CO2 emissions is up to 65/ton in Canada and 200/ton in US for mobile on-road sector. For EGU sources, co-benefits are estimated at up to 100/ton and 10/ton for the US and Canada respectively. For Canada, the calculated co-benefits through gaseous pollutants including NOx is larger than those through PM2.5 due to the official association between NO2 exposure and chronic mortality. Calculated co-benefits show a great deal of spatial variability across emission locations for different sectors and sub-sectors. Implications of such spatial variability in devising control policy options that effectively address both climate and air quality objectives will be discussed.

Slope tomography based on eikonal solvers and the adjoint-state method

NASA Astrophysics Data System (ADS)

Tavakoli F., B.; Operto, S.; Ribodetti, A.; Virieux, J.

2017-06-01

Velocity macromodel building is a crucial step in the seismic imaging workflow as it provides the necessary background model for migration or full waveform inversion. In this study, we present a new formulation of stereotomography that can handle more efficiently long-offset acquisition, complex geological structures and large-scale data sets. Stereotomography is a slope tomographic method based upon a semi-automatic picking of local coherent events. Each local coherent event, characterized by its two-way traveltime and two slopes in common-shot and common-receiver gathers, is tied to a scatterer or a reflector segment in the subsurface. Ray tracing provides a natural forward engine to compute traveltime and slopes but can suffer from non-uniform ray sampling in presence of complex media and long-offset acquisitions. Moreover, most implementations of stereotomography explicitly build a sensitivity matrix, leading to the resolution of large systems of linear equations, which can be cumbersome when large-scale data sets are considered. Overcoming these issues comes with a new matrix-free formulation of stereotomography: a factored eikonal solver based on the fast sweeping method to compute first-arrival traveltimes and an adjoint-state formulation to compute the gradient of the misfit function. By solving eikonal equation from sources and receivers, we make the computational cost proportional to the number of sources and receivers while it is independent of picked events density in each shot and receiver gather. The model space involves the subsurface velocities and the scatterer coordinates, while the dips of the reflector segments are implicitly represented by the spatial support of the adjoint sources and are updated through the joint localization of nearby scatterers. We present an application on the complex Marmousi model for a towed-streamer acquisition and a realistic distribution of local events. We show that the estimated model, built without any prior knowledge of the velocities, provides a reliable initial model for frequency-domain FWI of long-offset data for a starting frequency of 4 Hz, although some artefacts at the reservoir level result from a deficit of illumination. This formulation of slope tomography provides a computationally efficient alternative to waveform inversion method such as reflection waveform inversion or differential-semblance optimization to build an initial model for pre-stack depth migration and conventional FWI.

Axisymmetric problem of fretting wear for a foundation with a nonuniform coating and rough punch

NASA Astrophysics Data System (ADS)

Manzhirov, A. V.; Kazakov, K. E.

2018-05-01

The axisymmetric contact problem with fretting wear for an elastic foundation with a longitudinally nonuniform (surface nonuniform) coating and a rigid punch with a rough foundation has been solved for the first time. The case of linear wear is considered. The nonuniformity of the coating and punch roughness are described by a different rapidly changing functions. This strong nonuniformity arises when coatings are deposited using modern additive manufacturing technologies. The problem is reduced the solution of an integral equation with two different integral operators: a compact self-adjoint positively defined operator with respect to the coordinate and the non-self-adjoint integral Volterra operator with respect to time. The solution is obtained in series using the projection method of the authors. The efficiency of the proposed approach for constructing a high-accuracy approximate solution to the problem (with only a few expansion terms retained) is demonstrated.

Periodic differential equations with self-adjoint monodromy operator

NASA Astrophysics Data System (ADS)

Yudovich, V. I.

2001-04-01

A linear differential equation \\dot u=A(t)u with p-periodic (generally speaking, unbounded) operator coefficient in a Euclidean or a Hilbert space \\mathbb H is considered. It is proved under natural constraints that the monodromy operator U_p is self-adjoint and strictly positive if A^*(-t)=A(t) for all t\\in\\mathbb R.It is shown that Hamiltonian systems in the class under consideration are usually unstable and, if they are stable, then the operator U_p reduces to the identity and all solutions are p-periodic.For higher frequencies averaged equations are derived. Remarkably, high-frequency modulation may double the number of critical values.General results are applied to rotational flows with cylindrical components of the velocity a_r=a_z=0, a_\\theta=\\lambda c(t)r^\\beta, \\beta<-1, c(t) is an even p-periodic function, and also to several problems of free gravitational convection of fluids in periodic fields.

On the Direct Assimilation of Along-track Sea Surface Height Observations into a Free-surface Ocean Model Using a Weak Constraints Four Dimensional Variational (4dvar) Method

NASA Astrophysics Data System (ADS)

Ngodock, H.; Carrier, M.; Smith, S. R.; Souopgui, I.; Martin, P.; Jacobs, G. A.

2016-02-01

The representer method is adopted for solving a weak constraints 4dvar problem for the assimilation of ocean observations including along-track SSH, using a free surface ocean model. Direct 4dvar assimilation of SSH observations along the satellite tracks requires that the adjoint model be integrated with Dirac impulses on the right hand side of the adjoint equations for the surface elevation equation. The solution of this adjoint model will inevitably include surface gravity waves, and it constitutes the forcing for the tangent linear model (TLM) according to the representer method. This yields an analysis that is contaminated by gravity waves. A method for avoiding the generation of the surface gravity waves in the analysis is proposed in this study; it consists of removing the adjoint of the free surface from the right hand side (rhs) of the free surface mode in the TLM. The information from the SSH observations will still propagate to all other variables via the adjoint of the balance relationship between the barotropic and baroclinic modes, resulting in the correction to the surface elevation. Two assimilation experiments are carried out in the Gulf of Mexico: one with adjoint forcing included on the rhs of the TLM free surface equation, and the other without. Both analyses are evaluated against the assimilated SSH observations, SSH maps from Aviso and independent surface drifters, showing that the analysis that did not include adjoint forcing in the free surface is more accurate. This study shows that when a weak constraint 4dvar approach is considered for the assimilation of along-track SSH observations using a free surface model, with the aim of correcting the mesoscale circulation, an independent model error should not be assigned to the free surface.

An optimal control method for fluid structure interaction systems via adjoint boundary pressure

NASA Astrophysics Data System (ADS)

Chirco, L.; Da Vià, R.; Manservisi, S.

2017-11-01

In recent year, in spite of the computational complexity, Fluid-structure interaction (FSI) problems have been widely studied due to their applicability in science and engineering. Fluid-structure interaction systems consist of one or more solid structures that deform by interacting with a surrounding fluid flow. FSI simulations evaluate the tensional state of the mechanical component and take into account the effects of the solid deformations on the motion of the interior fluids. The inverse FSI problem can be described as the achievement of a certain objective by changing some design parameters such as forces, boundary conditions and geometrical domain shapes. In this paper we would like to study the inverse FSI problem by using an optimal control approach. In particular we propose a pressure boundary optimal control method based on Lagrangian multipliers and adjoint variables. The objective is the minimization of a solid domain displacement matching functional obtained by finding the optimal pressure on the inlet boundary. The optimality system is derived from the first order necessary conditions by taking the Fréchet derivatives of the Lagrangian with respect to all the variables involved. The optimal solution is then obtained through a standard steepest descent algorithm applied to the optimality system. The approach presented in this work is general and could be used to assess other objective functionals and controls. In order to support the proposed approach we perform a few numerical tests where the fluid pressure on the domain inlet controls the displacement that occurs in a well defined region of the solid domain.

Spectral-Element Seismic Wave Propagation Codes for both Forward Modeling in Complex Media and Adjoint Tomography

NASA Astrophysics Data System (ADS)

Smith, J. A.; Peter, D. B.; Tromp, J.; Komatitsch, D.; Lefebvre, M. P.

2015-12-01

We present both SPECFEM3D_Cartesian and SPECFEM3D_GLOBE open-source codes, representing high-performance numerical wave solvers simulating seismic wave propagation for local-, regional-, and global-scale application. These codes are suitable for both forward propagation in complex media and tomographic imaging. Both solvers compute highly accurate seismic wave fields using the continuous Galerkin spectral-element method on unstructured meshes. Lateral variations in compressional- and shear-wave speeds, density, as well as 3D attenuation Q models, topography and fluid-solid coupling are all readily included in both codes. For global simulations, effects due to rotation, ellipticity, the oceans, 3D crustal models, and self-gravitation are additionally included. Both packages provide forward and adjoint functionality suitable for adjoint tomography on high-performance computing architectures. We highlight the most recent release of the global version which includes improved performance, simultaneous MPI runs, OpenCL and CUDA support via an automatic source-to-source transformation library (BOAST), parallel I/O readers and writers for databases using ADIOS and seismograms using the recently developed Adaptable Seismic Data Format (ASDF) with built-in provenance. This makes our spectral-element solvers current state-of-the-art, open-source community codes for high-performance seismic wave propagation on arbitrarily complex 3D models. Together with these solvers, we provide full-waveform inversion tools to image the Earth's interior at unprecedented resolution.

Application of the adjoint optimisation of shock control bump for ONERA-M6 wing

NASA Astrophysics Data System (ADS)

Nejati, A.; Mazaheri, K.

2017-11-01

This article is devoted to the numerical investigation of the shock wave/boundary layer interaction (SWBLI) as the main factor influencing the aerodynamic performance of transonic bumped airfoils and wings. The numerical analysis is conducted for the ONERA-M6 wing through a shock control bump (SCB) shape optimisation process using the adjoint optimisation method. SWBLI is analyzed for both clean and bumped airfoils and wings, and it is shown how the modified wave structure originating from upstream of the SCB reduces the wave drag, by improving the boundary layer velocity profile downstream of the shock wave. The numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm are used to find the optimum location and shape of the SCB for the ONERA-M6 airfoil and wing. Two different geometrical models are introduced for the 3D SCB, one with linear variations, and another with periodic variations. Both configurations result in drag reduction and improvement in the aerodynamic efficiency, but the periodic model is more effective. Although the three-dimensional flow structure involves much more complexities, the overall results are shown to be similar to the two-dimensional case.

Adjoint-Based Methodology for Time-Dependent Optimal Control (AMTOC)

NASA Technical Reports Server (NTRS)

Yamaleev, Nail; Diskin, boris; Nishikawa, Hiroaki

2012-01-01

During the five years of this project, the AMTOC team developed an adjoint-based methodology for design and optimization of complex time-dependent flows, implemented AMTOC in a testbed environment, directly assisted in implementation of this methodology in the state-of-the-art NASA's unstructured CFD code FUN3D, and successfully demonstrated applications of this methodology to large-scale optimization of several supersonic and other aerodynamic systems, such as fighter jet, subsonic aircraft, rotorcraft, high-lift, wind-turbine, and flapping-wing configurations. In the course of this project, the AMTOC team has published 13 refereed journal articles, 21 refereed conference papers, and 2 NIA reports. The AMTOC team presented the results of this research at 36 international and national conferences, meeting and seminars, including International Conference on CFD, and numerous AIAA conferences and meetings. Selected publications that include the major results of the AMTOC project are enclosed in this report.

Multimodel methods for optimal control of aeroacoustics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Guoquan; Collis, Samuel Scott

2005-01-01

A new multidomain/multiphysics computational framework for optimal control of aeroacoustic noise has been developed based on a near-field compressible Navier-Stokes solver coupled with a far-field linearized Euler solver both based on a discontinuous Galerkin formulation. In this approach, the coupling of near- and far-field domains is achieved by weakly enforcing continuity of normal fluxes across a coupling surface that encloses all nonlinearities and noise sources. For optimal control, gradient information is obtained by the solution of an appropriate adjoint problem that involves the propagation of adjoint information from the far-field to the near-field. This computational framework has been successfully appliedmore » to study optimal boundary-control of blade-vortex interaction, which is a significant noise source for helicopters on approach to landing. In the model-problem presented here, the noise propagated toward the ground is reduced by 12dB.« less

Comparison of adjoint and analytical Bayesian inversion methods for constraining Asian sources of carbon monoxide using satellite (MOPITT) measurements of CO columns

NASA Astrophysics Data System (ADS)

Kopacz, Monika; Jacob, Daniel J.; Henze, Daven K.; Heald, Colette L.; Streets, David G.; Zhang, Qiang

2009-02-01

We apply the adjoint of an atmospheric chemical transport model (GEOS-Chem CTM) to constrain Asian sources of carbon monoxide (CO) with 2° × 2.5° spatial resolution using Measurement of Pollution in the Troposphere (MOPITT) satellite observations of CO columns in February-April 2001. Results are compared to the more common analytical method for solving the same Bayesian inverse problem and applied to the same data set. The analytical method is more exact but because of computational limitations it can only constrain emissions over coarse regions. We find that the correction factors to the a priori CO emission inventory from the adjoint inversion are generally consistent with those of the analytical inversion when averaged over the large regions of the latter. The adjoint solution reveals fine-scale variability (cities, political boundaries) that the analytical inversion cannot resolve, for example, in the Indian subcontinent or between Korea and Japan, and some of that variability is of opposite sign which points to large aggregation errors in the analytical solution. Upward correction factors to Chinese emissions from the prior inventory are largest in central and eastern China, consistent with a recent bottom-up revision of that inventory, although the revised inventory also sees the need for upward corrections in southern China where the adjoint and analytical inversions call for downward correction. Correction factors for biomass burning emissions derived from the adjoint and analytical inversions are consistent with a recent bottom-up inventory on the basis of MODIS satellite fire data.

Control Theory based Shape Design for the Incompressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Cowles, G.; Martinelli, L.

2003-12-01

A design method for shape optimization in incompressible turbulent viscous flow has been developed and validated for inverse design. The gradient information is determined using a control theory based algorithm. With such an approach, the cost of computing the gradient is negligible. An additional adjoint system must be solved which requires the cost of a single steady state flow solution. Thus, this method has an enormous advantage over traditional finite-difference based algorithms. The method of artificial compressibility is utilized to solve both the flow and adjoint systems. An algebraic turbulence model is used to compute the eddy viscosity. The method is validated using several inverse wing design test cases. In each case, the program must modify the shape of the initial wing such that its pressure distribution matches that of the target wing. Results are shown for the inversion of both finite thickness wings as well as zero thickness wings which can be considered a model of yacht sails.

Optimal startup control of a jacketed tubular reactor.

NASA Technical Reports Server (NTRS)

Hahn, D. R.; Fan, L. T.; Hwang, C. L.

1971-01-01

The optimal startup policy of a jacketed tubular reactor, in which a first-order, reversible, exothermic reaction takes place, is presented. A distributed maximum principle is presented for determining weak necessary conditions for optimality of a diffusional distributed parameter system. A numerical technique is developed for practical implementation of the distributed maximum principle. This involves the sequential solution of the state and adjoint equations, in conjunction with a functional gradient technique for iteratively improving the control function.

Comparison of four stable numerical methods for Abel's integral equation

NASA Technical Reports Server (NTRS)

Murio, Diego A.; Mejia, Carlos E.

1991-01-01

The 3-D image reconstruction from cone-beam projections in computerized tomography leads naturally, in the case of radial symmetry, to the study of Abel-type integral equations. If the experimental information is obtained from measured data, on a discrete set of points, special methods are needed in order to restore continuity with respect to the data. A new combined Regularized-Adjoint-Conjugate Gradient algorithm, together with two different implementations of the Mollification Method (one based on a data filtering technique and the other on the mollification of the kernal function) and a regularization by truncation method (initially proposed for 2-D ray sample schemes and more recently extended to 3-D cone-beam image reconstruction) are extensively tested and compared for accuracy and numerical stability as functions of the level of noise in the data.

Spectral-Element Simulations of Wave Propagation in Porous Media: Finite-Frequency Sensitivity Kernels Based Upon Adjoint Methods

NASA Astrophysics Data System (ADS)

Morency, C.; Tromp, J.

2008-12-01

The mathematical formulation of wave propagation in porous media developed by Biot is based upon the principle of virtual work, ignoring processes at the microscopic level, and does not explicitly incorporate gradients in porosity. Based on recent studies focusing on averaging techniques, we derive the macroscopic porous medium equations from the microscale, with a particular emphasis on the effects of gradients in porosity. In doing so, we are able to naturally determine two key terms in the momentum equations and constitutive relationships, directly translating the coupling between the solid and fluid phases, namely a drag force and an interfacial strain tensor. In both terms, gradients in porosity arise. One remarkable result is that when we rewrite this set of equations in terms of the well known Biot variables us, w), terms involving gradients in porosity are naturally accommodated by gradients involving w, the fluid motion relative to the solid, and Biot's formulation is recovered, i.e., it remains valid in the presence of porosity gradients We have developed a numerical implementation of the Biot equations for two-dimensional problems based upon the spectral-element method (SEM) in the time domain. The SEM is a high-order variational method, which has the advantage of accommodating complex geometries like a finite-element method, while keeping the exponential convergence rate of (pseudo)spectral methods. As in the elastic and acoustic cases, poroelastic wave propagation based upon the SEM involves a diagonal mass matrix, which leads to explicit time integration schemes that are well-suited to simulations on parallel computers. Effects associated with physical dispersion & attenuation and frequency-dependent viscous resistance are addressed by using a memory variable approach. Various benchmarks involving poroelastic wave propagation in the high- and low-frequency regimes, and acoustic-poroelastic and poroelastic-poroelastic discontinuities have been successfully performed. We present finite-frequency sensitivity kernels for wave propagation in porous media based upon adjoint methods. We first show that the adjoint equations in porous media are similar to the regular Biot equations upon defining an appropriate adjoint source. Then we present finite-frequency kernels for seismic phases in porous media (e.g., fast P, slow P, and S). These kernels illustrate the sensitivity of seismic observables to structural parameters and form the basis of tomographic inversions. Finally, we show an application of this imaging technique related to the detection of buried landmines and unexploded ordnance (UXO) in porous environments.

PWR Facility Dose Modeling Using MCNP5 and the CADIS/ADVANTG Variance-Reduction Methodology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blakeman, Edward D; Peplow, Douglas E.; Wagner, John C

2007-09-01

The feasibility of modeling a pressurized-water-reactor (PWR) facility and calculating dose rates at all locations within the containment and adjoining structures using MCNP5 with mesh tallies is presented. Calculations of dose rates resulting from neutron and photon sources from the reactor (operating and shut down for various periods) and the spent fuel pool, as well as for the photon source from the primary coolant loop, were all of interest. Identification of the PWR facility, development of the MCNP-based model and automation of the run process, calculation of the various sources, and development of methods for visually examining mesh tally filesmore » and extracting dose rates were all a significant part of the project. Advanced variance reduction, which was required because of the size of the model and the large amount of shielding, was performed via the CADIS/ADVANTG approach. This methodology uses an automatically generated three-dimensional discrete ordinates model to calculate adjoint fluxes from which MCNP weight windows and source bias parameters are generated. Investigative calculations were performed using a simple block model and a simplified full-scale model of the PWR containment, in which the adjoint source was placed in various regions. In general, it was shown that placement of the adjoint source on the periphery of the model provided adequate results for regions reasonably close to the source (e.g., within the containment structure for the reactor source). A modification to the CADIS/ADVANTG methodology was also studied in which a global adjoint source is weighted by the reciprocal of the dose response calculated by an earlier forward discrete ordinates calculation. This method showed improved results over those using the standard CADIS/ADVANTG approach, and its further investigation is recommended for future efforts.« less

Wavelet-based multiscale adjoint waveform-difference tomography using body and surface waves

NASA Astrophysics Data System (ADS)

Yuan, Y. O.; Simons, F. J.; Bozdag, E.

2014-12-01

We present a multi-scale scheme for full elastic waveform-difference inversion. Using a wavelet transform proves to be a key factor to mitigate cycle-skipping effects. We start with coarse representations of the seismogram to correct a large-scale background model, and subsequently explain the residuals in the fine scales of the seismogram to map the heterogeneities with great complexity. We have previously applied the multi-scale approach successfully to body waves generated in a standard model from the exploration industry: a modified two-dimensional elastic Marmousi model. With this model we explored the optimal choice of wavelet family, number of vanishing moments and decomposition depth. For this presentation we explore the sensitivity of surface waves in waveform-difference tomography. The incorporation of surface waves is rife with cycle-skipping problems compared to the inversions considering body waves only. We implemented an envelope-based objective function probed via a multi-scale wavelet analysis to measure the distance between predicted and target surface-wave waveforms in a synthetic model of heterogeneous near-surface structure. Our proposed method successfully purges the local minima present in the waveform-difference misfit surface. An elastic shallow model with 100~m in depth is used to test the surface-wave inversion scheme. We also analyzed the sensitivities of surface waves and body waves in full waveform inversions, as well as the effects of incorrect density information on elastic parameter inversions. Based on those numerical experiments, we ultimately formalized a flexible scheme to consider both body and surface waves in adjoint tomography. While our early examples are constructed from exploration-style settings, our procedure will be very valuable for the study of global network data.

Optimizing spectral wave estimates with adjoint-based sensitivity maps

NASA Astrophysics Data System (ADS)

Orzech, Mark; Veeramony, Jay; Flampouris, Stylianos

2014-04-01

A discrete numerical adjoint has recently been developed for the stochastic wave model SWAN. In the present study, this adjoint code is used to construct spectral sensitivity maps for two nearshore domains. The maps display the correlations of spectral energy levels throughout the domain with the observed energy levels at a selected location or region of interest (LOI/ROI), providing a full spectrum of values at all locations in the domain. We investigate the effectiveness of sensitivity maps based on significant wave height ( H s ) in determining alternate offshore instrument deployment sites when a chosen nearshore location or region is inaccessible. Wave and bathymetry datasets are employed from one shallower, small-scale domain (Duck, NC) and one deeper, larger-scale domain (San Diego, CA). The effects of seasonal changes in wave climate, errors in bathymetry, and multiple assimilation points on sensitivity map shapes and model performance are investigated. Model accuracy is evaluated by comparing spectral statistics as well as with an RMS skill score, which estimates a mean model-data error across all spectral bins. Results indicate that data assimilation from identified high-sensitivity alternate locations consistently improves model performance at nearshore LOIs, while assimilation from low-sensitivity locations results in lesser or no improvement. Use of sub-sampled or alongshore-averaged bathymetry has a domain-specific effect on model performance when assimilating from a high-sensitivity alternate location. When multiple alternate assimilation locations are used from areas of lower sensitivity, model performance may be worse than with a single, high-sensitivity assimilation point.

Assimilating Remote Ammonia Observations with a Refined Aerosol Thermodynamics Adjoint"

EPA Science Inventory

Ammonia emissions parameters in North America can be refined in order to improve the evaluation of modeled concentrations against observations. Here, we seek to do so by developing and applying the GEOS-Chem adjoint nested over North America to conductassimilation of observations...

Metallic and antiferromagnetic fixed points from gravity

NASA Astrophysics Data System (ADS)

Paul, Chandrima

2018-06-01

We consider SU(2) × U(1) gauge theory coupled to matter field in adjoints and study RG group flow. We constructed Callan-Symanzik equation and subsequent β functions and study the fixed points. We find there are two fixed points, showing metallic and antiferromagnetic behavior. We have shown that metallic phase develops an instability if certain parametric conditions are satisfied.

Classical gluon and graviton radiation from the bi-adjoint scalar double copy

NASA Astrophysics Data System (ADS)

Goldberger, Walter D.; Prabhu, Siddharth G.; Thompson, Jedidiah O.

2017-09-01

We find double-copy relations between classical radiating solutions in Yang-Mills theory coupled to dynamical color charges and their counterparts in a cubic bi-adjoint scalar field theory which interacts linearly with particles carrying bi-adjoint charge. The particular color-to-kinematics replacements we employ are motivated by the Bern-Carrasco-Johansson double-copy correspondence for on-shell amplitudes in gauge and gravity theories. They are identical to those recently used to establish relations between classical radiating solutions in gauge theory and in dilaton gravity. Our explicit bi-adjoint solutions are constructed to second order in a perturbative expansion, and map under the double copy onto gauge theory solutions which involve at most cubic gluon self-interactions. If the correspondence is found to persist to higher orders in perturbation theory, our results suggest the possibility of calculating gravitational radiation from colliding compact objects, directly from a scalar field with vastly simpler (purely cubic) Feynman vertices.

Direct and inverse modelling for environmental risk assessment and emission control

NASA Astrophysics Data System (ADS)

Penenko, V.; Baklanov, A.; Tsvetova, E.; Mahura, A.

2009-04-01

A concept of environmental modelling and its applications for Siberian regions are presented. The regions are considered both as sources and receptors of pollution as elements of the global climatic system. A methodology has been developed to build the combined methods of forward and inverse modelling for the problems of the air quality, environmental risk assessment and control. It is based on variational principles and methods of adjoint sensitivity theory. This allows obtaining the optimal numerical schemes and universal algorithm of the forward-inverse modelling. Following the concept, the functionals (describing the generalised characteristics of the processes, data, and models) are considered together with the basic model components. To combine all these elements in the frames of forward and inverse relations, we suppose that each of them may contain uncertainty. In this case, it is naturally to formulate a weak-constraint variational principle for the augmented functional which contains the model description in the form of integral identity and the cost functional including the total measure of all uncertainties. The stationary conditions for the augmented functional with respect to the variations its functional arguments define the mutually agreed structure of numerical schemes for forward and adjoint problems, and sensitivity relations. For quantitative risk assessment the following characteristics are useful: (i) values of goal functionals and their variations in a form of sensitivity relations; (ii) risk and sensitivity functions to the variations of the sources. It is convenient to take the risk function multiplied by the source function as a distributed risk measure. The variational technique provides the backward propagation of information, contained in the target functionals, to parameters and sources of the models through the sensitivity and uncertainty functions. This gives a base for realisation of the feedback algorithms and methods of control theory, which are necessary for formulation of multi-criteria optimisation accounting different constraints of ecological, economical, and social essence while solving environmental problems such as air pollution control, placement design for new industrial units, etc. The problems of the long-term environmental forecasting demand revealing the dynamical active zones and the areas of increased sensitivity to the variations of forcings (model parameters). The proposed methodology of accounting the climatic data into environmental studies is suitable for studying such problems. Analysis of the long-term behaviour of the global climatic system and orthogonal decomposition of the multivariate series of meteorological data with respect to the scales of processes allows identifying the activity centers and using this information for construction of scenarios for assessment of risk/vulnerability for sources/receptors. Such analysis for Siberian regions showed that Siberia is situated in areas which separate circulation systems of high energy activity. For winter, they are the Pacific and Atlantic energy-active zones, whereas the Arctic and South-Asian zones withstand in Siberia in summer. These facts allow an interpretation of climatic instability inherent in the region. During the autumn-winter season, the instability expresses as sharp alteration of weather cycles. The formation of Altai-Sayan cyclogenesis (which is of the same intensity as the Mediterranean) is observed for the warm seasons in the southern Siberia. In climatology it is referred as a lee-type cyclogenesis. This is the large scale phenomenon in the climatic system of the central part of Eurasia. Such specific hydrodynamic background defines environment quality in Siberia. From the point of view of system analysis, the methods of sensitivity theory, risk assessment and control along with scenario approach offer a tool which allows bringing the results of the global atmospheric and climatic studies onto the regional level. Namely, this level puts the concrete questions on the environment quality and its changes such as a choice of plausible strategy for sources control and mitigation of the man-induced impact on environment. Some environmental problems for Siberian regions are discussed, and a number of forward, adjoint and inverse problems for different risk sites and goal functionals are presented.

Low Boom Configuration Analysis with FUN3D Adjoint Simulation Framework

NASA Technical Reports Server (NTRS)

Park, Michael A.

2011-01-01

Off-body pressure, forces, and moments for the Gulfstream Low Boom Model are computed with a Reynolds Averaged Navier Stokes solver coupled with the Spalart-Allmaras (SA) turbulence model. This is the first application of viscous output-based adaptation to reduce estimated discretization errors in off-body pressure for a wing body configuration. The output adaptation approach is compared to an a priori grid adaptation technique designed to resolve the signature on the centerline by stretching and aligning the grid to the freestream Mach angle. The output-based approach produced good predictions of centerline and off-centerline measurements. Eddy viscosity predicted by the SA turbulence model increased significantly with grid adaptation. Computed lift as a function of drag compares well with wind tunnel measurements for positive lift, but predicted lift, drag, and pitching moment as a function of angle of attack has significant differences from the measured data. The sensitivity of longitudinal forces and moment to grid refinement is much smaller than the differences between the computed and measured data.

Stratospheric Water Vapor and the Asian Monsoon: An Adjoint Model Investigation

NASA Technical Reports Server (NTRS)

Olsen, Mark A.; Andrews, Arlyn E.

2003-01-01

A new adjoint model of the Goddard Parameterized Chemistry and Transport Model is used to investigate the role that the Asian monsoon plays in transporting water to the stratosphere. The adjoint model provides a unique perspective compared to non-diffusive and non-mixing Lagrangian trajectory analysis. The quantity of water vapor transported from the monsoon and the pathways into the stratosphere are examined. The emphasis is on the amount of water originating from the monsoon that contributes to the tropical tape recorder signal. The cross-tropopause flux of water from the monsoon to the midlatitude lower stratosphere will also be discussed.

NEMOTAM: tangent and adjoint models for the ocean modelling platform NEMO

NASA Astrophysics Data System (ADS)

Vidard, A.; Bouttier, P.-A.; Vigilant, F.

2015-04-01

Tangent linear and adjoint models (TAMs) are efficient tools to analyse and to control dynamical systems such as NEMO. They can be involved in a large range of applications such as sensitivity analysis, parameter estimation or the computation of characteristic vectors. A TAM is also required by the 4D-Var algorithm, which is one of the major methods in data assimilation. This paper describes the development and the validation of the tangent linear and adjoint model for the NEMO ocean modelling platform (NEMOTAM). The diagnostic tools that are available alongside NEMOTAM are detailed and discussed, and several applications are also presented.

NEMOTAM: tangent and adjoint models for the ocean modelling platform NEMO

NASA Astrophysics Data System (ADS)

Vidard, A.; Bouttier, P.-A.; Vigilant, F.

2014-10-01

The tangent linear and adjoint model (TAM) are efficient tools to analyse and to control dynamical systems such as NEMO. They can be involved in a large range of applications such as sensitivity analysis, parameter estimation or the computation of characteristics vectors. TAM is also required by the 4-D-VAR algorithm which is one of the major method in Data Assimilation. This paper describes the development and the validation of the Tangent linear and Adjoint Model for the NEMO ocean modelling platform (NEMOTAM). The diagnostic tools that are available alongside NEMOTAM are detailed and discussed and several applications are also presented.

On universal knot polynomials

NASA Astrophysics Data System (ADS)

Mironov, A.; Mkrtchyan, R.; Morozov, A.

2016-02-01

We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, respectively and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representations. Properties of universal polynomials and applications of these results are discussed.

Adjoint-state inversion of electric resistivity tomography data of seawater intrusion at the Argentona coastal aquifer (Spain)

NASA Astrophysics Data System (ADS)

Fernández-López, Sheila; Carrera, Jesús; Ledo, Juanjo; Queralt, Pilar; Luquot, Linda; Martínez, Laura; Bellmunt, Fabián

2016-04-01

Seawater intrusion in aquifers is a complex phenomenon that can be characterized with the help of electric resistivity tomography (ERT) because of the low resistivity of seawater, which underlies the freshwater floating on top. The problem is complex because of the need for joint inversion of electrical and hydraulic (density dependent flow) data. Here we present an adjoint-state algorithm to treat electrical data. This method is a common technique to obtain derivatives of an objective function, depending on potentials with respect to model parameters. The main advantages of it are its simplicity in stationary problems and the reduction of computational cost respect others methodologies. The relationship between the concentration of chlorides and the resistivity values of the field is well known. Also, these resistivities are related to the values of potentials measured using ERT. Taking this into account, it will be possible to define the different resistivities zones from the field data of potential distribution using the basis of inverse problem. In this case, the studied zone is situated in Argentona (Baix Maresme, Catalonia), where the values of chlorides obtained in some wells of the zone are too high. The adjoint-state method will be used to invert the measured data using a new finite element code in C ++ language developed in an open-source framework called Kratos. Finally, the information obtained numerically with our code will be checked with the information obtained with other codes.

Receptivity of a precessing vortex core to open-loop forcing in a swirling jet and its predictability by linear stability adjoint theory

NASA Astrophysics Data System (ADS)

Müller, Jens; Lückoff, Finn; Oberleithner, Kilian

2017-11-01

The precessing vortex core (PVC) is a dominant coherent structure which occurs in swirling jets such as in swirl-stabilised gas turbine combustors. It stems from a global hydrodynamic instability caused by an internal feedback mechanism within the jet core. In this work, open-loop forcing is applied to a generic non-reacting swirling jet to investigate its receptivity to external actuation regarding lock-in behaviour of the PVC for different streamwise positions and Reynolds numbers. The forcing is periodically exerted by zero net mass flux synthetic jets which are introduced radially through slits inside the duct walls upstream of the swirling jet's exit plane. Time-resolved pressure measurements are conducted to identify the PVC frequency and stereo PIV combined with proper orthogonal decomposition in the duct and free field is used to extract the mean flow and the PVC mode. The data is used in a global linear stability framework to gain the adjoint of the PVC which reveals the regions of highest receptivity to periodic forcing based on mean flow input only. This theoretical receptivity model is compared with the experimentally obtained receptivity results and the validity and applicability of the adjoint model for the prediction of optimal forcing positions is discussed.

Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation

NASA Technical Reports Server (NTRS)

Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David

1996-01-01

This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.

Optimization of computations for adjoint field and Jacobian needed in 3D CSEM inversion

NASA Astrophysics Data System (ADS)

Dehiya, Rahul; Singh, Arun; Gupta, Pravin K.; Israil, M.

2017-01-01

We present the features and results of a newly developed code, based on Gauss-Newton optimization technique, for solving three-dimensional Controlled-Source Electromagnetic inverse problem. In this code a special emphasis has been put on representing the operations by block matrices for conjugate gradient iteration. We show how in the computation of Jacobian, the matrix formed by differentiation of system matrix can be made independent of frequency to optimize the operations at conjugate gradient step. The coarse level parallel computing, using OpenMP framework, is used primarily due to its simplicity in implementation and accessibility of shared memory multi-core computing machine to almost anyone. We demonstrate how the coarseness of modeling grid in comparison to source (comp`utational receivers) spacing can be exploited for efficient computing, without compromising the quality of the inverted model, by reducing the number of adjoint calls. It is also demonstrated that the adjoint field can even be computed on a grid coarser than the modeling grid without affecting the inversion outcome. These observations were reconfirmed using an experiment design where the deviation of source from straight tow line is considered. Finally, a real field data inversion experiment is presented to demonstrate robustness of the code.

Data Assimilation on a Quantum Annealing Computer: Feasibility and Scalability

NASA Astrophysics Data System (ADS)

Nearing, G. S.; Halem, M.; Chapman, D. R.; Pelissier, C. S.

2014-12-01

Data assimilation is one of the ubiquitous and computationally hard problems in the Earth Sciences. In particular, ensemble-based methods require a large number of model evaluations to estimate the prior probability density over system states, and variational methods require adjoint calculations and iteration to locate the maximum a posteriori solution in the presence of nonlinear models and observation operators. Quantum annealing computers (QAC) like the new D-Wave housed at the NASA Ames Research Center can be used for optimization and sampling, and therefore offers a new possibility for efficiently solving hard data assimilation problems. Coding on the QAC is not straightforward: a problem must be posed as a Quadratic Unconstrained Binary Optimization (QUBO) and mapped to a spherical Chimera graph. We have developed a method for compiling nonlinear 4D-Var problems on the D-Wave that consists of five steps: Emulating the nonlinear model and/or observation function using radial basis functions (RBF) or Chebyshev polynomials. Truncating a Taylor series around each RBF kernel. Reducing the Taylor polynomial to a quadratic using ancilla gadgets. Mapping the real-valued quadratic to a fixed-precision binary quadratic. Mapping the fully coupled binary quadratic to a partially coupled spherical Chimera graph using ancilla gadgets. At present the D-Wave contains 512 qbits (with 1024 and 2048 qbit machines due in the next two years); this machine size allows us to estimate only 3 state variables at each satellite overpass. However, QAC's solve optimization problems using a physical (quantum) system, and therefore do not require iterations or calculation of model adjoints. This has the potential to revolutionize our ability to efficiently perform variational data assimilation, as the size of these computers grows in the coming years.

A level set-based topology optimization method for simultaneous design of elastic structure and coupled acoustic cavity using a two-phase material model

NASA Astrophysics Data System (ADS)

Noguchi, Yuki; Yamamoto, Takashi; Yamada, Takayuki; Izui, Kazuhiro; Nishiwaki, Shinji

2017-09-01

This papers proposes a level set-based topology optimization method for the simultaneous design of acoustic and structural material distributions. In this study, we develop a two-phase material model that is a mixture of an elastic material and acoustic medium, to represent an elastic structure and an acoustic cavity by controlling a volume fraction parameter. In the proposed model, boundary conditions at the two-phase material boundaries are satisfied naturally, avoiding the need to express these boundaries explicitly. We formulate a topology optimization problem to minimize the sound pressure level using this two-phase material model and a level set-based method that obtains topologies free from grayscales. The topological derivative of the objective functional is approximately derived using a variational approach and the adjoint variable method and is utilized to update the level set function via a time evolutionary reaction-diffusion equation. Several numerical examples present optimal acoustic and structural topologies that minimize the sound pressure generated from a vibrating elastic structure.

Gravity Wave Predictability and Dynamics in Deepwave

NASA Astrophysics Data System (ADS)

Doyle, J. D.; Fritts, D. C.; Smith, R. B.; Eckermann, S. D.; Taylor, M. J.; Dörnbrack, A.; Uddstrom, M.; Reynolds, C. A.; Reinecke, A.; Jiang, Q.

2015-12-01

The DEEP propagating gravity WAVE program (DEEPWAVE) is a comprehensive, airborne and ground-based measurement and modeling program centered on New Zealand and focused on providing a new understanding of gravity wave dynamics and impacts from the troposphere through the mesosphere and lower thermosphere (MLT). This program employed the NSF/NCAR GV (NGV) research aircraft from a base in New Zealand in a 6-week field measurement campaign in June-July 2014. During the field phase, the NGV was equipped with new lidar and airglow instruments, as well as dropwindsondes and a full suite of flight level instruments including the microwave temperature profiler (MTP), providing temperatures and vertical winds spanning altitudes from immediately above the NGV flight altitude (~13 km) to ~100 km. The region near New Zealand was chosen since all the relevant GW sources (e.g., mountains, cyclones, jet streams) occur strongly here, and upper-level winds in austral winter permit gravity waves to propagate to very high altitudes. The COAMPS adjoint modeling system provided forecast sensitivity in real time during the six-week DEEPWAVE field phase. Five missions were conducted using the NGV to observe regions of high forecast sensitivity, as diagnosed using the COAMPS adjoint model. In this presentation, we provide a summary of the sensitivity characteristics and explore the implications for predictability of low-level winds crucial for gravity wave launching, as well as predictability of gravity wave characteristics in the stratosphere. In general, the sensitive regions were characterized by localized strong dynamics, often involving intense baroclinic systems with deep convection. The results of the adjoint modeling system suggest that gravity wave launching and the characteristics of the gravity waves can be linked to these sensitive regions near frontal zones within baroclinic systems. The predictability links between the tropospheric fronts, cyclones, jet regions, and gravity waves that vertically propagate upward through the stratosphere will be addressed further in the presentation. We examine RF23 during DEEPWAVE, which sampled deep propagating gravity waves over Auckland and Macquarie Islands. We provide insight into the gravity wave dynamics through applying the COAMPS and its adjoint at high resolution.

Adjoint-based Simultaneous Estimation Method of Fault Slip and Asthenosphere Viscosity Using Large-Scale Finite Element Simulation of Viscoelastic Deformation

NASA Astrophysics Data System (ADS)

Agata, R.; Ichimura, T.; Hori, T.; Hirahara, K.; Hashimoto, C.; Hori, M.

2016-12-01

Estimation of the coseismic/postseismic slip using postseismic deformation observation data is an important topic in the field of geodetic inversion. Estimation methods for this purpose are expected to be improved by introducing numerical simulation tools (e.g. finite element (FE) method) of viscoelastic deformation, in which the computation model is of high fidelity to the available high-resolution crustal data. The authors have proposed a large-scale simulation method using such FE high-fidelity models (HFM), assuming use of a large-scale computation environment such as the K computer in Japan (Ichimura et al. 2016). On the other hand, the values of viscosity in the heterogeneous viscoelastic structure in the high-fidelity model are not trivial. In this study, we developed an adjoint-based optimization method incorporating HFM, in which fault slip and asthenosphere viscosity are simultaneously estimated. We carried out numerical experiments using synthetic crustal deformation data. We constructed an HFM in the domain of 2048x1536x850 km, which includes the Tohoku region in northeast Japan based on Ichimura et al. (2013). We used the model geometry data set of JTOPO30 (2003), Koketsu et al. (2008) and CAMP standard model (Hashimoto et al. 2004). The geometry of crustal structures in HFM is in 1km resolution, resulting in 36 billion degrees-of-freedom. Synthetic crustal deformation data due to prescribed coseismic slip and after slips in the location of GEONET, GPS/A observation points, and S-net are used. The target inverse analysis is formulated as minimization of L2 norm of the difference between the FE simulation results and the observation data with respect to viscosity and fault slip, combining the quasi-Newton algorithm with the adjoint method. Use of this combination decreases the necessary number of forward analyses in the optimization calculation. As a result, we are now able to finish the estimation using 2560 computer nodes of the K computer for less than 17 hours. Thus, the target inverse analysis is completed in a realistic time because of the combination of the fast solver and the adjoint method. In the future, we would like to apply the method to the actual data.

Electron Cyclotron Current Drive Efficiency in General Tokamak Geometry and Its Application to Advanced Tokamak Plasmas

NASA Astrophysics Data System (ADS)

Lin-Liu, Y. R.; Chan, V. S.; Luce, T. C.; Prater, R.

1998-11-01

Owing to relativistic mass shift in the cyclotron resonance condition, a simple and accurate interpolation formula for estimating the current drive efficiency, such as those(S.C. Chiu et al.), Nucl. Fusion 29, 2175 (1989).^,(D.A. Ehst and C.F.F. Karney, Nucl. Fusion 31), 1933 (1991). commonly used in FWCD, is not available in the case of ECCD. In this work, we model ECCD using the adjoint techniques. A semi-analytic adjoint function appropriate for general tokamak geometry is obtained using Fisch's relativistic collision model. Predictions of off-axis ECCD qualitatively and semi-quantitatively agrees with those of Cohen,(R.H. Cohen, Phys. Fluids 30), 2442 (1987). currently implemented in the raytracing code TORAY. The dependences of the current drive efficiency on the wave launch configuration and the plasma parameters will be presented. Strong absorption of the wave away from the resonance layer is shown to be an important factor in optimizing the off-axis ECCD for application to advanced tokamak operations.

Detection of critical PM2.5 emission sources and their contributions to a heavy haze episode in Beijing, China, using an adjoint model

NASA Astrophysics Data System (ADS)

Zhai, Shixian; An, Xingqin; Zhao, Tianliang; Sun, Zhaobin; Wang, Wei; Hou, Qing; Guo, Zengyuan; Wang, Chao

2018-05-01

Air pollution sources and their regional transport are important issues for air quality control. The Global-Regional Assimilation and Prediction System coupled with the China Meteorological Administration Unified Atmospheric Chemistry Environment (GRAPES-CUACE) aerosol adjoint model was applied to detect the sensitive primary emission sources of a haze episode in Beijing occurring between 19 and 21 November 2012. The high PM2.5 concentration peaks occurring at 05:00 and 23:00 LT (GMT+8) over Beijing on 21 November 2012 were set as the cost functions for the aerosol adjoint model. The critical emission regions of the first PM2.5 concentration peak were tracked to the west and south of Beijing, with 2 to 3 days of cumulative transport of air pollutants to Beijing. The critical emission regions of the second peak were mainly located to the south of Beijing, where southeasterly moist air transport led to the hygroscopic growth of particles and pollutant convergence in front of the Taihang Mountains during the daytime on 21 November. The temporal variations in the sensitivity coefficients for the two PM2.5 concentration peaks revealed that the response time of the onset of Beijing haze pollution from the local primary emissions is approximately 1-2 h and that from the surrounding primary emissions it is approximately 7-12 h. The upstream Hebei province has the largest impact on the two PM2.5 concentration peaks, and the contribution of emissions from Hebei province to the first PM2.5 concentration peak (43.6 %) is greater than that to the second PM2.5 concentration peak (41.5 %). The second most influential province for the 05:00 LT PM2.5 concentration peak is Beijing (31.2 %), followed by Shanxi (9.8 %), Tianjin (9.8 %), and Shandong (5.7 %). The second most influential province for the 23:00 LT PM2.5 concentration peak is Beijing (35.7 %), followed by Shanxi (8.1 %), Shandong (8.0 %), and Tianjin (6.7 %). The adjoint model results were compared with the forward sensitivity simulations of the Models-3/CMAQ system. The two modeling approaches are highly comparable in their assessments of atmospheric pollution control schemes for critical emission regions, but the adjoint method has higher computational efficiency than the forward sensitivity method. The results also imply that critical regional emission reduction could be more efficient than individual peak emission control for improving regional PM2.5 air quality.

Inverse problems in heterogeneous and fractured media using peridynamics

DOE PAGES

Turner, Daniel Z.; van Bloemen Waanders, Bart G.; Parks, Michael L.

2015-12-10

The following work presents an adjoint-based methodology for solving inverse problems in heterogeneous and fractured media using state-based peridynamics. We show that the inner product involving the peridynamic operators is self-adjoint. The proposed method is illustrated for several numerical examples with constant and spatially varying material parameters as well as in the context of fractures. We also present a framework for obtaining material parameters by integrating digital image correlation (DIC) with inverse analysis. This framework is demonstrated by evaluating the bulk and shear moduli for a sample of nuclear graphite using digital photographs taken during the experiment. The resulting measuredmore » values correspond well with other results reported in the literature. Lastly, we show that this framework can be used to determine the load state given observed measurements of a crack opening. Furthermore, this type of analysis has many applications in characterizing subsurface stress-state conditions given fracture patterns in cores of geologic material.« less

Cart3D Simulations for the First AIAA Sonic Boom Prediction Workshop

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J.; Nemec, Marian

2014-01-01

Simulation results for the First AIAA Sonic Boom Prediction Workshop (LBW1) are presented using an inviscid, embedded-boundary Cartesian mesh method. The method employs adjoint-based error estimation and adaptive meshing to automatically determine resolution requirements of the computational domain. Results are presented for both mandatory and optional test cases. These include an axisymmetric body of revolution, a 69deg delta wing model and a complete model of the Lockheed N+2 supersonic tri-jet with V-tail and flow through nacelles. In addition to formal mesh refinement studies and examination of the adjoint-based error estimates, mesh convergence is assessed by presenting simulation results for meshes at several resolutions which are comparable in size to the unstructured grids distributed by the workshop organizers. Data provided includes both the pressure signals required by the workshop and information on code performance in both memory and processing time. Various enhanced techniques offering improved simulation efficiency will be demonstrated and discussed.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

NASA Astrophysics Data System (ADS)

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; Wildey, T. M.; Pawlowski, R. P.

2016-09-01

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier-Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shadid, J.N., E-mail: jnshadi@sandia.gov; Department of Mathematics and Statistics, University of New Mexico; Smith, T.M.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts tomore » apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Comparison of some optimal control methods for the design of turbine blades

NASA Technical Reports Server (NTRS)

Desilva, B. M. E.; Grant, G. N. C.

1977-01-01

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Particle Creation at a Point Source by Means of Interior-Boundary Conditions

NASA Astrophysics Data System (ADS)

Lampart, Jonas; Schmidt, Julian; Teufel, Stefan; Tumulka, Roderich

2018-06-01

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cut-off (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC.

An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem

DOE PAGES

Goldberg, Daniel N.; Narayanan, Sri Hari Krishna; Hascoet, Laurent; ...

2016-05-20

We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enablingmore » larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. Finally, the methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.« less

A predictive control framework for optimal energy extraction of wind farms

NASA Astrophysics Data System (ADS)

Vali, M.; van Wingerden, J. W.; Boersma, S.; Petrović, V.; Kühn, M.

2016-09-01

This paper proposes an adjoint-based model predictive control for optimal energy extraction of wind farms. It employs the axial induction factor of wind turbines to influence their aerodynamic interactions through the wake. The performance index is defined here as the total power production of the wind farm over a finite prediction horizon. A medium-fidelity wind farm model is utilized to predict the inflow propagation in advance. The adjoint method is employed to solve the formulated optimization problem in a cost effective way and the first part of the optimal solution is implemented over the control horizon. This procedure is repeated at the next controller sample time providing the feedback into the optimization. The effectiveness and some key features of the proposed approach are studied for a two turbine test case through simulations.

Raw Pressure Data from Boise Hydrogeophysical Research Site (BHRS)

DOE Data Explorer

David Lim

2013-07-17

Pressure data from a phreatic aquifer was collected in the summer of 2013 during Multi-frequency Oscillatory Hydraulic Tomography pumping tests. All tests were performed at the Boise Hydrogeophysical Research Site. The data will be inverted using a fast steady-periodic adjoint-based inverse code.

Fully automatic time-window selection using machine learning for global adjoint tomography

NASA Astrophysics Data System (ADS)

Chen, Y.; Hill, J.; Lei, W.; Lefebvre, M. P.; Bozdag, E.; Komatitsch, D.; Tromp, J.

2017-12-01

Selecting time windows from seismograms such that the synthetic measurements (from simulations) and measured observations are sufficiently close is indispensable in a global adjoint tomography framework. The increasing amount of seismic data collected everyday around the world demands "intelligent" algorithms for seismic window selection. While the traditional FLEXWIN algorithm can be "automatic" to some extent, it still requires both human input and human knowledge or experience, and thus is not deemed to be fully automatic. The goal of intelligent window selection is to automatically select windows based on a learnt engine that is built upon a huge number of existing windows generated through the adjoint tomography project. We have formulated the automatic window selection problem as a classification problem. All possible misfit calculation windows are classified as either usable or unusable. Given a large number of windows with a known selection mode (select or not select), we train a neural network to predict the selection mode of an arbitrary input window. Currently, the five features we extract from the windows are its cross-correlation value, cross-correlation time lag, amplitude ratio between observed and synthetic data, window length, and minimum STA/LTA value. More features can be included in the future. We use these features to characterize each window for training a multilayer perceptron neural network (MPNN). Training the MPNN is equivalent to solve a non-linear optimization problem. We use backward propagation to derive the gradient of the loss function with respect to the weighting matrices and bias vectors and use the mini-batch stochastic gradient method to iteratively optimize the MPNN. Numerical tests show that with a careful selection of the training data and a sufficient amount of training data, we are able to train a robust neural network that is capable of detecting the waveforms in an arbitrary earthquake data with negligible detection error compared to existing selection methods (e.g. FLEXWIN). We will introduce in detail the mathematical formulation of the window-selection-oriented MPNN and show very encouraging results when applying the new algorithm to real earthquake data.

Variational data assimilation for the initial-value dynamo problem.

PubMed

Li, Kuan; Jackson, Andrew; Livermore, Philip W

2011-11-01

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries.

An algorithm for variational data assimilation of contact concentration measurements for atmospheric chemistry models

NASA Astrophysics Data System (ADS)

Penenko, Alexey; Penenko, Vladimir

2014-05-01

Contact concentration measurement data assimilation problem is considered for convection-diffusion-reaction models originating from the atmospheric chemistry study. High dimensionality of models imposes strict requirements on the computational efficiency of the algorithms. Data assimilation is carried out within the variation approach on a single time step of the approximated model. A control function is introduced into the source term of the model to provide flexibility for data assimilation. This function is evaluated as the minimum of the target functional that connects its norm to a misfit between measured and model-simulated data. In the case mathematical model acts as a natural Tikhonov regularizer for the ill-posed measurement data inversion problem. This provides flow-dependent and physically-plausible structure of the resulting analysis and reduces a need to calculate model error covariance matrices that are sought within conventional approach to data assimilation. The advantage comes at the cost of the adjoint problem solution. This issue is solved within the frameworks of splitting-based realization of the basic convection-diffusion-reaction model. The model is split with respect to physical processes and spatial variables. A contact measurement data is assimilated on each one-dimensional convection-diffusion splitting stage. In this case a computationally-efficient direct scheme for both direct and adjoint problem solution can be constructed based on the matrix sweep method. Data assimilation (or regularization) parameter that regulates ratio between model and data in the resulting analysis is obtained with Morozov discrepancy principle. For the proper performance the algorithm takes measurement noise estimation. In the case of Gaussian errors the probability that the used Chi-squared-based estimate is the upper one acts as the assimilation parameter. A solution obtained can be used as the initial guess for data assimilation algorithms that assimilate outside the splitting stages and involve iterations. Splitting method stage that is responsible for chemical transformation processes is realized with the explicit discrete-analytical scheme with respect to time. The scheme is based on analytical extraction of the exponential terms from the solution. This provides unconditional positive sign for the evaluated concentrations. Splitting-based structure of the algorithm provides means for efficient parallel realization. The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004.

Ames Optimized TCA Configuration

NASA Technical Reports Server (NTRS)

Cliff, Susan E.; Reuther, James J.; Hicks, Raymond M.

1999-01-01

Configuration design at Ames was carried out with the SYN87-SB (single block) Euler code using a 193 x 49 x 65 C-H grid. The Euler solver is coupled to the constrained (NPSOL) and the unconstrained (QNMDIF) optimization packages. Since the single block grid is able to model only wing-body configurations, the nacelle/diverter effects were included in the optimization process by SYN87's option to superimpose the nacelle/diverter interference pressures on the wing. These interference pressures were calculated using the AIRPLANE code. AIRPLANE is an Euler solver that uses a unstructured tetrahedral mesh and is capable of computations about arbitrary complete configurations. In addition, the buoyancy effects of the nacelle/diverters were also included in the design process by imposing the pressure field obtained during the design process onto the triangulated surfaces of the nacelle/diverter mesh generated by AIRPLANE. The interference pressures and nacelle buoyancy effects are added to the final forces after each flow field calculation. Full details of the (recently enhanced) ghost nacelle capability are given in a related talk. The pseudo nacelle corrections were greatly improved during this design cycle. During the Ref H and Cycle 1 design activities, the nacelles were only translated and pitched. In the cycle 2 design effort the nacelles can translate vertically, and pitch to accommodate the changes in the lower surface geometry. The diverter heights (between their leading and trailing edges) were modified during design as the shape of the lower wing changed, with the drag of the diverter changing accordingly. Both adjoint and finite difference gradients were used during optimization. The adjoint-based gradients were found to give good direction in the design space for configurations near the starting point, but as the design approached a minimum, the finite difference gradients were found to be more accurate. Use of finite difference gradients was limited by the CPU time limit available on the Cray machines. A typical optimization run using finite difference gradients can use only 30 to 40 design variables and one optimization iteration within the 8 hour queue limit for the chosen grid size and convergence level. The efficiency afforded by the adjoint method allowed for 50-120 design variables and 5-10 optimization iterations in the 8 hour queue. Geometric perturbations to the wing and fuselage were made using the Hicks/Henne (HH) shape functions. The HH functions were distributed uniformly along the chords of the wing defining sections and lofted linearly. During single-surface design, constraints on thickness and volume at selected wing stations were imposed. Both fuselage camber and cross-sectional area distributions were permitted to change during design. The major disadvantage to the use of these functions is the inherent surface waviness produced by repeated use of such functions. Many smoothing operations were required following optimization runs to produce a configuration with reasonable smoothness. Wagner functions were also used on the wing sections but were never used on the fuselage. The Wagner functions are a family of increasingly oscillatory functions that have also been used extensively in airfoil design. The leading and trailing edge regions of the wing were designed by use of polynomial and monomial functions respectively. Twist was attempted but was abandoned because of little performance improvement available from changing the baseline twist.

Prediction of Broadband Shock-Associated Noise Including Propagation Effects Originating NASA

NASA Technical Reports Server (NTRS)

Miller, Steven; Morris, Philip J.

2012-01-01

An acoustic analogy is developed based on the Euler equations for broadband shock-associated noise (BBSAN) that directly incorporates the vector Green s function of the linearized Euler equations and a steady Reynolds-Averaged Navier-Stokes solution (SRANS) to describe the mean flow. The vector Green s function allows the BBSAN propagation through the jet shear layer to be determined. The large-scale coherent turbulence is modeled by two-point second order velocity cross-correlations. Turbulent length and time scales are related to the turbulent kinetic energy and dissipation rate. An adjoint vector Green s function solver is implemented to determine the vector Green s function based on a locally parallel mean flow at different streamwise locations. The newly developed acoustic analogy can be simplified to one that uses the Green s function associated with the Helmholtz equation, which is consistent with a previous formulation by the authors. A large number of predictions are generated using three different nozzles over a wide range of fully-expanded jet Mach numbers and jet stagnation temperatures. These predictions are compared with experimental data from multiple jet noise experimental facilities. In addition, two models for the so-called fine-scale mixing noise are included in the comparisons. Improved BBSAN predictions are obtained relative to other models that do not include propagation effects.

Time reversal imaging, Inverse problems and Adjoint Tomography}

NASA Astrophysics Data System (ADS)

Montagner, J.; Larmat, C. S.; Capdeville, Y.; Kawakatsu, H.; Fink, M.

2010-12-01

With the increasing power of computers and numerical techniques (such as spectral element methods), it is possible to address a new class of seismological problems. The propagation of seismic waves in heterogeneous media is simulated more and more accurately and new applications developed, in particular time reversal methods and adjoint tomography in the three-dimensional Earth. Since the pioneering work of J. Claerbout, theorized by A. Tarantola, many similarities were found between time-reversal methods, cross-correlations techniques, inverse problems and adjoint tomography. By using normal mode theory, we generalize the scalar approach of Draeger and Fink (1999) and Lobkis and Weaver (2001) to the 3D- elastic Earth, for theoretically understanding time-reversal method on global scale. It is shown how to relate time-reversal methods on one hand, with auto-correlations of seismograms for source imaging and on the other hand, with cross-correlations between receivers for structural imaging and retrieving Green function. Time-reversal methods were successfully applied in the past to acoustic waves in many fields such as medical imaging, underwater acoustics, non destructive testing and to seismic waves in seismology for earthquake imaging. In the case of source imaging, time reversal techniques make it possible an automatic location in time and space as well as the retrieval of focal mechanism of earthquakes or unknown environmental sources . We present here some applications at the global scale of these techniques on synthetic tests and on real data, such as Sumatra-Andaman (Dec. 2004), Haiti (Jan. 2010), as well as glacial earthquakes and seismic hum.

Combining Ensemble and Variational Data Assimilation

DTIC Science & Technology

2013-09-30

the river plume, simulating the effect of more turbid waters within the plume). Analysis of adjoint sensitivity fields and representer functions...that the are many assimilated temperature and salinity profiles to the north of the Hawaiian Islands, but very few to the south and west .] 5...Great Barrier Reef, the Great Australian Bight, parts of the north– west shelf, and the Gulf of Carpentaria. The assessment of IMOS performed by Oke

Backward semi-linear parabolic equations with time-dependent coefficients and local Lipschitz source

NASA Astrophysics Data System (ADS)

Nho Hào, Dinh; Van Duc, Nguyen; Van Thang, Nguyen

2018-05-01

Let H be a Hilbert space with the inner product and the norm , a positive self-adjoint unbounded time-dependent operator on H and . We establish stability estimates of Hölder type and propose a regularization method with error estimates of Hölder type for the ill-posed backward semi-linear parabolic equation with the source function f satisfying a local Lipschitz condition.

Transmutation approximations for the application of hybrid Monte Carlo/deterministic neutron transport to shutdown dose rate analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biondo, Elliott D.; Wilson, Paul P. H.

In fusion energy systems (FES) neutrons born from burning plasma activate system components. The photon dose rate after shutdown from resulting radionuclides must be quantified. This shutdown dose rate (SDR) is calculated by coupling neutron transport, activation analysis, and photon transport. The size, complexity, and attenuating configuration of FES motivate the use of hybrid Monte Carlo (MC)/deterministic neutron transport. The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) method can be used to optimize MC neutron transport for coupled multiphysics problems, including SDR analysis, using deterministic estimates of adjoint flux distributions. When used for SDR analysis, MS-CADIS requires the formulation ofmore » an adjoint neutron source that approximates the transmutation process. In this work, transmutation approximations are used to derive a solution for this adjoint neutron source. It is shown that these approximations are reasonably met for typical FES neutron spectra and materials over a range of irradiation scenarios. When these approximations are met, the Groupwise Transmutation (GT)-CADIS method, proposed here, can be used effectively. GT-CADIS is an implementation of the MS-CADIS method for SDR analysis that uses a series of single-energy-group irradiations to calculate the adjoint neutron source. For a simple SDR problem, GT-CADIS provides speedups of 200 100 relative to global variance reduction with the Forward-Weighted (FW)-CADIS method and 9 ± 5 • 104 relative to analog. As a result, this work shows that GT-CADIS is broadly applicable to FES problems and will significantly reduce the computational resources necessary for SDR analysis.« less

Sensitivity analysis of a model of CO2 exchange in tundra ecosystems by the adjoint method

NASA Technical Reports Server (NTRS)

Waelbroek, C.; Louis, J.-F.

1995-01-01

A model of net primary production (NPP), decomposition, and nitrogen cycling in tundra ecosystems has been developed. The adjoint technique is used to study the sensitivity of the computed annual net CO2 flux to perturbation in initial conditions, climatic inputs, and model's main parameters describing current seasonal CO2 exchange in wet sedge tundra at Barrow, Alaska. The results show that net CO2 flux is most sensitive to parameters characterizing litter chemical composition and more sensitive to decomposition parameters than to NPP parameters. This underlines the fact that in nutrient-limited ecosystems, decomposition drives net CO2 exchange by controlling mineralization of main nutrients. The results also indicate that the short-term (1 year) response of wet sedge tundra to CO2-induced warming is a significant increase in CO2 emission, creating a positive feedback to atmosphreic CO2 accumulation. However, a cloudiness increase during the same year can severely alter this response and lead to either a slight decrease or a strong increase in emitted CO2, depending on its exact timing. These results demonstrate that the adjoint method is well suited to study systems encountering regime changes, as a single run of the adjoint model provides sensitivities of the net CO2 flux to perturbations in all parameters and variables at any time of the year. Moreover, it is shown that large errors due to the presence of thresholds can be avoided by first delimiting the range of applicability of the adjoint results.

Transmutation approximations for the application of hybrid Monte Carlo/deterministic neutron transport to shutdown dose rate analysis

DOE PAGES

Biondo, Elliott D.; Wilson, Paul P. H.

2017-05-08

In fusion energy systems (FES) neutrons born from burning plasma activate system components. The photon dose rate after shutdown from resulting radionuclides must be quantified. This shutdown dose rate (SDR) is calculated by coupling neutron transport, activation analysis, and photon transport. The size, complexity, and attenuating configuration of FES motivate the use of hybrid Monte Carlo (MC)/deterministic neutron transport. The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) method can be used to optimize MC neutron transport for coupled multiphysics problems, including SDR analysis, using deterministic estimates of adjoint flux distributions. When used for SDR analysis, MS-CADIS requires the formulation ofmore » an adjoint neutron source that approximates the transmutation process. In this work, transmutation approximations are used to derive a solution for this adjoint neutron source. It is shown that these approximations are reasonably met for typical FES neutron spectra and materials over a range of irradiation scenarios. When these approximations are met, the Groupwise Transmutation (GT)-CADIS method, proposed here, can be used effectively. GT-CADIS is an implementation of the MS-CADIS method for SDR analysis that uses a series of single-energy-group irradiations to calculate the adjoint neutron source. For a simple SDR problem, GT-CADIS provides speedups of 200 100 relative to global variance reduction with the Forward-Weighted (FW)-CADIS method and 9 ± 5 • 104 relative to analog. As a result, this work shows that GT-CADIS is broadly applicable to FES problems and will significantly reduce the computational resources necessary for SDR analysis.« less

Spectral monodromy of non-self-adjoint operators

NASA Astrophysics Data System (ADS)

Phan, Quang Sang

2014-01-01

In the present paper, we build a combinatorial invariant, called the "spectral monodromy" from the spectrum of a single (non-self-adjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting self-adjoint h-pseudodifferential operators, given by S. Vu Ngoc ["Quantum monodromy in integrable systems," Commun. Math. Phys. 203(2), 465-479 (1999)]. The first simple case that we treat in this work is a normal operator. In this case, the discrete spectrum can be identified with the joint spectrum of an integrable quantum system. The second more complex case we propose is a small perturbation of a self-adjoint operator with a classical integrability property. We show that the discrete spectrum (in a small band around the real axis) also has a combinatorial monodromy. The main difficulty in this case is that we do not know the description of the spectrum everywhere, but only in a Cantor type set. In addition, we also show that the corresponding monodromy can be identified with the classical monodromy, defined by J. Duistermaat ["On global action-angle coordinates," Commun. Pure Appl. Math. 33(6), 687-706 (1980)].

Fluorescence molecular imaging based on the adjoint radiative transport equation

NASA Astrophysics Data System (ADS)

Asllanaj, Fatmir; Addoum, Ahmad; Rodolphe Roche, Jean

2018-07-01

A new reconstruction algorithm for fluorescence diffuse optical tomography of biological tissues is proposed. The radiative transport equation in the frequency domain is used to model light propagation. The adjoint method studied in this work provides an efficient way for solving the inverse problem. The methodology is applied to a 2D tissue-like phantom subjected to a collimated laser beam. Indocyanine Green is used as fluorophore. Reconstructed images of the spatial fluorophore absorption distribution is assessed taking into account the residual fluorescence in the medium. We show that illuminating the tissue surface from a collimated centered direction near the inclusion gaves a better reconstruction quality. Two closely positioned inclusions can be accurately localized. Additionally, their fluorophore absorption coefficients can be quantified. However, the algorithm failes to reconstruct smaller or deeper inclusions. This is due to light attenuation in the medium. Reconstructions with noisy data are also achieved with a reasonable accuracy.

Toward Automatic Verification of Goal-Oriented Flow Simulations

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2014-01-01

We demonstrate the power of adaptive mesh refinement with adjoint-based error estimates in verification of simulations governed by the steady Euler equations. The flow equations are discretized using a finite volume scheme on a Cartesian mesh with cut cells at the wall boundaries. The discretization error in selected simulation outputs is estimated using the method of adjoint-weighted residuals. Practical aspects of the implementation are emphasized, particularly in the formulation of the refinement criterion and the mesh adaptation strategy. Following a thorough code verification example, we demonstrate simulation verification of two- and three-dimensional problems. These involve an airfoil performance database, a pressure signature of a body in supersonic flow and a launch abort with strong jet interactions. The results show reliable estimates and automatic control of discretization error in all simulations at an affordable computational cost. Moreover, the approach remains effective even when theoretical assumptions, e.g., steady-state and solution smoothness, are relaxed.

Spatial optimal disturbances in swept-wing boundary layers

NASA Astrophysics Data System (ADS)

Chen, Cheng

2018-04-01

With the use of the adjoint-based optimization method proposed by Tempelmann et al. (J. Fluid Mech., vol. 704, 2012, pp. 251-279), in which the parabolized stability equation (PSE) and so-called adjoint parabolized stability equation (APSE) are solved iteratively, we obtain the spatial optimal disturbance shape and investigate its dependence on the parameters of disturbance wave and wall condition, such as radial frequency ω and wall temperature Twall, in a swept-wing boundary layer flow. Further, the non-modal growth mechanism of this optimal disturbance has been also discussed, regarding its spatial evolution way in the streamwise direction. The results imply that the spanwise wavenumber, disturbance frequency and wall cooling do not change the physical mechanism of perturbation growth, just with a substantial effect on the magnitude of perturbation growth. Further, wall cooling may have enhancing or suppressing effect on spatial optimal disturbance growth, depending on the streamwise location.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Favorite, Jeffrey A.; Gonzalez, Esteban

Adjoint-based first-order perturbation theory is applied again to boundary perturbation problems. Rahnema developed a perturbation estimate that gives an accurate first-order approximation of a flux or reaction rate within a radioactive system when the boundary is perturbed. When the response of interest is the flux or leakage current on the boundary, the Roussopoulos perturbation estimate has long been used. The Rahnema and Roussopoulos estimates differ in one term. Our paper shows that the Rahnema and Roussopoulos estimates can be derived consistently, using different responses, from a single variational functional (due to Gheorghiu and Rahnema), resolving any apparent contradiction. In analyticmore » test problems, Rahnema’s estimate and the Roussopoulos estimate produce exact first derivatives of the response of interest when appropriately applied. We also present a realistic, nonanalytic test problem.« less

Simulation of a class of hazardous situations in the ICS «INM RAS - Baltic Sea»

NASA Astrophysics Data System (ADS)

Zakharova, Natalia; Agoshkov, Valery; Aseev, Nikita; Parmuzin, Eugene; Sheloput, Tateana; Shutyaev, Victor

2017-04-01

Development of Informational Computational Systems (ICS) for data assimilation procedures is one of multidisciplinary problems. To study and solve these problems one needs to apply modern results from different disciplines and recent developments in mathematical modeling, theory of adjoint equations and optimal control, inverse problems, numerical methods theory, numerical algebra, scientific computing and processing of satellite data. In this work the results on the ICS development for PC-ICS "INM RAS - Baltic Sea" are presented. We discuss practical problems studied by ICS. The System includes numerical model of the Baltic Sea thermodynamics, the new oil spill model describing the propagation of a slick at the Sea surface (Agoshkov, Aseev et al., 2014) and the optimal ship route calculating block (Agoshkov, Zayachkovsky et al., 2014). The ICS is based on the INMOM numerical model of the Baltic Sea thermodynamics (Zalesny et al., 2013). It is possible to calculate main hydrodynamic parameters (temperature, salinity, velocities, sea level) using user-friendly interface of the ICS. The System includes data assimilation procedures (Agoshkov, 2003, Parmuzin, Agoshkov, 2012) and one can use the block of variational assimilation of the sea surface temperature in order to obtain main hydrodynamic parameters. Main possibilities of the ICS and several numerical experiments are presented in the work. By the problem of risk control is meant a problem of determination of optimal resources quantity which are necessary for decreasing the risk to some acceptable value. Mass of oil slick is chosen as a function of control. For the realization of the random variable the quadratic "functional of cost" is introduced. It comprises cleaning costs and deviation of damage of oil pollution from its acceptable value. The problem of minimization of this functional is solved based on the methods of optimal control and the theory of adjoint equations. The solution of this problem is explicitly found. The study was supported by the Russian Foundation for Basic Research (project 16-31-00510) and by the Russian Science Foundation (project №14-11-00609). V. I. Agoshkov, Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). V. B. Zalesny, A. V. Gusev, V. O. Ivchenko, R. Tamsalu, and R. Aps, Numerical model of the Baltic Sea circulation. Russ. J. Numer. Anal. Math. Modelling 28 (2013), No. 1, 85-100. V.I. Agoshkov, A.O. Zayachkovskiy, R. Aps, P. Kujala, and J. Rytkönen. Risk theory based solution to the problem of optimal vessel route // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 69-78. Agoshkov, V., Aseev, N., Aps, R., Kujala, P., Rytkönen, J., Zalesny, V. The problem of control of oil pollution risk in the Baltic Sea // Russian Journal of Numerical Analysis and Mathematical Modelling. 2014. Volume 29, Issue 2, Pages 93-105. E. I. Parmuzin and V. I. Agoshkov, Numerical solution of the variational assimilation problem for sea surface temperature in the model of the Black Sea dynamics. Russ. J. Numer. Anal. Math. Modelling 27 (2012), No. 1, 69-94. Olof Liungman and Johan Mattsson. Scientic Documentation of Seatrack Web; physical processes, algorithms and references, 2011.

A forward-adjoint operator pair based on the elastic wave equation for use in transcranial photoacoustic computed tomography

PubMed Central

Mitsuhashi, Kenji; Poudel, Joemini; Matthews, Thomas P.; Garcia-Uribe, Alejandro; Wang, Lihong V.; Anastasio, Mark A.

2017-01-01

Photoacoustic computed tomography (PACT) is an emerging imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to an inverse source problem in which the initial pressure distribution is recovered from measurements of the radiated wavefield. A major challenge in transcranial PACT brain imaging is compensation for aberrations in the measured data due to the presence of the skull. Ultrasonic waves undergo absorption, scattering and longitudinal-to-shear wave mode conversion as they propagate through the skull. To properly account for these effects, a wave-equation-based inversion method should be employed that can model the heterogeneous elastic properties of the skull. In this work, a forward model based on a finite-difference time-domain discretization of the three-dimensional elastic wave equation is established and a procedure for computing the corresponding adjoint of the forward operator is presented. Massively parallel implementations of these operators employing multiple graphics processing units (GPUs) are also developed. The developed numerical framework is validated and investigated in computer19 simulation and experimental phantom studies whose designs are motivated by transcranial PACT applications. PMID:29387291

Robustness of reduced-order observer-based controllers in transitional 2D Blasius boundary layers

NASA Astrophysics Data System (ADS)

Belson, Brandt; Semeraro, Onofrio; Rowley, Clarence; Pralits, Jan; Henningson, Dan

2011-11-01

In this work, we seek to delay transition in the Blasius boundary layer. We trip the flow with an upstream disturbance and dampen the growth of the resulting structures downstream. The observer-based controllers use a single sensor and a single localized body force near the wall. To formulate the controllers, we first find a reduced-order model of the system via the Eigensystem Realization Algorithm (ERA), then find the H2 optimal controller for this reduced-order system. We find the resulting controllers are effective only when the sensor is upstream of the actuator (in a feedforward configuration), but as is expected, are sensitive to model uncertainty. When the sensor is downstream of the actuator (in a feedback configuration), the reduced-order observer-based controllers are not robust and ineffective on the full system. In order to investigate the robustness properties of the system, an iterative technique called the adjoint of the direct adjoint (ADA) is employed to find a full-dimensional H2 optimal controller. This avoids the reduced-order modelling step and serves as a reference point. ADA is promising for investigating the lack of robustness previously mentioned.

Output-Adaptive Tetrahedral Cut-Cell Validation for Sonic Boom Prediction

NASA Technical Reports Server (NTRS)

Park, Michael A.; Darmofal, David L.

2008-01-01

A cut-cell approach to Computational Fluid Dynamics (CFD) that utilizes the median dual of a tetrahedral background grid is described. The discrete adjoint is also calculated, which permits adaptation based on improving the calculation of a specified output (off-body pressure signature) in supersonic inviscid flow. These predicted signatures are compared to wind tunnel measurements on and off the configuration centerline 10 body lengths below the model to validate the method for sonic boom prediction. Accurate mid-field sonic boom pressure signatures are calculated with the Euler equations without the use of hybrid grid or signature propagation methods. Highly-refined, shock-aligned anisotropic grids were produced by this method from coarse isotropic grids created without prior knowledge of shock locations. A heuristic reconstruction limiter provided stable flow and adjoint solution schemes while producing similar signatures to Barth-Jespersen and Venkatakrishnan limiters. The use of cut-cells with an output-based adaptive scheme completely automated this accurate prediction capability after a triangular mesh is generated for the cut surface. This automation drastically reduces the manual intervention required by existing methods.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shadid, J. N.; Smith, T. M.; Cyr, E. C.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE PAGES

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; ...

2016-05-20

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

The development of global GRAPES 4DVAR

NASA Astrophysics Data System (ADS)

Liu, Yongzhu

2017-04-01

Four-dimensional variation data assimilation (4DVAR) has given a great contribution to the improvement of NWP system over the past twenty years. Therefore, our strategy is to develop an operational global 4D-Var system from the outset. The aim at the paper is to introduce the development of the global GRAPES four-dimensional variation data assimilation (4DVAR) using incremental analysis schemes and to presents results of a comparison between 4DVAR using 6-hour assimilation window and simplified physics during the minimization with three-dimensional variation data assimilation (3DVAR). The dynamical cores of the tangent-linear and adjoint models are developed directly based on the non-hydrostatic forecast model. In addition, the standard correctness checks have been performed. As well as the development adjoint codes, most of our work is focused on improving the computational efficiency since the bulk of the computational cost of 4D-Var is in the integration of the tangent-linear and adjoint models. In terms of tangent-linear model, the wall-clock time is reduced to about 1.2 times as much as one of nonlinear model through the optimizing of the software framework. The significant computational cost savings on adjoint model result from the removing the redundant recompilations of model trajectories. It is encouraging that the wall-clock time of adjoint model is less than 1.5 times as much as one of nonlinear model. The current difficulty is that the numerical scheme used within the linear model is based on strategically on the numeric of the corresponding nonlinear model. Further computational acceleration should be expected from the improvement on nonlinear numerical algorithm. A series of linearized physical parameterization schemes has been developed to improve the representation of perturbed fields in the linear model. It consists of horizontal and vertical diffusion, sub-grid scale orographic gravity wave drag, large-scale condensation and cumulus convection schemes. We also found the straightforward linearization based on the nonlinear physical scheme might lead to significant growing of spurious unstable perturbations. It is essential to simplify the linear physics with respect to the non-linear schemes. The improvement on the perturbed fields in the tangent-linear model is visible with the linear physics included, especially at the low level. GRAPES variation data assimilation system adopts the incremental approach. The work is ongoing to develop a pre-operational 4DVAR suite with 0.25° outer loop resolution and multiple outer-loops configurations. One 4DVAR analysis using 6-hour assimilation windows can be finished within 40-minutes when using the available conventional and satellite data. In summary, it was found that the analysis over the northern, southern hemispheres, tropical region and East Asian area of GRAPES 4DVAR performed better than GRAPES 3DVAR for one month experiments. Moreover, the forecast results show that northern and southern extra-tropical scores for GRAPES 4DVAR are already better than GRAPES 3DVAR, but the tropical performance needs further investigations. Therefore, the subsequent main improvements will aim to enhance its computational efficiency and accuracy in 2017. The global GRAPES 4DVAR is planned for operation in 2018.

On quantum integrability of the Landau-Lifshitz model

NASA Astrophysics Data System (ADS)

Melikyan, A.; Pinzul, A.

2009-10-01

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Investigating Sensitivity to Saharan Dust in Tropical Cyclone Formation Using Nasa's Adjoint Model

NASA Technical Reports Server (NTRS)

Holdaway, Daniel

2015-01-01

As tropical cyclones develop from easterly waves coming of the coast of Africa they interact with dust from the Sahara desert. There is a long standing debate over whether this dust inhibits or advances the developing storm and how much influence it has. Dust can surround the storm and absorb incoming solar radiation, cooling the air below. As a result an energy source for the system is potentially diminished, inhibiting growth of the storm. Alternatively dust may interact with clouds through micro-physical processes, for example by causing more moisture to condense, potentially increasing the strength. As a result of climate change, concentrations and amount of dust in the atmosphere will likely change. It it is important to properly understand its effect on tropical storm formation. The adjoint of an atmospheric general circulation model provides a very powerful tool for investigating sensitivity to initial conditions. The National Aeronautics and Space Administration (NASA) has recently developed an adjoint version of the Goddard Earth Observing System version 5 (GEOS-5) dynamical core, convection scheme, cloud model and radiation schemes. This is extended so that the interaction between dust and radiation is also accounted for in the adjoint model. This provides a framework for examining the sensitivity to dust in the initial conditions. Specifically the set up allows for an investigation into the extent to which dust affects cyclone strength through absorption of radiation. In this work we investigate the validity of using an adjoint model for examining sensitivity to dust in hurricane formation. We present sensitivity results for a number of systems that developed during the Atlantic hurricane season of 2006. During this period there was a significant outbreak of Saharan dust and it is has been argued that this outbreak was responsible for the relatively calm season. This period was also covered by an extensive observation campaign. It is shown that the adjoint can provide insight into the sensitivity and reveals a relatively low sensitivity to dust compared to, for example, the thermodynamic variables. However a secondary sensitivity though moisture is seen. If dust dries the air it can significantly reduce the cyclone intensity through the moisture.

Investigating sensitivity to Saharan dust in tropical cyclone formation using NASA's adjoint model

NASA Astrophysics Data System (ADS)

Holdaway, Daniel

2015-04-01

As tropical cyclones develop from easterly waves coming off the coast of Africa they interact with dust from the Sahara desert. There is a long standing debate over whether this dust inhibits or advances the developing storm and how much influence it has. Dust can surround the storm and absorb incoming solar radiation, cooling the air below. As a result an energy source for the system is potentially diminished, inhibiting growth of the storm. Alternatively dust may interact with clouds through micro-physical processes, for example by causing more moisture to condense, potentially increasing the strength. As a result of climate change, concentrations and amount of dust in the atmosphere will likely change. It it is important to properly understand its effect on tropical storm formation. The adjoint of an atmospheric general circulation model provides a very powerful tool for investigating sensitivity to initial conditions. The National Aeronautics and Space Administration (NASA) has recently developed an adjoint version of the Goddard Earth Observing System version 5 (GEOS-5) dynamical core, convection scheme, cloud model and radiation schemes. This is extended so that the interaction between dust and radiation is also accounted for in the adjoint model. This provides a framework for examining the sensitivity to dust in the initial conditions. Specifically the set up allows for an investigation into the extent to which dust affects cyclone strength through absorption of radiation. In this work we investigate the validity of using an adjoint model for examining sensitivity to dust in hurricane formation. We present sensitivity results for a number of systems that developed during the Atlantic hurricane season of 2006. During this period there was a significant outbreak of Saharan dust and it is has been argued that this outbreak was responsible for the relatively calm season. This period was also covered by an extensive observation campaign. It is shown that the adjoint can provide insight into the sensitivity and reveals a relatively low sensitivity to dust compared to, for example, the thermodynamic variables. However a secondary sensitivity though moisture is seen. If dust dries the air it can significantly reduce the cyclone intensity through the moisture.

Ozone Climate Penalty and Mortality in a Changing World

NASA Astrophysics Data System (ADS)

Hakami, A.; Zhao, S.; Pappin, A.; Mesbah, M.

2013-12-01

The expected increase in ozone concentrations with temperature is referred to as the climate penalty factor (CPF). Observed ozone trends have resulted in estimations of regional CPFs in the range of 1-3 ppb/K in the Eastern US, and larger values around the globe. We use the adjoint of a regional model (CMAQ) for attributing changes in ozone mortality and attainment metrics to increased temperature levels at each location in North America during the summer of 2007. Unlike previous forward sensitivity analysis studies, we estimate how changes in temperatures at various locations influence such policy-relevant metrics. Our analysis accounts for separate temperature impact pathways through gas-phase chemistry, moisture abundance, and biogenic emissions. We find that water vapor impact, while mostly negative, is positive and large for temperature changes in urban areas. We also find that increased biogenic emissions plays an important role in the overall temperature influence. Our simulations show a wide range of spatial variability in CPFs between -0.4 and 6.2 ppb/K with largest values in urban areas. We also estimate mortality-based CPFs of up to 4 deaths/K for each grid cell, again with large localization in urban areas. This amounts to an estimated 370 deaths/K for the 3-month period of the simulation. We find that this number is almost equivalent to 5% reduction in anthropogenic NOx emissions for each degree increase in temperature. We show how the CPF will change as the result progressive NOx emission controls from various anthropogenic sectors and sources at different locations. Our findings suggest that urban NOx control can be regarded as an adaptation strategy with regards to ozone air quality. Also, the strong temperature dependence in urban environments suggests that the health and attainment burden of urban heat island may be more substantial than previously thought. Spatial distribution of average adjoint-based CPFs Adjoint-based CPF and Mortality CPF (domainwide)

Seismic Window Selection and Misfit Measurements for Global Adjoint Tomography

NASA Astrophysics Data System (ADS)

Lei, W.; Bozdag, E.; Lefebvre, M.; Podhorszki, N.; Smith, J. A.; Tromp, J.

2013-12-01

Global Adjoint Tomography requires fast parallel processing of large datasets. After obtaing the preprocessed observed and synthetic seismograms, we use the open source software packages FLEXWIN (Maggi et al. 2007) to select time windows and MEASURE_ADJ to make measurements. These measurements define adjoint sources for data assimilation. Previous versions of these tools work on a pair of SAC files---observed and synthetic seismic data for the same component and station, and loop over all seismic records associated with one earthquake. Given the large number of stations and earthquakes, the frequent read and write operations create severe I/O bottlenecks on modern computing platforms. We present new versions of these tools utilizing a new seismic data format, namely the Adaptive Seismic Data Format(ASDF). This new format shows superior scalability for applications on high-performance computers and accommodates various types of data, including earthquake, industry and seismic interferometry datasets. ASDF also provides user-friendly APIs, which can be easily integrated into the adjoint tomography workflow and combined with other data processing tools. In addition to solving the I/O bottleneck, we are making several improvements to these tools. For example, FLEXWIN is tuned to select windows for different types of earthquakes. To capture their distinct features, we categorize earthquakes by their depths and frequency bands. Moreover, instead of only picking phases between the first P arrival and the surface-wave arrivals, our aim is to select and assimilate many other later prominent phases in adjoint tomography. For example, in the body-wave band (17 s - 60 s), we include SKS, sSKS and their multiple, while in the surface-wave band (60 s - 120 s) we incorporate major-arc surface waves.

Optimizing Spectral Wave Estimates with Adjoint-Based Sensitivity Maps

DTIC Science & Technology

2014-02-18

J, Orzech MD, Ngodock HE (2013) Validation of a wave data assimilation system based on SWAN. Geophys Res Abst, (15), EGU2013-5951-1, EGU General ...surface wave spectra. Sensitivity maps are generally constructed for a selected system indicator (e.g., vorticity) by computing the differential of...spectral action balance Eq. 2, generally initialized at the off- shore boundary with spectral wave and other outputs from regional models such as

Understanding Cirrus Ice Crystal Number Variability for Different Heterogeneous Ice Nucleation Spectra

NASA Technical Reports Server (NTRS)

Sullivan, Sylvia C.; Betancourt, Ricardo Morales; Barahona, Donifan; Nenes, Athanasios

2016-01-01

Along with minimizing parameter uncertainty, understanding the cause of temporal and spatial variability of the nucleated ice crystal number, Ni, is key to improving the representation of cirrus clouds in climate models. To this end, sensitivities of Ni to input variables like aerosol number and diameter provide valuable information about nucleation regime and efficiency for a given model formulation. Here we use the adjoint model of the adjoint of a cirrus formation parameterization (Barahona and Nenes, 2009b) to understand Ni variability for various ice-nucleating particle (INP) spectra. Inputs are generated with the Community Atmosphere Model version 5, and simulations are done with a theoretically derived spectrum, an empirical lab-based spectrum and two field-based empirical spectra that differ in the nucleation threshold for black carbon particles and in the active site density for dust. The magnitude and sign of Ni sensitivity to insoluble aerosol number can be directly linked to nucleation regime and efficiency of various INP. The lab-based spectrum calculates much higher INP efficiencies than field-based ones, which reveals a disparity in aerosol surface properties. Ni sensitivity to temperature tends to be low, due to the compensating effects of temperature on INP spectrum parameters; this low temperature sensitivity regime has been experimentally reported before but never deconstructed as done here.

Determination of the self-adjoint matrix Schrödinger operators without the bound state data

NASA Astrophysics Data System (ADS)

Xu, Xiao-Chuan; Yang, Chuan-Fu

2018-06-01

(i) For the matrix Schrödinger operator on the half line, it is shown that the scattering data, which consists of the scattering matrix and the bound state data, uniquely determines the potential and the boundary condition. It is also shown that only the scattering matrix uniquely determines the self-adjoint potential and the boundary condition if either the potential exponentially decreases fast enough or the potential is known a priori on (), where a is an any fixed positive number. (ii) For the matrix Schrödinger operator on the full line, it is shown that the left (or right) reflection coefficient uniquely determine the self-adjoint potential if either the potential exponentially decreases fast enough or the potential is known a priori on (or ()), where b is an any fixed number.

Adjoint equations and analysis of complex systems: Application to virus infection modelling

NASA Astrophysics Data System (ADS)

Marchuk, G. I.; Shutyaev, V.; Bocharov, G.

2005-12-01

Recent development of applied mathematics is characterized by ever increasing attempts to apply the modelling and computational approaches across various areas of the life sciences. The need for a rigorous analysis of the complex system dynamics in immunology has been recognized since more than three decades ago. The aim of the present paper is to draw attention to the method of adjoint equations. The methodology enables to obtain information about physical processes and examine the sensitivity of complex dynamical systems. This provides a basis for a better understanding of the causal relationships between the immune system's performance and its parameters and helps to improve the experimental design in the solution of applied problems. We show how the adjoint equations can be used to explain the changes in hepatitis B virus infection dynamics between individual patients.

SISYPHUS: A high performance seismic inversion factory

NASA Astrophysics Data System (ADS)

Gokhberg, Alexey; Simutė, Saulė; Boehm, Christian; Fichtner, Andreas

2016-04-01

In the recent years the massively parallel high performance computers became the standard instruments for solving the forward and inverse problems in seismology. The respective software packages dedicated to forward and inverse waveform modelling specially designed for such computers (SPECFEM3D, SES3D) became mature and widely available. These packages achieve significant computational performance and provide researchers with an opportunity to solve problems of bigger size at higher resolution within a shorter time. However, a typical seismic inversion process contains various activities that are beyond the common solver functionality. They include management of information on seismic events and stations, 3D models, observed and synthetic seismograms, pre-processing of the observed signals, computation of misfits and adjoint sources, minimization of misfits, and process workflow management. These activities are time consuming, seldom sufficiently automated, and therefore represent a bottleneck that can substantially offset performance benefits provided by even the most powerful modern supercomputers. Furthermore, a typical system architecture of modern supercomputing platforms is oriented towards the maximum computational performance and provides limited standard facilities for automation of the supporting activities. We present a prototype solution that automates all aspects of the seismic inversion process and is tuned for the modern massively parallel high performance computing systems. We address several major aspects of the solution architecture, which include (1) design of an inversion state database for tracing all relevant aspects of the entire solution process, (2) design of an extensible workflow management framework, (3) integration with wave propagation solvers, (4) integration with optimization packages, (5) computation of misfits and adjoint sources, and (6) process monitoring. The inversion state database represents a hierarchical structure with branches for the static process setup, inversion iterations, and solver runs, each branch specifying information at the event, station and channel levels. The workflow management framework is based on an embedded scripting engine that allows definition of various workflow scenarios using a high-level scripting language and provides access to all available inversion components represented as standard library functions. At present the SES3D wave propagation solver is integrated in the solution; the work is in progress for interfacing with SPECFEM3D. A separate framework is designed for interoperability with an optimization module; the workflow manager and optimization process run in parallel and cooperate by exchanging messages according to a specially designed protocol. A library of high-performance modules implementing signal pre-processing, misfit and adjoint computations according to established good practices is included. Monitoring is based on information stored in the inversion state database and at present implements a command line interface; design of a graphical user interface is in progress. The software design fits well into the common massively parallel system architecture featuring a large number of computational nodes running distributed applications under control of batch-oriented resource managers. The solution prototype has been implemented on the "Piz Daint" supercomputer provided by the Swiss Supercomputing Centre (CSCS).

Seeking Energy System Pathways to Reduce Ozone Damage to Ecosystems through Adjoint-based Sensitivity Analysis

NASA Astrophysics Data System (ADS)

Capps, S. L.; Pinder, R. W.; Loughlin, D. H.; Bash, J. O.; Turner, M. D.; Henze, D. K.; Percell, P.; Zhao, S.; Russell, M. G.; Hakami, A.

2014-12-01

Tropospheric ozone (O3) affects the productivity of ecosystems in addition to degrading human health. Concentrations of this pollutant are significantly influenced by precursor gas emissions, many of which emanate from energy production and use processes. Energy system optimization models could inform policy decisions that are intended to reduce these harmful effects if the contribution of precursor gas emissions to human health and ecosystem degradation could be elucidated. Nevertheless, determining the degree to which precursor gas emissions harm ecosystems and human health is challenging because of the photochemical production of ozone and the distinct mechanisms by which ozone causes harm to different crops, tree species, and humans. Here, the adjoint of a regional chemical transport model is employed to efficiently calculate the relative influences of ozone precursor gas emissions on ecosystem and human health degradation, which informs an energy system optimization. Specifically, for the summer of 2007 the Community Multiscale Air Quality (CMAQ) model adjoint is used to calculate the location- and sector-specific influences of precursor gas emissions on potential productivity losses for the major crops and sensitive tree species as well as human mortality attributable to chronic ozone exposure in the continental U.S. The atmospheric concentrations are evaluated with 12-km horizontal resolution with crop production and timber biomass data gridded similarly. These location-specific factors inform the energy production and use technologies selected in the MARKet ALlocation (MARKAL) model.

Domain decomposition method for the Baltic Sea based on theory of adjoint equation and inverse problem.

NASA Astrophysics Data System (ADS)

Lezina, Natalya; Agoshkov, Valery

2017-04-01

Domain decomposition method (DDM) allows one to present a domain with complex geometry as a set of essentially simpler subdomains. This method is particularly applied for the hydrodynamics of oceans and seas. In each subdomain the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations is solved. The problem of obtaining solution in the whole domain is that it is necessary to combine solutions in subdomains. For this purposes iterative algorithm is created and numerical experiments are conducted to investigate an effectiveness of developed algorithm using DDM. For symmetric operators in DDM, Poincare-Steklov's operators [1] are used, but for the problems of the hydrodynamics, it is not suitable. In this case for the problem, adjoint equation method [2] and inverse problem theory are used. In addition, it is possible to create algorithms for the parallel calculations using DDM on multiprocessor computer system. DDM for the model of the Baltic Sea dynamics is numerically studied. The results of numerical experiments using DDM are compared with the solution of the system of hydrodynamic equations in the whole domain. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments). [1] V.I. Agoshkov, Domain Decompositions Methods in the Mathematical Physics Problem // Numerical processes and systems, No 8, Moscow, 1991 (in Russian). [2] V.I. Agoshkov, Optimal Control Approaches and Adjoint Equations in the Mathematical Physics Problem, Institute of Numerical Mathematics, RAS, Moscow, 2003 (in Russian).

Crypto-Unitary Forms of Quantum Evolution Operators

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2013-06-01

The description of quantum evolution using unitary operator {u}(t)=exp(-i{h}t) requires that the underlying self-adjoint quantum Hamiltonian {h} remains time-independent. In a way extending the so called {PT}-symmetric quantum mechanics to the models with manifestly time-dependent "charge" {C}(t) we propose and describe an extension of such an exponential-operator approach to evolution to the manifestly time-dependent self-adjoint quantum Hamiltonians {h}(t).

Relationship between the mechanisms of gamma rhythm generation and the magnitude of the macroscopic phase response function in a population of excitatory and inhibitory modified quadratic integrate-and-fire neurons

NASA Astrophysics Data System (ADS)

Akao, Akihiko; Ogawa, Yutaro; Jimbo, Yasuhiko; Ermentrout, G. Bard; Kotani, Kiyoshi

2018-01-01

Gamma oscillations are thought to play an important role in brain function. Interneuron gamma (ING) and pyramidal interneuron gamma (PING) mechanisms have been proposed as generation mechanisms for these oscillations. However, the relation between the generation mechanisms and the dynamical properties of the gamma oscillation are still unclear. Among the dynamical properties of the gamma oscillation, the phase response function (PRF) is important because it encodes the response of the oscillation to inputs. Recently, the PRF for an inhibitory population of modified theta neurons that generate an ING rhythm was computed by the adjoint method applied to the associated Fokker-Planck equation (FPE) for the model. The modified theta model incorporates conductance-based synapses as well as the voltage and current dynamics. Here, we extended this previous work by creating an excitatory-inhibitory (E-I) network using the modified theta model and described the population dynamics with the corresponding FPE. We conducted a bifurcation analysis of the FPE to find parameter regions which generate gamma oscillations. In order to label the oscillatory parameter regions by their generation mechanisms, we defined ING- and PING-type gamma oscillation in a mathematically plausible way based on the driver of the inhibitory population. We labeled the oscillatory parameter regions by these generation mechanisms and derived PRFs via the adjoint method on the FPE in order to investigate the differences in the responses of each type of oscillation to inputs. PRFs for PING and ING mechanisms are derived and compared. We found the amplitude of the PRF for the excitatory population is larger in the PING case than in the ING case. Finally, the E-I population of the modified theta neuron enabled us to analyze the PRFs of PING-type gamma oscillation and the entrainment ability of E and I populations. We found a parameter region in which PRFs of E and I are both purely positive in the case of PING oscillations. The different entrainment abilities of E and I stimulation as governed by the respective PRFs was compared to direct simulations of finite populations of model neurons. We find that it is easier to entrain the gamma rhythm by stimulating the inhibitory population than by stimulating the excitatory population as has been found experimentally.

Neural networks for feedback feedforward nonlinear control systems.

PubMed

Parisini, T; Zoppoli, R

1994-01-01

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

Efficient Computation of Info-Gap Robustness for Finite Element Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stull, Christopher J.; Hemez, Francois M.; Williams, Brian J.

2012-07-05

A recent research effort at LANL proposed info-gap decision theory as a framework by which to measure the predictive maturity of numerical models. Info-gap theory explores the trade-offs between accuracy, that is, the extent to which predictions reproduce the physical measurements, and robustness, that is, the extent to which predictions are insensitive to modeling assumptions. Both accuracy and robustness are necessary to demonstrate predictive maturity. However, conducting an info-gap analysis can present a formidable challenge, from the standpoint of the required computational resources. This is because a robustness function requires the resolution of multiple optimization problems. This report offers anmore » alternative, adjoint methodology to assess the info-gap robustness of Ax = b-like numerical models solved for a solution x. Two situations that can arise in structural analysis and design are briefly described and contextualized within the info-gap decision theory framework. The treatments of the info-gap problems, using the adjoint methodology are outlined in detail, and the latter problem is solved for four separate finite element models. As compared to statistical sampling, the proposed methodology offers highly accurate approximations of info-gap robustness functions for the finite element models considered in the report, at a small fraction of the computational cost. It is noted that this report considers only linear systems; a natural follow-on study would extend the methodologies described herein to include nonlinear systems.« less

Coupling coefficients for tensor product representations of quantum SU(2)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Groenevelt, Wolter, E-mail: w.g.m.groenevelt@tudelft.nl

2014-10-15

We study tensor products of infinite dimensional irreducible {sup *}-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometricmore » orthogonal polynomials and q-Bessel-type functions.« less

5D Super Yang-Mills on Y p, q Sasaki-Einstein Manifolds

NASA Astrophysics Data System (ADS)

Qiu, Jian; Zabzine, Maxim

2015-01-01

On any simply connected Sasaki-Einstein five dimensional manifold one can construct a super Yang-Mills theory which preserves at least two supersymmetries. We study the special case of toric Sasaki-Einstein manifolds known as Y p, q manifolds. We use the localisation technique to compute the full perturbative part of the partition function. The full equivariant result is expressed in terms of a certain special function which appears to be a curious generalisation of the triple sine function. As an application of our general result we study the large N behaviour for the case of single hypermultiplet in adjoint representation and we derive the N 3-behaviour in this case.

Naval Research Laboratory Multiscale Targeting Guidance for T-PARC and TCS-08

DTIC Science & Technology

2010-01-01

Naval Research Laboratory Multiscale Targeting Guidance for T- PARC and TCS-08 CAROLYN A. REYNOLDS AND JAMES D. DOYLE Marine Meteorology Division...of The Observing System Research and Predictability Experiment (THORPEX) Pacific Asian Regional Campaign (T- PARC ) and the Office of Naval Research’s...These products were produced with 24-, 36-, and 48-h lead times. The nonhydrostatic adjoint system used during T- PARC /TCS-08 contains an exact adjoint to

Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces

NASA Astrophysics Data System (ADS)

Mantile, Andrea; Posilicano, Andrea; Sini, Mourad

2016-07-01

The theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic differential operator on Rn with linear boundary conditions on (a relatively open part of) a compact hypersurface. Our approach allows to obtain Kreĭn-like resolvent formulae where the reference operator coincides with the ;free; operator with domain H2 (Rn); this provides an useful tool for the scattering problem from a hypersurface. Concrete examples of this construction are developed in connection with the standard boundary conditions, Dirichlet, Neumann, Robin, δ and δ‧-type, assigned either on a (n - 1) dimensional compact boundary Γ = ∂ Ω or on a relatively open part Σ ⊂ Γ. Schatten-von Neumann estimates for the difference of the powers of resolvents of the free and the perturbed operators are also proven; these give existence and completeness of the wave operators of the associated scattering systems.

Generalized Ince Gaussian beams

NASA Astrophysics Data System (ADS)

Bandres, Miguel A.; Gutiérrez-Vega, Julio C.

2006-08-01

In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.

Sensitivity Kernels for the Cross-Convolution Measure: Eliminate the Source in Waveform Tomography

NASA Astrophysics Data System (ADS)

Menke, W. H.

2017-12-01

We use the adjoint method to derive sensitivity kernels for the cross-convolution measure, a goodness-of-fit criterion that is applicable to seismic data containing closely-spaced multiple arrivals, such as reverberating compressional waves and split shear waves. In addition to a general formulation, specific expressions for sensitivity with respect to density, Lamé parameter and shear modulus are derived for a isotropic elastic solid. As is typical of adjoint methods, the kernels depend upon an adjoint field, the source of which, in this case, is the reference displacement field, pre-multiplied by a matrix of cross-correlations of components of the observed field. We use a numerical simulation to evaluate the resolving power of a topographic inversion that employs the cross-convolution measure. The estimated resolving kernel shows is point-like, indicating that the cross-convolution measure will perform well in waveform tomography settings.

A double commutant theorem for Murray–von Neumann algebras

PubMed Central

Liu, Zhe

2012-01-01

Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double commutant theorem characterizes von Neumann algebras as those for which , where , the commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double commutant theorem for Murray–von Neumann algebras. PMID:22543165

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haghighat, A.; Sjoden, G.E.; Wagner, J.C.

In the past 10 yr, the Penn State Transport Theory Group (PSTTG) has concentrated its efforts on developing accurate and efficient particle transport codes to address increasing needs for efficient and accurate simulation of nuclear systems. The PSTTG's efforts have primarily focused on shielding applications that are generally treated using multigroup, multidimensional, discrete ordinates (S{sub n}) deterministic and/or statistical Monte Carlo methods. The difficulty with the existing public codes is that they require significant (impractical) computation time for simulation of complex three-dimensional (3-D) problems. For the S{sub n} codes, the large memory requirements are handled through the use of scratchmore » files (i.e., read-from and write-to-disk) that significantly increases the necessary execution time. Further, the lack of flexible features and/or utilities for preparing input and processing output makes these codes difficult to use. The Monte Carlo method becomes impractical because variance reduction (VR) methods have to be used, and normally determination of the necessary parameters for the VR methods is very difficult and time consuming for a complex 3-D problem. For the deterministic method, the authors have developed the 3-D parallel PENTRAN (Parallel Environment Neutral-particle TRANsport) code system that, in addition to a parallel 3-D S{sub n} solver, includes pre- and postprocessing utilities. PENTRAN provides for full phase-space decomposition, memory partitioning, and parallel input/output to provide the capability of solving large problems in a relatively short time. Besides having a modular parallel structure, PENTRAN has several unique new formulations and features that are necessary for achieving high parallel performance. For the Monte Carlo method, the major difficulty currently facing most users is the selection of an effective VR method and its associated parameters. For complex problems, generally, this process is very time consuming and may be complicated due to the possibility of biasing the results. In an attempt to eliminate this problem, the authors have developed the A{sup 3}MCNP (automated adjoint accelerated MCNP) code that automatically prepares parameters for source and transport biasing within a weight-window VR approach based on the S{sub n} adjoint function. A{sup 3}MCNP prepares the necessary input files for performing multigroup, 3-D adjoint S{sub n} calculations using TORT.« less

Data and Workflow Management Challenges in Global Adjoint Tomography

NASA Astrophysics Data System (ADS)

Lei, W.; Ruan, Y.; Smith, J. A.; Modrak, R. T.; Orsvuran, R.; Krischer, L.; Chen, Y.; Balasubramanian, V.; Hill, J.; Turilli, M.; Bozdag, E.; Lefebvre, M. P.; Jha, S.; Tromp, J.

2017-12-01

It is crucial to take the complete physics of wave propagation into account in seismic tomography to further improve the resolution of tomographic images. The adjoint method is an efficient way of incorporating 3D wave simulations in seismic tomography. However, global adjoint tomography is computationally expensive, requiring thousands of wavefield simulations and massive data processing. Through our collaboration with the Oak Ridge National Laboratory (ORNL) computing group and an allocation on Titan, ORNL's GPU-accelerated supercomputer, we are now performing our global inversions by assimilating waveform data from over 1,000 earthquakes. The first challenge we encountered is dealing with the sheer amount of seismic data. Data processing based on conventional data formats and processing tools (such as SAC), which are not designed for parallel systems, becomes our major bottleneck. To facilitate the data processing procedures, we designed the Adaptive Seismic Data Format (ASDF) and developed a set of Python-based processing tools to replace legacy FORTRAN-based software. These tools greatly enhance reproducibility and accountability while taking full advantage of highly parallel system and showing superior scaling on modern computational platforms. The second challenge is that the data processing workflow contains more than 10 sub-procedures, making it delicate to handle and prone to human mistakes. To reduce human intervention as much as possible, we are developing a framework specifically designed for seismic inversion based on the state-of-the art workflow management research, specifically the Ensemble Toolkit (EnTK), in collaboration with the RADICAL team from Rutgers University. Using the initial developments of the EnTK, we are able to utilize the full computing power of the data processing cluster RHEA at ORNL while keeping human interaction to a minimum and greatly reducing the data processing time. Thanks to all the improvements, we are now able to perform iterations fast enough on more than a 1,000 earthquakes dataset. Starting from model GLAD-M15 (Bozdag et al., 2016), an elastic 3D model with a transversely isotropic upper mantle, we have successfully performed 5 iterations. Our goal is to finish 10 iterations, i.e., generating GLAD M25* by the end of this year.

Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems

DOE PAGES

Favorite, Jeffrey A.; Gonzalez, Esteban

2017-03-10

Adjoint-based first-order perturbation theory is applied again to boundary perturbation problems. Rahnema developed a perturbation estimate that gives an accurate first-order approximation of a flux or reaction rate within a radioactive system when the boundary is perturbed. When the response of interest is the flux or leakage current on the boundary, the Roussopoulos perturbation estimate has long been used. The Rahnema and Roussopoulos estimates differ in one term. Our paper shows that the Rahnema and Roussopoulos estimates can be derived consistently, using different responses, from a single variational functional (due to Gheorghiu and Rahnema), resolving any apparent contradiction. In analyticmore » test problems, Rahnema’s estimate and the Roussopoulos estimate produce exact first derivatives of the response of interest when appropriately applied. We also present a realistic, nonanalytic test problem.« less

Optimization with Fuzzy Data via Evolutionary Algorithms

NASA Astrophysics Data System (ADS)

Kosiński, Witold

2010-09-01

Order fuzzy numbers (OFN) that make possible to deal with fuzzy inputs quantitatively, exactly in the same way as with real numbers, have been recently defined by the author and his 2 coworkers. The set of OFN forms a normed space and is a partially ordered ring. The case when the numbers are presented in the form of step functions, with finite resolution, simplifies all operations and the representation of defuzzification functionals. A general optimization problem with fuzzy data is formulated. Its fitness function attains fuzzy values. Since the adjoint space to the space of OFN is finite dimensional, a convex combination of all linear defuzzification functionals may be used to introduce a total order and a real-valued fitness function. Genetic operations on individuals representing fuzzy data are defined.

Global Adjoint Tomography: Next-Generation Models

NASA Astrophysics Data System (ADS)

Bozdag, Ebru; Lefebvre, Matthieu; Lei, Wenjie; Orsvuran, Ridvan; Peter, Daniel; Ruan, Youyi; Smith, James; Komatitsch, Dimitri; Tromp, Jeroen

2017-04-01

The first-generation global adjoint tomography model GLAD-M15 (Bozdag et al. 2016) is the result of 15 conjugate-gradient iterations based on GPU-accelerated spectral-element simulations of 3D wave propagation and Fréchet kernels. For simplicity, GLAD-M15 was constructed as an elastic model with transverse isotropy confined to the upper mantle. However, Earth's mantle and crust show significant evidence of anisotropy as a result of its composition and deformation. There may be different sources of seismic anisotropy affecting both body and surface waves. As a first attempt, we initially tackle with surface-wave anisotropy and proceed iterations using the same 253 earthquake data set used in GLAD-M15 with an emphasize on upper-mantle. Furthermore, we explore new misfits, such as double-difference measurements (Yuan et al. 2016), to better deal with the possible artifacts of the uneven distribution of seismic stations globally and minimize source uncertainties in structural inversions. We will present our observations with the initial results of azimuthally anisotropic inversions and also discuss the next generation global models with various parametrizations. Meanwhile our goal is to use all available seismic data in imaging. This however requires a solid framework to perform iterative adjoint tomography workflows with big data on supercomputers. We will talk about developments in adjoint tomography workflow from the need of defining new seismic and computational data formats (e.g., ASDF by Krischer et al. 2016, ADIOS by Liu et al. 2011) to developing new pre- and post-processing tools together with experimenting workflow management tools, such as Pegasus (Deelman et al. 2015). All our simulations are performed on Oak Ridge National Laboratory's Cray XK7 "Titan" system. Our ultimate aim is to get ready to harness ORNL's next-generation supercomputer "Summit", an IBM with Power-9 CPUs and NVIDIA Volta GPU accelerators, to be ready by 2018 which will enable us to reduce the shortest period in our global simulations from 17 s to 9 s, and exascale systems will reduce this further to just a few seconds.

Linearized radiative transfer models for retrieval of cloud parameters from EPIC/DSCOVR measurements

NASA Astrophysics Data System (ADS)

Molina García, Víctor; Sasi, Sruthy; Efremenko, Dmitry S.; Doicu, Adrian; Loyola, Diego

2018-07-01

In this paper, we describe several linearized radiative transfer models which can be used for the retrieval of cloud parameters from EPIC (Earth Polychromatic Imaging Camera) measurements. The approaches under examination are (1) the linearized forward approach, represented in this paper by the linearized discrete ordinate and matrix operator methods with matrix exponential, and (2) the forward-adjoint approach based on the discrete ordinate method with matrix exponential. To enhance the performance of the radiative transfer computations, the correlated k-distribution method and the Principal Component Analysis (PCA) technique are used. We provide a compact description of the proposed methods, as well as a numerical analysis of their accuracy and efficiency when simulating EPIC measurements in the oxygen A-band channel at 764 nm. We found that the computation time of the forward-adjoint approach using the correlated k-distribution method in conjunction with PCA is approximately 13 s for simultaneously computing the derivatives with respect to cloud optical thickness and cloud top height.

Usefulness of Wave Data Assimilation to the WAVE WATCH III Modeling System

NASA Astrophysics Data System (ADS)

Choi, J. K.; Dykes, J. D.; Yaremchuk, M.; Wittmann, P.

2017-12-01

In-situ and remote-sensed wave data are more abundant currently than in years past, with excellent accuracy at global scales. Forecast skill of the WAVE WATCH III model is improved by assimilation of these measurements and they are also useful for model validation and calibration. It has been known that the impact of assimilation in wind-sea conditions is not large, but spectra that result in large swell with long term propagation are identified and assimilated, the improved accuracy of the initial conditions improve the long-term forecasts. The Navy's assimilation method started with the simple Optimal Interpolation (OI) method. Operationally, Fleet Numerical Meteorology and Oceanography Center uses the sequential 2DVar scheme, but a new approach has been tested based on an adjoint-free method to variational assimilation in WAVE WATCH III. We will present the status of wave data assimilation into the WAVE WATCH III numerical model and upcoming development of this new adjoint-free variational approach.

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

NASA Astrophysics Data System (ADS)

Komatitsch, Dimitri; Xie, Zhinan; Bozdaǧ, Ebru; Sales de Andrade, Elliott; Peter, Daniel; Liu, Qinya; Tromp, Jeroen

2016-09-01

We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the Kα sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels.

Second level semi-degenerate fields in W_3 Toda theory: matrix element and differential equation

NASA Astrophysics Data System (ADS)

Belavin, Vladimir; Cao, Xiangyu; Estienne, Benoit; Santachiara, Raoul

2017-03-01

In a recent study we considered W_3 Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl_3 . We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.

Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goffin, Mark A., E-mail: mark.a.goffin@gmail.com; Buchan, Andrew G.; Dargaville, Steven

2015-01-15

A method for applying goal-based adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an inner-element sub-grid scale finite element method. The goal-based adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goal-based error estimators require the solution of an adjoint system to determine the importance to the specifiedmore » functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goal-based adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation. -- Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvements in computational efficiency.« less

Accurate reconstruction of the optical parameter distribution in participating medium based on the frequency-domain radiative transfer equation

NASA Astrophysics Data System (ADS)

Qiao, Yao-Bin; Qi, Hong; Zhao, Fang-Zhou; Ruan, Li-Ming

2016-12-01

Reconstructing the distribution of optical parameters in the participating medium based on the frequency-domain radiative transfer equation (FD-RTE) to probe the internal structure of the medium is investigated in the present work. The forward model of FD-RTE is solved via the finite volume method (FVM). The regularization term formatted by the generalized Gaussian Markov random field model is used in the objective function to overcome the ill-posed nature of the inverse problem. The multi-start conjugate gradient (MCG) method is employed to search the minimum of the objective function and increase the efficiency of convergence. A modified adjoint differentiation technique using the collimated radiative intensity is developed to calculate the gradient of the objective function with respect to the optical parameters. All simulation results show that the proposed reconstruction algorithm based on FD-RTE can obtain the accurate distributions of absorption and scattering coefficients. The reconstructed images of the scattering coefficient have less errors than those of the absorption coefficient, which indicates the former are more suitable to probing the inner structure. Project supported by the National Natural Science Foundation of China (Grant No. 51476043), the Major National Scientific Instruments and Equipment Development Special Foundation of China (Grant No. 51327803), and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51121004).

Chiral phases of fundamental and adjoint quarks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Natale, A. A.; Instituto de Física Teórica - UNESP Rua Dr. Bento T. Ferraz, 271, Bl.II - 01140-070, São Paulo, SP

2016-01-22

We consider a QCD chiral symmetry breaking model where the gap equation contains an effective confining propagator and a dressed gluon propagator with a dynamically generated mass. This model is able to explain the ratios between the chiral transition and deconfinement temperatures in the case of fundamental and adjoint quarks. It also predicts the recovery of the chiral symmetry for a large number of quarks (n{sub f} ≈ 11 – 13) in agreement with lattice data.

Towards efficient backward-in-time adjoint computations using data compression techniques

DOE PAGES

Cyr, E. C.; Shadid, J. N.; Wildey, T.

2014-12-16

In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for themore » difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintaining reasonable accuracy in the error-estimates.« less

Inverse modeling methods for indoor airborne pollutant tracking: literature review and fundamentals.

PubMed

Liu, X; Zhai, Z

2007-12-01

Reduction in indoor environment quality calls for effective control and improvement measures. Accurate and prompt identification of contaminant sources ensures that they can be quickly removed and contaminated spaces isolated and cleaned. This paper discusses the use of inverse modeling to identify potential indoor pollutant sources with limited pollutant sensor data. The study reviews various inverse modeling methods for advection-dispersion problems and summarizes the methods into three major categories: forward, backward, and probability inverse modeling methods. The adjoint probability inverse modeling method is indicated as an appropriate model for indoor air pollutant tracking because it can quickly find source location, strength and release time without prior information. The paper introduces the principles of the adjoint probability method and establishes the corresponding adjoint equations for both multi-zone airflow models and computational fluid dynamics (CFD) models. The study proposes a two-stage inverse modeling approach integrating both multi-zone and CFD models, which can provide a rapid estimate of indoor pollution status and history for a whole building. Preliminary case study results indicate that the adjoint probability method is feasible for indoor pollutant inverse modeling. The proposed method can help identify contaminant source characteristics (location and release time) with limited sensor outputs. This will ensure an effective and prompt execution of building management strategies and thus achieve a healthy and safe indoor environment. The method can also help design optimal sensor networks.

Choice of regularization in adjoint tomography based on two-dimensional synthetic tests

NASA Astrophysics Data System (ADS)

Valentová, Lubica; Gallovič, František; Růžek, Bohuslav; de la Puente, Josep; Moczo, Peter

2015-08-01

We present synthetic tests of 2-D adjoint tomography of surface wave traveltimes obtained by the ambient noise cross-correlation analysis across the Czech Republic. The data coverage may be considered perfect for tomography due to the density of the station distribution. Nevertheless, artefacts in the inferred velocity models arising from the data noise may be still observed when weak regularization (Gaussian smoothing of the misfit gradient) or too many iterations are considered. To examine the effect of the regularization and iteration number on the performance of the tomography in more detail we performed extensive synthetic tests. Instead of the typically used (although criticized) checkerboard test, we propose to carry out the tests with two different target models-simple smooth and complex realistic models. The first test reveals the sensitivity of the result on the data noise, while the second helps to analyse the resolving power of the data set. For various noise and Gaussian smoothing levels, we analysed the convergence towards (or divergence from) the target model with increasing number of iterations. Based on the tests we identified the optimal regularization, which we then employed in the inversion of 16 and 20 s Love-wave group traveltimes.

High-Fidelity Multidisciplinary Design Optimization of Aircraft Configurations

NASA Technical Reports Server (NTRS)

Martins, Joaquim R. R. A.; Kenway, Gaetan K. W.; Burdette, David; Jonsson, Eirikur; Kennedy, Graeme J.

2017-01-01

To evaluate new airframe technologies we need design tools based on high-fidelity models that consider multidisciplinary interactions early in the design process. The overarching goal of this NRA is to develop tools that enable high-fidelity multidisciplinary design optimization of aircraft configurations, and to apply these tools to the design of high aspect ratio flexible wings. We develop a geometry engine that is capable of quickly generating conventional and unconventional aircraft configurations including the internal structure. This geometry engine features adjoint derivative computation for efficient gradient-based optimization. We also added overset capability to a computational fluid dynamics solver, complete with an adjoint implementation and semiautomatic mesh generation. We also developed an approach to constraining buffet and started the development of an approach for constraining utter. On the applications side, we developed a new common high-fidelity model for aeroelastic studies of high aspect ratio wings. We performed optimal design trade-o s between fuel burn and aircraft weight for metal, conventional composite, and carbon nanotube composite wings. We also assessed a continuous morphing trailing edge technology applied to high aspect ratio wings. This research resulted in the publication of 26 manuscripts so far, and the developed methodologies were used in two other NRAs. 1

Adjoint-based optimization of mechanical performance in polycrystalline materials and structures through texture control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gu, Grace; Brown, Judith Alice; Bishop, Joseph E.

The texture of a polycrystalline material refers to the preferred orientation of the grains within the material. In metallic materials, texture can significantly affect the mechanical properties such as elastic moduli, yield stress, strain hardening, and fracture toughness. Recent advances in additive manufacturing of metallic materials offer the possibility in the not too distant future of controlling the spatial variation of texture. In this work, we investigate the advantages, in terms of mechanical performance, of allowing the texture to vary spatially. We use an adjoint-based gradient optimization algorithm within a finite element solver (COMSOL) to optimize several engineering quantities ofmore » interest in a simple structure (hole in a plate) and loading (uniaxial tension) condition. As a first step to general texture optimization, we consider the idealized case of a pure fiber texture in which the homogenized properties are transversely isotropic. In this special case, the only spatially varying design variables are the three Euler angles that prescribe the orientation of the homogenized material at each point within the structure. This work paves a new way to design metallic materials for tunable mechanical properties at the microstructure level.« less

Sensitivity analysis for the control of supersonic impinging jet noise

NASA Astrophysics Data System (ADS)

Nichols, Joseph W.; Hildebrand, Nathaniel

2016-11-01

The dynamics of a supersonic jet that impinges perpendicularly on a flat plate depend on complex interactions between fluid turbulence, shock waves, and acoustics. Strongly organized oscillations emerge, however, and they induce loud, often damaging, tones. We investigate this phenomenon using unstructured, high-fidelity Large Eddy Simulation (LES) and global stability analysis. Our flow configurations precisely match laboratory experiments with nozzle-to-wall distances of 4 and 4.5 jet diameters. We use multi-block shift-and-invert Arnoldi iteration to extract both direct and adjoint global modes that extend upstream into the nozzle. The frequency of the most unstable global mode agrees well with that of the emergent oscillations in the LES. We compute the "wavemaker" associated with this mode by multiplying it by its corresponding adjoint mode. The wavemaker shows that this instability is most sensitive to changes in the base flow slightly downstream of the nozzle exit. By modifying the base flow in this region, we then demonstrate that the flow can indeed be stabilized. This explains the success of microjets as an effective noise control measure when they are positioned around the nozzle lip. Computational resources were provided by the Argonne Leadership Computing Facility.

Quantum motion of a point particle in the presence of the Aharonov–Bohm potential in curved space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Silva, Edilberto O., E-mail: edilbertoo@gmail.com; Ulhoa, Sérgio C., E-mail: sc.ulhoa@gmail.com; Andrade, Fabiano M., E-mail: f.andrade@ucl.ac.uk

The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov–Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The geometry of this line element establishes that the motion of the particle can occur on the surface of a cone or an anti-cone. As a consequence of the nontrivial topology of the cone and also because of two-dimensional confinement, the geometric potential should be taken into account. At first, we establish the conditions for the particle describing a circular path in suchmore » a context. Because of the presence of the geometric potential, which contains a singular term, we use the self-adjoint extension method in order to describe the dynamics in all space including the singularity. Expressions are obtained for the bound state energies and wave functions. -- Highlights: •Motion of particle under the influence of magnetic field in curved space. •Bound state for Aharonov–Bohm problem. •Particle describing a circular path. •Determination of the self-adjoint extension parameter.« less

Understanding cirrus ice crystal number variability for different heterogeneous ice nucleation spectra

DOE PAGES

Sullivan, Sylvia C.; Morales Betancourt, Ricardo; Barahona, Donifan; ...

2016-03-03

Along with minimizing parameter uncertainty, understanding the cause of temporal and spatial variability of the nucleated ice crystal number, N i, is key to improving the representation of cirrus clouds in climate models. To this end, sensitivities of N i to input variables like aerosol number and diameter provide valuable information about nucleation regime and efficiency for a given model formulation. Here we use the adjoint model of the adjoint of a cirrus formation parameterization (Barahona and Nenes, 2009b) to understand N i variability for various ice-nucleating particle (INP) spectra. Inputs are generated with the Community Atmosphere Model version 5, andmore » simulations are done with a theoretically derived spectrum, an empirical lab-based spectrum and two field-based empirical spectra that differ in the nucleation threshold for black carbon particles and in the active site density for dust. The magnitude and sign of N i sensitivity to insoluble aerosol number can be directly linked to nucleation regime and efficiency of various INP. The lab-based spectrum calculates much higher INP efficiencies than field-based ones, which reveals a disparity in aerosol surface properties. In conclusion, N i sensitivity to temperature tends to be low, due to the compensating effects of temperature on INP spectrum parameters; this low temperature sensitivity regime has been experimentally reported before but never deconstructed as done here.« less

Adjoint BFKL at finite coupling: a short-cut from the collinear limit

DOE PAGES

Basso, Benjamin; Caron-Huot, Simon; Sever, Amit

2015-01-08

In the high energy Regge limit, the six gluons scattering amplitude is controlled by the adjoint BFKL eigenvalue and impact factor. In this paper we determine these two building blocks at any value of the ’t Hooft coupling in planar N=4 SYM theory. This is achieved by means of analytic continuations from the collinear limit, where similar all loops expressions were recently established. We check our predictions against all available data at weak and strong coupling.

Coalition Interoperability Measurement Frameworks Literature Survey

DTIC Science & Technology

2011-08-01

National Defence, 2011 © Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de la Défense nationale, 2011 Abstract...interarmées élabore actuellement ce cadre et les travaux sont parrainés par le Groupe du Sous- ministre adjoint ( Gestion de l’information). L’intérêt...Groupe du Sous-ministre adjoint ( Gestion de l’information). Le type d’interopérabilité qui nous intéresse : 1. touche les Cinq pays (Australie

Toward the Development of a Coupled COAMPS-ROMS Ensemble Kalman Filter and Adjoint with a focus on the Indian Ocean and the Intraseasonal Oscillation

DTIC Science & Technology

2015-09-30

1 Approved for public release; distribution is unlimited. Toward the Development of a Coupled COAMPS-ROMS Ensemble Kalman Filter and Adjoint...system at NCAR. (2) Compare the performance of the Ensemble Kalman Filter (EnKF) using the Data Assimilation Research Testbed (DART) and 4...undercurrent is clearly visible. Figure 2 shows the horizontal temperature structure and circulation at a depth of 50 m within the surface mixed layer

Banach Synaptic Algebras

NASA Astrophysics Data System (ADS)

Foulis, David J.; Pulmannov, Sylvia

2018-04-01

Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C∗-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW∗-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

Elementary operators on self-adjoint operators

NASA Astrophysics Data System (ADS)

Molnar, Lajos; Semrl, Peter

2007-03-01

Let H be a Hilbert space and let and be standard *-operator algebras on H. Denote by and the set of all self-adjoint operators in and , respectively. Assume that and are surjective maps such that M(AM*(B)A)=M(A)BM(A) and M*(BM(A)B)=M*(B)AM*(B) for every pair , . Then there exist an invertible bounded linear or conjugate-linear operator and a constant c[set membership, variant]{-1,1} such that M(A)=cTAT*, , and M*(B)=cT*BT, .

Application of quasi-distributions for solving inverse problems of neutron and {gamma}-ray transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pogosbekyan, L.R.; Lysov, D.A.

The considered inverse problems deal with the calculation of the unknown values of nuclear installations by means of the known (goal) functionals of neutron/{gamma}-ray distributions. The example of these problems might be the calculation of the automatic control rods position as function of neutron sensors reading, or the calculation of experimentally-corrected values of cross-sections, isotopes concentration, fuel enrichment via the measured functional. The authors have developed the new method to solve inverse problem. It finds flux density as quasi-solution of the particles conservation linear system adjointed to equalities for functionals. The method is more effective compared to the one basedmore » on the classical perturbation theory. It is suitable for vectorization and it can be used successfully in optimization codes.« less

Tracking sensitive source areas of different weather pollution types using GRAPES-CUACE adjoint model

NASA Astrophysics Data System (ADS)

Wang, Chao; An, Xingqin; Zhai, Shixian; Hou, Qing; Sun, Zhaobin

2018-02-01

In this study, the sustained pollution processes were selected during which daily PM2.5 concentration exceeded 75 μg/m3 for three days continuously based on the hourly data of Beijing observation sites from July 2012 to December 2015. Using the China Meteorological Administration (CMA) MICAPS meteorological processing system, synoptic situation during PM2.5 pollution processes was classified into five weather types: low pressure and weak high pressure alternating control, weak high pressure, low pressure control, high rear, and uniform pressure field. Then, we chose the representative pollution cases corresponding to each type, adopted the GRAPES-CUACE adjoint model tracking the sensitive source areas of the five types, and analyzed the critical discharge periods of Beijing and neighboring provinces as well as their contribution to the PM2.5 peak concentration in Beijing. The results showed that the local source plays the main theme in the 30 h before the objective time, and prior to 72 h before the objective time contribution of local sources for the five pollution types are 37.5%, 25.0%, 39.4%, 31.2%, and 42.4%, respectively; the Hebei source contributes constantly in the 57 h ahead of the objective time with the contribution proportion ranging from 37% to 64%; the contribution period and rate of Tianjin and Shanxi sources are shorter and smaller. Based on the adjoint sensitivity analysis, we further discussed the effect of emission reduction control measures in different types, finding that the effect of local source reduction in the first 20 h of the objective time is better, and if the local source is reduced 50% within 72 h before the objective time, the decline rates of PM2.5 in the five types are 11.6%, 9.4%, 13.8%, 9.9% and 15.2% respectively. And the reduction effect of the neighboring sources is better within the 3-57 h before the objective time.

FAST TRACK COMMUNICATION: SUSY transformations with complex factorization constants: application to spectral singularities

NASA Astrophysics Data System (ADS)

Samsonov, Boris F.

2010-10-01

Supersymmetric (SUSY) transformation operators with complex factorization constants are analyzed as operators acting in the Hilbert space of functions square integrable on the positive semiaxis. The obtained results are applied to Hamiltonians possessing spectral singularities which are non-Hermitian SUSY partners of self-adjoint operators. A new regularization procedure for the resolution of the identity operator in terms of a continuous biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed. It is also argued that if the binorm of continuous spectrum eigenfunctions is interpreted in the same way as the norm of similar functions in the usual Hermitian case, then one can state that the function corresponding to a spectral singularity has zero binorm.

Microseismic Image-domain Velocity Inversion: Case Study From The Marcellus Shale

NASA Astrophysics Data System (ADS)

Shragge, J.; Witten, B.

2017-12-01

Seismic monitoring at injection wells relies on generating accurate location estimates of detected (micro-)seismicity. Event location estimates assist in optimizing well and stage spacings, assessing potential hazards, and establishing causation of larger events. The largest impediment to generating accurate location estimates is an accurate velocity model. For surface-based monitoring the model should capture 3D velocity variation, yet, rarely is the laterally heterogeneous nature of the velocity field captured. Another complication for surface monitoring is that the data often suffer from low signal-to-noise levels, making velocity updating with established techniques difficult due to uncertainties in the arrival picks. We use surface-monitored field data to demonstrate that a new method requiring no arrival picking can improve microseismic locations by jointly locating events and updating 3D P- and S-wave velocity models through image-domain adjoint-state tomography. This approach creates a complementary set of images for each chosen event through wave-equation propagation and correlating combinations of P- and S-wavefield energy. The method updates the velocity models to optimize the focal consistency of the images through adjoint-state inversions. We demonstrate the functionality of the method using a surface array of 192 three-component geophones over a hydraulic stimulation in the Marcellus Shale. Applying the proposed joint location and velocity-inversion approach significantly improves the estimated locations. To assess event location accuracy, we propose a new measure of inconsistency derived from the complementary images. By this measure the location inconsistency decreases by 75%. The method has implications for improving the reliability of microseismic interpretation with low signal-to-noise data, which may increase hydrocarbon extraction efficiency and improve risk assessment from injection related seismicity.

Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint

NASA Technical Reports Server (NTRS)

Li, Y.; Navon, I. M.; Courtier, P.; Gauthier, P.

1993-01-01

An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.

Theoretical aspect of suitable spatial boundary condition specified for adjoint model on limited area

NASA Astrophysics Data System (ADS)

Wang, Yuan; Wu, Rongsheng

2001-12-01

Theoretical argumentation for so-called suitable spatial condition is conducted by the aid of homotopy framework to demonstrate that the proposed boundary condition does guarantee that the over-specification boundary condition resulting from an adjoint model on a limited-area is no longer an issue, and yet preserve its well-poseness and optimal character in the boundary setting. The ill-poseness of over-specified spatial boundary condition is in a sense, inevitable from an adjoint model since data assimilation processes have to adapt prescribed observations that used to be over-specified at the spatial boundaries of the modeling domain. In the view of pragmatic implement, the theoretical framework of our proposed condition for spatial boundaries indeed can be reduced to the hybrid formulation of nudging filter, radiation condition taking account of ambient forcing, together with Dirichlet kind of compatible boundary condition to the observations prescribed in data assimilation procedure. All of these treatments, no doubt, are very familiar to mesoscale modelers.

Sensitivity Analysis for Multidisciplinary Systems (SAMS)

DTIC Science & Technology

2016-12-01

support both mode-based structural representations and time-dependent, nonlinear finite element structural dynamics. This interim report describes...Adaptation, & Sensitivity Toolkit • Elasticity, heat transfer, & compressible flow • Adjoint solver for sensitivity analysis • High-order finite elements ...PROGRAM ELEMENT NUMBER 62201F 6. AUTHOR(S) Richard D. Snyder 5d. PROJECT NUMBER 2401 5e. TASK NUMBER N/A 5f. WORK UNIT NUMBER Q1FS 7

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

NASA Astrophysics Data System (ADS)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

P- and S-wave Receiver Function Imaging with Scattering Kernels

NASA Astrophysics Data System (ADS)

Hansen, S. M.; Schmandt, B.

2017-12-01

Full waveform inversion provides a flexible approach to the seismic parameter estimation problem and can account for the full physics of wave propagation using numeric simulations. However, this approach requires significant computational resources due to the demanding nature of solving the forward and adjoint problems. This issue is particularly acute for temporary passive-source seismic experiments (e.g. PASSCAL) that have traditionally relied on teleseismic earthquakes as sources resulting in a global scale forward problem. Various approximation strategies have been proposed to reduce the computational burden such as hybrid methods that embed a heterogeneous regional scale model in a 1D global model. In this study, we focus specifically on the problem of scattered wave imaging (migration) using both P- and S-wave receiver function data. The proposed method relies on body-wave scattering kernels that are derived from the adjoint data sensitivity kernels which are typically used for full waveform inversion. The forward problem is approximated using ray theory yielding a computationally efficient imaging algorithm that can resolve dipping and discontinuous velocity interfaces in 3D. From the imaging perspective, this approach is closely related to elastic reverse time migration. An energy stable finite-difference method is used to simulate elastic wave propagation in a 2D hypothetical subduction zone model. The resulting synthetic P- and S-wave receiver function datasets are used to validate the imaging method. The kernel images are compared with those generated by the Generalized Radon Transform (GRT) and Common Conversion Point stacking (CCP) methods. These results demonstrate the potential of the kernel imaging approach to constrain lithospheric structure in complex geologic environments with sufficiently dense recordings of teleseismic data. This is demonstrated using a receiver function dataset from the Central California Seismic Experiment which shows several dipping interfaces related to the tectonic assembly of this region. Figure 1. Scattering kernel examples for three receiver function phases. A) direct P-to-s (Ps), B) direct S-to-p and C) free-surface PP-to-s (PPs).

Improvement of basal conditions knowledge in Antarctica using data assimilation methods

NASA Astrophysics Data System (ADS)

Mosbeux, C.; Gillet-Chaulet, F.; Gagliardini, O.

2017-12-01

The current global warming seems to have direct consequences on ice-sheet mass loss. Unfortunately, as highlighted in the last IPCC report, current ice-sheets models face several difficulties in assessing the future evolution of the dynamics of ice sheets for the next century. Indeed, projections are still plagued with high uncertainties partially due to the poor representation of occurring physical processes, but also due to the poor initialisation of ice flow models. More specifically, simulations are very sensitive to initial parameters such as the basal friction between ice-sheet and bedrock and the bedrock topography which are still badly known because of a lack of direct observations or large uncertainty on measurements. Improving the knowledge of these two parameters in Greenland and Antarctica is therefore a prerequisite for making reliable projections. Data assimilation methods have been developed in order to overcome this problem such as the Bayesian approach of Pralong and Gudmundsson (2009) or the adjoint method tested by Goldberg and Heimbach (2013) and Perego et al. (2014). The present work is based on two different assimilation algorithms to better constrain both basal drag and bedrock elevation parameters. The first algorithm is entirely based on the adjoint method while the second one uses an iterative method coupling inversion of basal friction based on an adjoint method and through an inversion of bedrock topography using a nudging method. Both algorithms have been implemented in the finite element ice sheet and ice flow model Elmer/Ice and have been tested in a twin experiment showing a clear improvement of both parameters knowledge (Mosbeux et al., 2016). Here, the methods are applied to a real 3D case in East Antarctica and with an ensemble method approach. The application of both algorithms reduces the uncertainty on basal conditions, for instance by providing more details to the basal geometry when compared to usual DEM. Moreover, as in the previous experiment, the reconstruction of both basal elevation and basal friction significantly decreases ice flux divergence anomalies when compared to classical methods where only the friction is inverted. Finally, we conduct prognostic simulations, allowing to assess the impact of the different initialisations obtained with the ensemble method.

Integrated Tsunami Database: simulation and identification of seismic tsunami sources, 3D visualization and post-disaster assessment on the shore

NASA Astrophysics Data System (ADS)

Krivorot'ko, Olga; Kabanikhin, Sergey; Marinin, Igor; Karas, Adel; Khidasheli, David

2013-04-01

One of the most important problems of tsunami investigation is the problem of seismic tsunami source reconstruction. Non-profit organization WAPMERR (http://wapmerr.org) has provided a historical database of alleged tsunami sources around the world that obtained with the help of information about seaquakes. WAPMERR also has a database of observations of the tsunami waves in coastal areas. The main idea of presentation consists of determining of the tsunami source parameters using seismic data and observations of the tsunami waves on the shore, and the expansion and refinement of the database of presupposed tsunami sources for operative and accurate prediction of hazards and assessment of risks and consequences. Also we present 3D visualization of real-time tsunami wave propagation and loss assessment, characterizing the nature of the building stock in cities at risk, and monitoring by satellite images using modern GIS technology ITRIS (Integrated Tsunami Research and Information System) developed by WAPMERR and Informap Ltd. The special scientific plug-in components are embedded in a specially developed GIS-type graphic shell for easy data retrieval, visualization and processing. The most suitable physical models related to simulation of tsunamis are based on shallow water equations. We consider the initial-boundary value problem in Ω := {(x,y) ?R2 : x ?(0,Lx ), y ?(0,Ly ), Lx,Ly > 0} for the well-known linear shallow water equations in the Cartesian coordinate system in terms of the liquid flow components in dimensional form Here ?(x,y,t) defines the free water surface vertical displacement, i.e. amplitude of a tsunami wave, q(x,y) is the initial amplitude of a tsunami wave. The lateral boundary is assumed to be a non-reflecting boundary of the domain, that is, it allows the free passage of the propagating waves. Assume that the free surface oscillation data at points (xm, ym) are given as a measured output data from tsunami records: fm(t) := ? (xm, ym,t), (xm,ym ) ?Ω, t ?(Tm1, Tm2), m = 1,2,...,M, M ?N (2) The problem of tsunami source reconstruction (inverse tsunami problem) consists of determining the unknown initial perturbation q(x,y) of the free surface defied in (1) from knowledge of the free surface oscillation data fm(t) given by (2). We present a numerical method to determine the tsunami source using measurements of the height of a passing tsunami wave. Proposed approach based on the weak solution theory for hyperbolic PDEs and adjoint problem method for minimization of the corresponding cost functional 2 J(q) = ?Aq - F? , F = (f1,...,fM ). (3) The adjoint problem is defined to obtain an explicit gradient formula for the cost functional (3). Different numerical algorithms (finite-difference approach and finite volume method) are proposed for the direct as well as adjoint problem. Conjugate gradient algorithm based on explicit gradient formula is used for numerical solution of the inverse problem (1)-(2). This work was partially supported by the Russian Foundation for Basic Research (project No. 12-01-00773) and by SB RAS interdisciplinary project 14 "Inverse Problems and Applications: Theory, Algorithms, Software".

Predicting Ice Sheet and Climate Evolution at Extreme Scales

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heimbach, Patrick

2016-02-06

A main research objectives of PISCEES is the development of formal methods for quantifying uncertainties in ice sheet modeling. Uncertainties in simulating and projecting mass loss from the polar ice sheets arise primarily from initial conditions, surface and basal boundary conditions, and model parameters. In general terms, two main chains of uncertainty propagation may be identified: 1. inverse propagation of observation and/or prior onto posterior control variable uncertainties; 2. forward propagation of prior or posterior control variable uncertainties onto those of target output quantities of interest (e.g., climate indices or ice sheet mass loss). A related goal is the developmentmore » of computationally efficient methods for producing initial conditions for an ice sheet that are close to available present-day observations and essentially free of artificial model drift, which is required in order to be useful for model projections (“initialization problem”). To be of maximum value, such optimal initial states should be accompanied by “useful” uncertainty estimates that account for the different sources of uncerainties, as well as the degree to which the optimum state is constrained by available observations. The PISCEES proposal outlined two approaches for quantifying uncertainties. The first targets the full exploration of the uncertainty in model projections with sampling-based methods and a workflow managed by DAKOTA (the main delivery vehicle for software developed under QUEST). This is feasible for low-dimensional problems, e.g., those with a handful of global parameters to be inferred. This approach can benefit from derivative/adjoint information, but it is not necessary, which is why it often referred to as “non-intrusive”. The second approach makes heavy use of derivative information from model adjoints to address quantifying uncertainty in high-dimensions (e.g., basal boundary conditions in ice sheet models). The use of local gradient, or Hessian information (i.e., second derivatives of the cost function), requires additional code development and implementation, and is thus often referred to as an “intrusive” approach. Within PISCEES, MIT has been tasked to develop methods for derivative-based UQ, the ”intrusive” approach discussed above. These methods rely on the availability of first (adjoint) and second (Hessian) derivative code, developed through intrusive methods such as algorithmic differentiation (AD). While representing a significant burden in terms of code development, derivative-baesd UQ is able to cope with very high-dimensional uncertainty spaces. That is, unlike sampling methods (all variations of Monte Carlo), calculational burden is independent of the dimension of the uncertainty space. This is a significant advantage for spatially distributed uncertainty fields, such as threedimensional initial conditions, three-dimensional parameter fields, or two-dimensional surface and basal boundary conditions. Importantly, uncertainty fields for ice sheet models generally fall into this category.« less

Toward a Comprehensive Carbon Budget for North America: Potential Applications of Adjoint Methods with Diverse Datasets

NASA Technical Reports Server (NTRS)

Andrews, A.

2002-01-01

A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future COS levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an "inverse problem," where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from long-term surface monitoring stations with data from intensive field campaigns and with proposed future satellite observations. A major advantage of the adjoint approach is that meteorological and surface data, as well as data for other atmospheric constituents and pollutants can be efficiently included in addition to observations of CO2 mixing ratios. This presentation will provide an overview of potentially useful datasets for carbon cycle research in general with an emphasis on planning for the North American Carbon Project. Areas of overlap with ongoing and proposed work on air quality/air pollution issues will be highlighted.

The specific purpose Monte Carlo code McENL for simulating the response of epithermal neutron lifetime well logging tools

NASA Astrophysics Data System (ADS)

Prettyman, T. H.; Gardner, R. P.; Verghese, K.

1993-08-01

A new specific purpose Monte Carlo code called McENL for modeling the time response of epithermal neutron lifetime tools is described. The weight windows technique, employing splitting and Russian roulette, is used with an automated importance function based on the solution of an adjoint diffusion model to improve the code efficiency. Complete composition and density correlated sampling is also included in the code, and can be used to study the effect on tool response of small variations in the formation, borehole, or logging tool composition and density. An illustration of the latter application is given for the density of a thermal neutron filter. McENL was benchmarked against test-pit data for the Mobil pulsed neutron porosity tool and was found to be very accurate. Results of the experimental validation and details of code performance are presented.

Towards a Full Waveform Ambient Noise Inversion

NASA Astrophysics Data System (ADS)

Sager, K.; Ermert, L. A.; Boehm, C.; Fichtner, A.

2015-12-01

Noise tomography usually works under the assumption that the inter-station ambient noise correlation is equal to a scaled version of the Green's function between the two receivers. This assumption, however, is only met under specific conditions, for instance, wavefield diffusivity and equipartitioning, zero attenuation, etc., that are typically not satisfied in the Earth. This inconsistency inhibits the exploitation of the full waveform information contained in noise correlations regarding Earth structure and noise generation. To overcome this limitation we attempt to develop a method that consistently accounts for noise distribution, 3D heterogeneous Earth structure and the full seismic wave propagation physics in order to improve the current resolution of tomographic images of the Earth. As an initial step towards a full waveform ambient noise inversion we develop a preliminary inversion scheme based on a 2D finite-difference code simulating correlation functions and on adjoint techniques. With respect to our final goal, a simultaneous inversion for noise distribution and Earth structure, we address the following two aspects: (1) the capabilities of different misfit functionals to image wave speed anomalies and source distribution and (2) possible source-structure trade-offs, especially to what extent unresolvable structure could be mapped into the inverted noise source distribution and vice versa.

Time-domain seismic modeling in viscoelastic media for full waveform inversion on heterogeneous computing platforms with OpenCL

NASA Astrophysics Data System (ADS)

Fabien-Ouellet, Gabriel; Gloaguen, Erwan; Giroux, Bernard

2017-03-01

Full Waveform Inversion (FWI) aims at recovering the elastic parameters of the Earth by matching recordings of the ground motion with the direct solution of the wave equation. Modeling the wave propagation for realistic scenarios is computationally intensive, which limits the applicability of FWI. The current hardware evolution brings increasing parallel computing power that can speed up the computations in FWI. However, to take advantage of the diversity of parallel architectures presently available, new programming approaches are required. In this work, we explore the use of OpenCL to develop a portable code that can take advantage of the many parallel processor architectures now available. We present a program called SeisCL for 2D and 3D viscoelastic FWI in the time domain. The code computes the forward and adjoint wavefields using finite-difference and outputs the gradient of the misfit function given by the adjoint state method. To demonstrate the code portability on different architectures, the performance of SeisCL is tested on three different devices: Intel CPUs, NVidia GPUs and Intel Xeon PHI. Results show that the use of GPUs with OpenCL can speed up the computations by nearly two orders of magnitudes over a single threaded application on the CPU. Although OpenCL allows code portability, we show that some device-specific optimization is still required to get the best performance out of a specific architecture. Using OpenCL in conjunction with MPI allows the domain decomposition of large models on several devices located on different nodes of a cluster. For large enough models, the speedup of the domain decomposition varies quasi-linearly with the number of devices. Finally, we investigate two different approaches to compute the gradient by the adjoint state method and show the significant advantages of using OpenCL for FWI.

The Scaling of Broadband Shock-Associated Noise with Increasing Temperature

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2013-01-01

A physical explanation for the saturation of broadband shock-associated noise (BBSAN) intensity with increasing jet stagnation temperature has eluded investigators. An explanation is proposed for this phenomenon with the use of an acoustic analogy. To isolate the relevant physics, the scaling of BBSAN peak intensity level at the sideline observer location is examined. The equivalent source within the framework of an acoustic analogy for BBSAN is based on local field quantities at shock wave shear layer interactions. The equivalent source combined with accurate calculations of the propagation of sound through the jet shear layer, using an adjoint vector Green's function solver of the linearized Euler equations, allows for predictions that retain the scaling with respect to stagnation pressure and allows for saturation of BBSAN with increasing stagnation temperature. The sources and vector Green's function have arguments involving the steady Reynolds- Averaged Navier-Stokes solution of the jet. It is proposed that saturation of BBSAN with increasing jet temperature occurs due to a balance between the amplication of the sound propagation through the shear layer and the source term scaling.

Optimal Harvesting in a Periodic Food Chain Model with Size Structures in Predators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Feng-Qin, E-mail: zhafq@263.net; Liu, Rong; Chen, Yuming, E-mail: ychen@wlu.ca

In this paper, we investigate a periodic food chain model with harvesting, where the predators have size structures and are described by first-order partial differential equations. First, we establish the existence of a unique non-negative solution by using the Banach fixed point theorem. Then, we provide optimality conditions by means of normal cone and adjoint system. Finally, we derive the existence of an optimal strategy by means of Ekeland’s variational principle. Here the objective functional represents the net economic benefit yielded from harvesting.

Groundwater Source Identification Using Backward Fractional-Derivative Models

NASA Astrophysics Data System (ADS)

Zhang, Y.; Sun, H.; Zheng, C.

2017-12-01

The forward Fractional Advection Dispersion Equation (FADE) provides a useful model for non-Fickian transport in heterogeneous porous media. This presentation introduces the corresponding backward FADE model, to identify groundwater source location and release time. The backward method is developed from the theory of inverse problems, and the resultant backward FADE differs significantly from the traditional backward ADE because the fractional derivative is not self-adjoint and the probability density function for backward locations is highly skewed. Finally, the method is validated using tracer data from well-known field experiments.

SAM-CE; A Three Dimensional Monte Carlo Code for the Dolution of the Forward Neutron and Forward and Adjoint Gamma Ray Transport Equations. Revision C

DTIC Science & Technology

1974-07-31

Multiple scoring regions are permitted and these may be either finite volume regions or point detectors or both. Other sccres of interest, e.g., collision... Multiplicities ...... . . . . 43 2,3.5.2 Photon Production Cross Sections. . 44 2.3.5.3 Anisotropy of Photon Production . . 44 2.3.5.4 Continuous...hepting, count rates, etc., are calculated as functions of energy, time and position. Multiple scoring regions are permitted and these may be either

Pricing of American style options with an adjoint process correction method

NASA Astrophysics Data System (ADS)

Jaekel, Uwe

2005-07-01

Pricing of American options is a more complicated problem than pricing of European options. In this work a formula is derived that allows the computation of the early exercise premium, i.e. the price difference between these two option types in terms of an adjoint process evolving in the reversed time direction of the original process determining the evolution of the European price. We show how this equation can be utilised to improve option price estimates from numerical schemes like finite difference or Monte Carlo methods.

Visualising Earth's Mantle based on Global Adjoint Tomography

NASA Astrophysics Data System (ADS)

Bozdag, E.; Pugmire, D.; Lefebvre, M. P.; Hill, J.; Komatitsch, D.; Peter, D. B.; Podhorszki, N.; Tromp, J.

2017-12-01

Recent advances in 3D wave propagation solvers and high-performance computing have enabled regional and global full-waveform inversions. Interpretation of tomographic models is often done on visually. Robust and efficient visualization tools are necessary to thoroughly investigate large model files, particularly at the global scale. In collaboration with Oak Ridge National Laboratory (ORNL), we have developed effective visualization tools and used for visualization of our first-generation global model, GLAD-M15 (Bozdag et al. 2016). VisIt (https://wci.llnl.gov/simulation/computer-codes/visit/) is used for initial exploration of the models and for extraction of seismological features. The broad capability of VisIt, and its demonstrated scalability proved valuable for experimenting with different visualization techniques, and in the creation of timely results. Utilizing VisIt's plugin-architecture, a data reader plugin was developed, which reads the ADIOS (https://www.olcf.ornl.gov/center-projects/adios/) format of our model files. Blender (https://www.blender.org) is used for the setup of lighting, materials, camera paths and rendering of geometry. Python scripting was used to control the orchestration of different geometries, as well as camera animation for 3D movies. While we continue producing 3D contour plots and movies for various seismic parameters to better visualize plume- and slab-like features as well as anisotropy throughout the mantle, our aim is to make visualization an integral part of our global adjoint tomography workflow to routinely produce various 2D cross-sections to facilitate examination of our models after each iteration. This will ultimately form the basis for use of pattern recognition techniques in our investigations. Simulations for global adjoint tomography are performed on ORNL's Titan system and visualization is done in parallel on ORNL's post-processing cluster Rhea.

Vertical eddy diffusivity as a control parameter in the tropical Pacific

NASA Astrophysics Data System (ADS)

Martinez Avellaneda, N.; Cornuelle, B.

2011-12-01

Ocean models suffer from errors in the treatment of turbulent sub-grid-scale motions responsible for mixing and energy dissipation. Unrealistic small-scale physics in models can have large-scale consequences, such as biases in the upper ocean temperature, a symptom of poorly-simulated upwelling, currents and air-sea interactions. This is of special importance in the tropical Pacific Ocean (TP), which is home to energetic air-sea interactions that affect global climate. It has been shown in a number of studies that the simulated ENSO variability is highly dependent on the state of the ocean (e.g.: background mixing). Moreover, the magnitude of the vertical numerical diffusion is of primary importance in properly reproducing the Pacific equatorial thermocline. This work is part of a NASA-funded project to estimate the space- and time-varying ocean mixing coefficients in an eddy-permitting (1/3dgr) model of the TP to obtain an improved estimate of its time-varying circulation and its underlying dynamics. While an estimation procedure for the TP (26dgr S - 30dgr N) in underway using the MIT general circulation model, complementary adjoint-based sensitivity studies have been carried out for the starting ocean state from Forget (2010). This analysis aids the interpretation of the estimated mixing coefficients and possible error compensation. The focus of the sensitivity tests is the Equatorial Undercurrent and sub-thermocline jets (i.e., Tsuchiya Jets), which have been thought to have strong dependence on vertical diffusivity and should provide checks on the estimated mixing parameters. In order to build intuition for the vertical diffusivity adjoint results in the TP, adjoint and forward perturbed simulations were carried out for an idealized sharp thermocline in a rectangular domain.

Adjoint tomography of the crust and upper mantle structure beneath the Kanto region using broadband seismograms

NASA Astrophysics Data System (ADS)

Miyoshi, Takayuki; Obayashi, Masayuki; Peter, Daniel; Tono, Yoko; Tsuboi, Seiji

2017-12-01

A three-dimensional seismic wave speed model in the Kanto region of Japan was developed using adjoint tomography for application in the effective reproduction of observed waveforms. Starting with a model based on previous travel time tomographic results, we inverted the waveforms obtained at seismic broadband stations from 140 local earthquakes in the Kanto region to obtain the P- and S-wave speeds V p and V s . Additionally, all centroid times of the source solutions were determined before the structural inversion. The synthetic displacements were calculated using the spectral-element method (SEM) in which the Kanto region was parameterized using 16 million grid points. The model parameters V p and V s were updated iteratively by Newton's method using the misfit and Hessian kernels until the misfit between the observed and synthetic waveforms was minimized. Computations of the forward and adjoint simulations were conducted on the K computer in Japan. The optimized SEM code required a total of 6720 simulations using approximately 62,000 node hours to obtain the final model after 16 iterations. The proposed model reveals several anomalous areas with extremely low- V s values in comparison with those of the initial model. These anomalies were found to correspond to geological features, earthquake sources, and volcanic regions with good data coverage and resolution. The synthetic waveforms obtained using the newly proposed model for the selected earthquakes showed better fit than the initial model to the observed waveforms in different period ranges within 5-30 s. This result indicates that the model can accurately predict actual waveforms. [Figure not available: see fulltext.

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

DOE PAGES

Slattery, Stuart R.; Evans, Thomas M.; Wilson, Paul P. H.

2015-09-08

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper- ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi- mation and the mean chord approximation are applied to estimate the leakagemore » frac- tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.« less

HT2DINV: A 2D forward and inverse code for steady-state and transient hydraulic tomography problems

NASA Astrophysics Data System (ADS)

Soueid Ahmed, A.; Jardani, A.; Revil, A.; Dupont, J. P.

2015-12-01

Hydraulic tomography is a technique used to characterize the spatial heterogeneities of storativity and transmissivity fields. The responses of an aquifer to a source of hydraulic stimulations are used to recover the features of the estimated fields using inverse techniques. We developed a 2D free source Matlab package for performing hydraulic tomography analysis in steady state and transient regimes. The package uses the finite elements method to solve the ground water flow equation for simple or complex geometries accounting for the anisotropy of the material properties. The inverse problem is based on implementing the geostatistical quasi-linear approach of Kitanidis combined with the adjoint-state method to compute the required sensitivity matrices. For undetermined inverse problems, the adjoint-state method provides a faster and more accurate approach for the evaluation of sensitivity matrices compared with the finite differences method. Our methodology is organized in a way that permits the end-user to activate parallel computing in order to reduce the computational burden. Three case studies are investigated demonstrating the robustness and efficiency of our approach for inverting hydraulic parameters.

Adjoint acceleration of Monte Carlo simulations using TORT/MCNP coupling approach: a case study on the shielding improvement for the cyclotron room of the Buddhist Tzu Chi General Hospital.

PubMed

Sheu, R J; Sheu, R D; Jiang, S H; Kao, C H

2005-01-01

Full-scale Monte Carlo simulations of the cyclotron room of the Buddhist Tzu Chi General Hospital were carried out to improve the original inadequate maze design. Variance reduction techniques are indispensable in this study to facilitate the simulations for testing a variety of configurations of shielding modification. The TORT/MCNP manual coupling approach based on the Consistent Adjoint Driven Importance Sampling (CADIS) methodology has been used throughout this study. The CADIS utilises the source and transport biasing in a consistent manner. With this method, the computational efficiency was increased significantly by more than two orders of magnitude and the statistical convergence was also improved compared to the unbiased Monte Carlo run. This paper describes the shielding problem encountered, the procedure for coupling the TORT and MCNP codes to accelerate the calculations and the calculation results for the original and improved shielding designs. In order to verify the calculation results and seek additional accelerations, sensitivity studies on the space-dependent and energy-dependent parameters were also conducted.

On predicting receptivity to surface roughness in a compressible infinite swept wing boundary layer

NASA Astrophysics Data System (ADS)

Thomas, Christian; Mughal, Shahid; Ashworth, Richard

2017-03-01

The receptivity of crossflow disturbances on an infinite swept wing is investigated using solutions of the adjoint linearised Navier-Stokes equations. The adjoint based method for predicting the magnitude of stationary disturbances generated by randomly distributed surface roughness is described, with the analysis extended to include both surface curvature and compressible flow effects. Receptivity is predicted for a broad spectrum of spanwise wavenumbers, variable freestream Reynolds numbers, and subsonic Mach numbers. Curvature is found to play a significant role in the receptivity calculations, while compressible flow effects are only found to marginally affect the initial size of the crossflow instability. A Monte Carlo type analysis is undertaken to establish the mean amplitude and variance of crossflow disturbances generated by the randomly distributed surface roughness. Mean amplitudes are determined for a range of flow parameters that are maximised for roughness distributions containing a broad spectrum of roughness wavelengths, including those that are most effective in generating stationary crossflow disturbances. A control mechanism is then developed where the short scale roughness wavelengths are damped, leading to significant reductions in the receptivity amplitude.

Characterization of measurements in quantum communication. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chan, V. W. S.

1975-01-01

A characterization of quantum measurements by operator valued measures is presented. The generalized measurements include simultaneous approximate measurement of noncommuting observables. This characterization is suitable for solving problems in quantum communication. Two realizations of such measurements are discussed. The first is by adjoining an apparatus to the system under observation and performing a measurement corresponding to a self-adjoint operator in the tensor-product Hilbert space of the system and apparatus spaces. The second realization is by performing, on the system alone, sequential measurements that correspond to self-adjoint operators, basing the choice of each measurement on the outcomes of previous measurements. Simultaneous generalized measurements are found to be equivalent to a single finer grain generalized measurement, and hence it is sufficient to consider the set of single measurements. An alternative characterization of generalized measurement is proposed. It is shown to be equivalent to the characterization by operator-values measures, but it is potentially more suitable for the treatment of estimation problems. Finally, a study of the interaction between the information-carrying system and a measurement apparatus provides clues for the physical realizations of abstractly characterized quantum measurements.

Physics-based Morphology Analysis and Adjoint Optimization of Flexible Flapping Wings

DTIC Science & Technology

2016-08-30

understand the underlying physics of flexible wings in flying insects and birds towards the bio -inspired wing designs with superior aerodynamic...flapping flights have been developed to understand the underlying physics of flexible wings in flying insects and birds towards the bio -inspired wing...been developed to understand the underlying physics of flexible wings in flying insects and birds towards the bio -inspired wing designs with superior

Control surface hinge moment prediction using computational fluid dynamics

NASA Astrophysics Data System (ADS)

Simpson, Christopher David

The following research determines the feasibility of predicting control surface hinge moments using various computational methods. A detailed analysis is conducted using a 2D GA(W)-1 airfoil with a 20% plain flap. Simple hinge moment prediction methods are tested, including empirical Datcom relations and XFOIL. Steady-state and time-accurate turbulent, viscous, Navier-Stokes solutions are computed using Fun3D. Hinge moment coefficients are computed. Mesh construction techniques are discussed. An adjoint-based mesh adaptation case is also evaluated. An NACA 0012 45-degree swept horizontal stabilizer with a 25% elevator is also evaluated using Fun3D. Results are compared with experimental wind-tunnel data obtained from references. Finally, the costs of various solution methods are estimated. Results indicate that while a steady-state Navier-Stokes solution can accurately predict control surface hinge moments for small angles of attack and deflection angles, a time-accurate solution is necessary to accurately predict hinge moments in the presence of flow separation. The ability to capture the unsteady vortex shedding behavior present in moderate to large control surface deflections is found to be critical to hinge moment prediction accuracy. Adjoint-based mesh adaptation is shown to give hinge moment predictions similar to a globally-refined mesh for a steady-state 2D simulation.

An adjoint method of sensitivity analysis for residual vibrations of structures subject to impacts

NASA Astrophysics Data System (ADS)

Yan, Kun; Cheng, Gengdong

2018-03-01

For structures subject to impact loads, the residual vibration reduction is more and more important as the machines become faster and lighter. An efficient sensitivity analysis of residual vibration with respect to structural or operational parameters is indispensable for using a gradient based optimization algorithm, which reduces the residual vibration in either active or passive way. In this paper, an integrated quadratic performance index is used as the measure of the residual vibration, since it globally measures the residual vibration response and its calculation can be simplified greatly with Lyapunov equation. Several sensitivity analysis approaches for performance index were developed based on the assumption that the initial excitations of residual vibration were given and independent of structural design. Since the resulting excitations by the impact load often depend on structural design, this paper aims to propose a new efficient sensitivity analysis method for residual vibration of structures subject to impacts to consider the dependence. The new method is developed by combining two existing methods and using adjoint variable approach. Three numerical examples are carried out and demonstrate the accuracy of the proposed method. The numerical results show that the dependence of initial excitations on structural design variables may strongly affects the accuracy of sensitivities.

Polymeric quantum mechanics and the zeros of the Riemann zeta function

NASA Astrophysics Data System (ADS)

Berra-Montiel, Jasel; Molgado, Alberto

We analyze the Berry-Keating model and the Sierra and Rodríguez-Laguna Hamiltonian within the polymeric quantization formalism. By using the polymer representation, we obtain for both models, the associated polymeric quantum Hamiltonians and the corresponding stationary wave functions. The self-adjointness condition provides a proper domain for the Hamiltonian operator and the energy spectrum, which turned out to be dependent on an introduced scale parameter. By performing a counting of semiclassical states, we prove that the polymer representation reproduces the smooth part of the Riemann-von Mangoldt formula, and also introduces a correction depending on the energy and the scale parameter. This may shed some light on the understanding of the fluctuation behavior of the zeros of the Riemann function from a purely quantum point of view.

Variational Methods in Design Optimization and Sensitivity Analysis for Two-Dimensional Euler Equations

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Tiwari, S. N.; Smith, R. E.

1997-01-01

Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Variational data assimilation for tropospheric chemistry modeling

NASA Astrophysics Data System (ADS)

Elbern, Hendrik; Schmidt, Hauke; Ebel, Adolf

1997-07-01

The method of variational adjoint data assimilation has been applied to assimilate chemistry observations into a comprehensive tropospheric gas phase model. The rationale of this method is to find the correct initial values for a subsequent atmospheric chemistry model run when observations scattered in time are available. The variational adjoint technique is esteemed to be a promising tool for future advanced meteorological forecasting. The stimulating experience gained with the application of four-dimensional variational data assimilation in this research area has motivated the attempt to apply the technique to air quality modeling and analysis of the chemical state of the atmosphere. The present study describes the development and application of the adjoint of the second-generation regional acid deposition model gas phase mechanism, which is used in the European air pollution dispersion model system. Performance results of the assimilation scheme using both model-generated data and real observations are presented for tropospheric conditions. In the former case it is demonstrated that time series of only few or even one measured key species convey sufficient information to improve considerably the analysis of unobserved species which are directly coupled with the observed species. In the latter case a Lagrangian approach is adopted where trajectory calculations between two comprehensively furnished measurement sites are carried out. The method allows us to analyze initial data for air pollution modeling even when only sparse observations are available. Besides remarkable improvements of the model performance by properly analyzed initial concentrations, it is shown that the adjoint algorithm offers the feasibility to estimate the sensitivity of ozone concentrations relative to its precursors.

Passive control of thermoacoustic oscillations with adjoint methods

NASA Astrophysics Data System (ADS)

Aguilar, Jose; Juniper, Matthew

2017-11-01

Strict pollutant regulations are driving gas turbine manufacturers to develop devices that operate under lean premixed conditions, which produce less NOx but encourage thermoacoustic oscillations. These are a form of unstable combustion that arise due to the coupling between the acoustic field and the fluctuating heat release in a combustion chamber. In such devices, in which safety is paramount, thermoacoustic oscillations must be eliminated passively, rather than through feedback control. The ideal way to eliminate thermoacoustic oscillations is by subtly changing the shape of the device. To achieve this, one must calculate the sensitivity of each unstable thermoacoustic mode to every geometric parameter. This is prohibitively expensive with standard methods, but is relatively cheap with adjoint methods. In this study we first present low-order network models as a tool to model and study the thermoacoustic behaviour of combustion chambers. Then we compute the continuous adjoint equations and the sensitivities to relevant parameters. With this, we run an optimization routine that modifies the parameters in order to stabilize all the resonant modes of a laboratory combustor rig.

Polyakov loop correlator in perturbation theory

DOE PAGES

Berwein, Matthias; Brambilla, Nora; Petreczky, Péter; ...

2017-07-25

We study the Polyakov loop correlator in the weak coupling expansion and show how the perturbative series re-exponentiates into singlet and adjoint contributions. We calculate the order g 7 correction to the Polyakov loop correlator in the short distance limit. We show how the singlet and adjoint free energies arising from the re-exponentiation formula of the Polyakov loop correlator are related to the gauge invariant singlet and octet free energies that can be defined in pNRQCD, namely we find that the two definitions agree at leading order in the multipole expansion, but differ at first order in the quark-antiquark distance.

Low-thrust trajectory analysis for the geosynchronous mission

NASA Technical Reports Server (NTRS)

Jasper, T. P.

1973-01-01

Methodology employed in development of a computer program designed to analyze optimal low-thrust trajectories is described, and application of the program to a Solar Electric Propulsion Stage (SEPS) geosynchronous mission is discussed. To avoid the zero inclination and eccentricity singularities which plague many small-force perturbation techniques, a special set of state variables (equinoctial) is used. Adjoint equations are derived for the minimum time problem and are also free from the singularities. Solutions to the state and adjoint equations are obtained by both orbit averaging and precision numerical integration; an evaluation of these approaches is made.

Lattice study of planar equivalence: The quark condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Armoni, Adi; Lucini, Biagio; Patella, Agostino

2008-08-15

We study quenched SU(N) gauge theories with fermions in the two-index symmetric, antisymmetric and the adjoint representations. Our main motivation is to check whether at large number of colors those theories become nonperturbatively equivalent. We prove the equivalence assuming that the charge-conjugation symmetry is not broken in pure Yang-Mills theory. We then carry out a quenched lattice simulation of the quark condensate in the symmetric, antisymmetric and the adjoint representations for SU(2), SU(3), SU(4), SU(6), and SU(8). We show that the data support the equivalence and discuss the size of subleading corrections.

Polyakov loop correlator in perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berwein, Matthias; Brambilla, Nora; Petreczky, Péter

We study the Polyakov loop correlator in the weak coupling expansion and show how the perturbative series re-exponentiates into singlet and adjoint contributions. We calculate the order g 7 correction to the Polyakov loop correlator in the short distance limit. We show how the singlet and adjoint free energies arising from the re-exponentiation formula of the Polyakov loop correlator are related to the gauge invariant singlet and octet free energies that can be defined in pNRQCD, namely we find that the two definitions agree at leading order in the multipole expansion, but differ at first order in the quark-antiquark distance.

Three-dimensional full waveform inversion of short-period teleseismic wavefields based upon the SEM-DSM hybrid method

NASA Astrophysics Data System (ADS)

Monteiller, Vadim; Chevrot, Sébastien; Komatitsch, Dimitri; Wang, Yi

2015-08-01

We present a method for high-resolution imaging of lithospheric structures based on full waveform inversion of teleseismic waveforms. We model the propagation of seismic waves using our recently developed direct solution method/spectral-element method hybrid technique, which allows us to simulate the propagation of short-period teleseismic waves through a regional 3-D model. We implement an iterative quasi-Newton method based upon the L-BFGS algorithm, where the gradient of the misfit function is computed using the adjoint-state method. Compared to gradient or conjugate-gradient methods, the L-BFGS algorithm has a much faster convergence rate. We illustrate the potential of this method on a synthetic test case that consists of a crustal model with a crustal discontinuity at 25 km depth and a sharp Moho jump. This model contains short- and long-wavelength heterogeneities along the lateral and vertical directions. The iterative inversion starts from a smooth 1-D model derived from the IASP91 reference Earth model. We invert both radial and vertical component waveforms, starting from long-period signals filtered at 10 s and gradually decreasing the cut-off period down to 1.25 s. This multiscale algorithm quickly converges towards a model that is very close to the true model, in contrast to inversions involving short-period waveforms only, which always get trapped into a local minimum of the cost function.

Optimal control and optimal trajectories of regional macroeconomic dynamics based on the Pontryagin maximum principle

NASA Astrophysics Data System (ADS)

Bulgakov, V. K.; Strigunov, V. V.

2009-05-01

The Pontryagin maximum principle is used to prove a theorem concerning optimal control in regional macroeconomics. A boundary value problem for optimal trajectories of the state and adjoint variables is formulated, and optimal curves are analyzed. An algorithm is proposed for solving the boundary value problem of optimal control. The performance of the algorithm is demonstrated by computing an optimal control and the corresponding optimal trajectories.

Big Data and High-Performance Computing in Global Seismology

NASA Astrophysics Data System (ADS)

Bozdag, Ebru; Lefebvre, Matthieu; Lei, Wenjie; Peter, Daniel; Smith, James; Komatitsch, Dimitri; Tromp, Jeroen

2014-05-01

Much of our knowledge of Earth's interior is based on seismic observations and measurements. Adjoint methods provide an efficient way of incorporating 3D full wave propagation in iterative seismic inversions to enhance tomographic images and thus our understanding of processes taking place inside the Earth. Our aim is to take adjoint tomography, which has been successfully applied to regional and continental scale problems, further to image the entire planet. This is one of the extreme imaging challenges in seismology, mainly due to the intense computational requirements and vast amount of high-quality seismic data that can potentially be assimilated. We have started low-resolution inversions (T > 30 s and T > 60 s for body and surface waves, respectively) with a limited data set (253 carefully selected earthquakes and seismic data from permanent and temporary networks) on Oak Ridge National Laboratory's Cray XK7 "Titan" system. Recent improvements in our 3D global wave propagation solvers, such as a GPU version of the SPECFEM3D_GLOBE package, will enable us perform higher-resolution (T > 9 s) and longer duration (~180 m) simulations to take the advantage of high-frequency body waves and major-arc surface waves, thereby improving imbalanced ray coverage as a result of the uneven global distribution of sources and receivers. Our ultimate goal is to use all earthquakes in the global CMT catalogue within the magnitude range of our interest and data from all available seismic networks. To take the full advantage of computational resources, we need a solid framework to manage big data sets during numerical simulations, pre-processing (i.e., data requests and quality checks, processing data, window selection, etc.) and post-processing (i.e., pre-conditioning and smoothing kernels, etc.). We address the bottlenecks in our global seismic workflow, which are mainly coming from heavy I/O traffic during simulations and the pre- and post-processing stages, by defining new data formats for seismograms and outputs of our 3D solvers (i.e., meshes, kernels, seismic models, etc.) based on ORNL's ADIOS libraries. We will discuss our global adjoint tomography workflow on HPC systems as well as the current status of our global inversions.

Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events

DOE PAGES

Butler, Troy; Wildey, Timothy

2018-01-01

In thist study, we develop a procedure to utilize error estimates for samples of a surrogate model to compute robust upper and lower bounds on estimates of probabilities of events. We show that these error estimates can also be used in an adaptive algorithm to simultaneously reduce the computational cost and increase the accuracy in estimating probabilities of events using computationally expensive high-fidelity models. Specifically, we introduce the notion of reliability of a sample of a surrogate model, and we prove that utilizing the surrogate model for the reliable samples and the high-fidelity model for the unreliable samples gives preciselymore » the same estimate of the probability of the output event as would be obtained by evaluation of the original model for each sample. The adaptive algorithm uses the additional evaluations of the high-fidelity model for the unreliable samples to locally improve the surrogate model near the limit state, which significantly reduces the number of high-fidelity model evaluations as the limit state is resolved. Numerical results based on a recently developed adjoint-based approach for estimating the error in samples of a surrogate are provided to demonstrate (1) the robustness of the bounds on the probability of an event, and (2) that the adaptive enhancement algorithm provides a more accurate estimate of the probability of the QoI event than standard response surface approximation methods at a lower computational cost.« less

Intelligent earthquake data processing for global adjoint tomography

NASA Astrophysics Data System (ADS)

Chen, Y.; Hill, J.; Li, T.; Lei, W.; Ruan, Y.; Lefebvre, M. P.; Tromp, J.

2016-12-01

Due to the increased computational capability afforded by modern and future computing architectures, the seismology community is demanding a more comprehensive understanding of the full waveform information from the recorded earthquake seismograms. Global waveform tomography is a complex workflow that matches observed seismic data with synthesized seismograms by iteratively updating the earth model parameters based on the adjoint state method. This methodology allows us to compute a very accurate model of the earth's interior. The synthetic data is simulated by solving the wave equation in the entire globe using a spectral-element method. In order to ensure the inversion accuracy and stability, both the synthesized and observed seismograms must be carefully pre-processed. Because the scale of the inversion problem is extremely large and there is a very large volume of data to both be read and written, an efficient and reliable pre-processing workflow must be developed. We are investigating intelligent algorithms based on a machine-learning (ML) framework that will automatically tune parameters for the data processing chain. One straightforward application of ML in data processing is to classify all possible misfit calculation windows into usable and unusable ones, based on some intelligent ML models such as neural network, support vector machine or principle component analysis. The intelligent earthquake data processing framework will enable the seismology community to compute the global waveform tomography using seismic data from an arbitrarily large number of earthquake events in the fastest, most efficient way.

Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events

DOE Office of Scientific and Technical Information (OSTI.GOV)

Butler, Troy; Wildey, Timothy

In thist study, we develop a procedure to utilize error estimates for samples of a surrogate model to compute robust upper and lower bounds on estimates of probabilities of events. We show that these error estimates can also be used in an adaptive algorithm to simultaneously reduce the computational cost and increase the accuracy in estimating probabilities of events using computationally expensive high-fidelity models. Specifically, we introduce the notion of reliability of a sample of a surrogate model, and we prove that utilizing the surrogate model for the reliable samples and the high-fidelity model for the unreliable samples gives preciselymore » the same estimate of the probability of the output event as would be obtained by evaluation of the original model for each sample. The adaptive algorithm uses the additional evaluations of the high-fidelity model for the unreliable samples to locally improve the surrogate model near the limit state, which significantly reduces the number of high-fidelity model evaluations as the limit state is resolved. Numerical results based on a recently developed adjoint-based approach for estimating the error in samples of a surrogate are provided to demonstrate (1) the robustness of the bounds on the probability of an event, and (2) that the adaptive enhancement algorithm provides a more accurate estimate of the probability of the QoI event than standard response surface approximation methods at a lower computational cost.« less

On the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_1^\\alpha ({T^N})

NASA Astrophysics Data System (ADS)

Ahmedov, Anvarjon; Materneh, Ehab; Zainuddin, Hishamuddin

2017-09-01

The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. In this work we study the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_p^α ({T^N}), related to the self-adjoint extension of the Laplace operator in torus TN . The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville L_p^α .

Resolution of quantum singularities

NASA Astrophysics Data System (ADS)

Konkowski, Deborah; Helliwell, Thomas

2017-01-01

A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.

Asymptotic freedom in certain S O (N ) and S U (N ) models

NASA Astrophysics Data System (ADS)

Einhorn, Martin B.; Jones, D. R. Timothy

2017-09-01

We calculate the β -functions for S O (N ) and S U (N ) gauge theories coupled to adjoint and fundamental scalar representations, correcting longstanding, previous results. We explore the constraints on N resulting from requiring asymptotic freedom for all couplings. When we take into account the actual allowed behavior of the gauge coupling, the minimum value of N in both cases turns out to be larger than realized in earlier treatments. We also show that in the large N limit, both models have large regions of parameter space corresponding to total asymptotic freedom.

Extremal values of the sojourn time

NASA Astrophysics Data System (ADS)

Astaburuaga, M. A.; Cortés, V. H.; Duclos, P.

2010-11-01

Consider a self-adjoint operator H on a separable Hilbert space \\ {H} with non-trivial absolutely continuous component. We study the general properties of the real-valued functional, \\tau _{H}(\\psi )=\\int _{{\\ R}}|(e^{-itH}\\psi,\\psi )|^2\\,dt, which in quantum mechanics represents the sojourn time (or life time) of an initial state \\psi \\in \\ {H}. We characterize the critical points of the sojourn time, τX, of the operator multiplication by x in L^2({\\ R}), and prove that it attains a global maximum in the unit sphere of the Sobolev space \\ {W}^{1,2}({\\ R}).

Enhanced global Radionuclide Source Attribution for the Nuclear-Test-Ban Verification by means of the Adjoint Ensemble Dispersion Modeling Technique applied at the IDC/CTBTO.

NASA Astrophysics Data System (ADS)

Becker, A.; Wotawa, G.; de Geer, L.

2006-05-01

The Provisional Technical Secretariat (PTS) of the CTBTO Preparatory Commission maintains and permanently updates a source-receptor matrix (SRM) describing the global monitoring capability of a highly sensitive 80 stations radionuclide (RN) network in order to verify states signatories' compliance of the comprehensive nuclear-test-ban treaty (CTBT). This is done by means of receptor-oriented Lagrangian particle dispersion modeling (LPDM) to help determine the region from which suspicious radionuclides may originate. In doing so the LPDM FLEXPART5.1 is integrated backward in time based on global analysis wind fields yielding global source-receptor sensitivity (SRS) fields stored in three-hour frequency and at 1º horizontal resolution. A database of these SRS fields substantially helps in improving the interpretation of the RN samples measurements and categorizations because it enables the testing of source-hypothesis's later on in a pure post-processing (SRM inversion) step being feasible on hardware with specifications comparable to currently sold PC's or Notebooks and at any place (decentralized), provided access to the SRS fields is warranted. Within the CTBT environment it is important to quickly achieve decision-makers confidence in the SRM based backtracking products issued by the PTS in the case of the occurrence of treaty relevant radionuclides. Therefore the PTS has set up a highly automated response system together with the Regional Specialized Meteorological Centers of the World Meteorological Organization in the field of dispersion modeling who committed themselves to provide the PTS with the same standard SRS fields as calculated by their systems for CTBT relevant cases. This system was twice utilized in 2005 in order to perform adjoint ensemble dispersion modeling (EDM) and demonstrated the potential of EDM based backtracking to improve the accuracy of the source location related to singular nuclear events thus serving the backward analogue to the findings of the ensemble dispersion modeling (EDM) technique No. 5 efforts performed by Galmarini et al, 2004 (Atmos. Env. 38, 4607-4617). As the scope of the adjoint EDM methodology is not limited to CTBT verification but can be applied to any kind of nuclear event monitoring and location it bears the potential to improve the design of manifold emergency response systems towards preparedness concepts as needed for mitigation of disasters (like Chernobyl) and pre-emptive estimation of pollution hazards.

Autofluorescence and diffuse reflectance patterns in cervical spectroscopy

NASA Astrophysics Data System (ADS)

Marin, Nena Maribel

Fluorescence and diffuse reflectance spectroscopy are two new optical technologies, which have shown promise to aid in the real time, non-invasive identification of cancers and precancers. Spectral patterns carry a fingerprint of scattering, absorption and fluorescence properties in tissue. Scattering, absorption and fluorescence in tissue are directly affected by biological features that are diagnostically significant, such as nuclear size, micro-vessel density, volume fraction of collagen fibers, tissue oxygenation and cell metabolism. Thus, analysis of spectral patterns can unlock a wealth of information directly related with the onset and progression of disease. Data from a Phase II clinical trial to assess the technical efficacy of fluorescence and diffuse reflectance spectroscopy acquired from 850 women at three clinical locations with two research grade optical devices is calibrated and analyzed. Tools to process and standardize spectra so that data from multiple spectrometers can be combined and analyzed are presented. Methodologies for calibration and quality assurance of optical systems are established to simplify design issues and ensure validity of data for future clinical trials. Empirically based algorithms, using multivariate statistical approaches are applied to spectra and evaluated as a clinical diagnostic tool. Physically based algorithms, using mathematical models of light propagation in tissue are presented. The presented mathematical model combines a diffusion theory in P3 approximation reflectance model and a 2-layer fluorescence model using exponential attenuation and diffusion theory. The resulting adjoint fluorescence and reflectance model extracts twelve optical properties characterizing fluorescence efficiency of cervical epithelium and stroma fluorophores, stromal hemoglobin and collagen absorption, oxygen saturation, and stromal scattering strength and shape. Validations with Monte Carlo simulations show that adjoint model extracted optical properties of the epithelium and the stroma can be estimated accurately. Adjoint model is applied to 926 clinical measurements from 503 patients. Mean values of extracted optical properties have demonstrated to characterize the biological changes associated with dysplastic progression. Finally, penalized logistic regression algorithms are applied to discriminate dysplastic stages in tissue based on extracted optical features. This work provides understandable and interpretable information regarding predictive and generalization ability of optical spectroscopy in neoplastic changes using a minimum subset of optical measurements. Ultimately these methodologies would facilitate the transfer of these optical technologies into clinical practice.

Mapping pan-Arctic CH4 emissions using an adjoint method by integrating process-based wetland and lake biogeochemical models and atmospheric CH4 concentrations

NASA Astrophysics Data System (ADS)

Tan, Z.; Zhuang, Q.; Henze, D. K.; Frankenberg, C.; Dlugokencky, E. J.; Sweeney, C.; Turner, A. J.

2015-12-01

Understanding CH4 emissions from wetlands and lakes are critical for the estimation of Arctic carbon balance under fast warming climatic conditions. To date, our knowledge about these two CH4 sources is almost solely built on the upscaling of discontinuous measurements in limited areas to the whole region. Many studies indicated that, the controls of CH4 emissions from wetlands and lakes including soil moisture, lake morphology and substrate content and quality are notoriously heterogeneous, thus the accuracy of those simple estimates could be questionable. Here we apply a high spatial resolution atmospheric inverse model (nested-grid GEOS-Chem Adjoint) over the Arctic by integrating SCIAMACHY and NOAA/ESRL CH4 measurements to constrain the CH4 emissions estimated with process-based wetland and lake biogeochemical models. Our modeling experiments using different wetland CH4 emission schemes and satellite and surface measurements show that the total amount of CH4 emitted from the Arctic wetlands is well constrained, but the spatial distribution of CH4 emissions is sensitive to priors. For CH4 emissions from lakes, our high-resolution inversion shows that the models overestimate CH4 emissions in Alaskan costal lowlands and East Siberian lowlands. Our study also indicates that the precision and coverage of measurements need to be improved to achieve more accurate high-resolution estimates.

New biorthogonality relations for inhomogeneous biisotropic planar waveguides

NASA Astrophysics Data System (ADS)

Topa, Antonio L.; Paiva, Carlos R.; Barbosa, Afonso M.

1994-04-01

Using a linear operator formalism this paper presents new biorthogonality relations for the hybrid modes supported by planar waveguides inhomogeneously filled with general biisotropic media. In the special case of lossless biisotropic media, the linear operator is self-adjoint, the original and adjoint waveguides are identical, and new orthogonality relations can be derived. As an example of application, the radiation modes of a grounded nonreciprocal and lossless biisotropic slab waveguide are analyzed in terms of a pair of incident transverse electric (ITE) and incident transverse magnetic (ITM) continuous modes, which have the advantage of being mutually orthogonal and of having a clear physical interpretation.

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Anderson, W. Kyle

1998-01-01

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks

PubMed Central

Kaltenbacher, Barbara; Hasenauer, Jan

2017-01-01

Mechanistic mathematical modeling of biochemical reaction networks using ordinary differential equation (ODE) models has improved our understanding of small- and medium-scale biological processes. While the same should in principle hold for large- and genome-scale processes, the computational methods for the analysis of ODE models which describe hundreds or thousands of biochemical species and reactions are missing so far. While individual simulations are feasible, the inference of the model parameters from experimental data is computationally too intensive. In this manuscript, we evaluate adjoint sensitivity analysis for parameter estimation in large scale biochemical reaction networks. We present the approach for time-discrete measurement and compare it to state-of-the-art methods used in systems and computational biology. Our comparison reveals a significantly improved computational efficiency and a superior scalability of adjoint sensitivity analysis. The computational complexity is effectively independent of the number of parameters, enabling the analysis of large- and genome-scale models. Our study of a comprehensive kinetic model of ErbB signaling shows that parameter estimation using adjoint sensitivity analysis requires a fraction of the computation time of established methods. The proposed method will facilitate mechanistic modeling of genome-scale cellular processes, as required in the age of omics. PMID:28114351

Assimilation of seasonal chlorophyll and nutrient data into an adjoint three-dimensional ocean carbon cycle model: Sensitivity analysis and ecosystem parameter optimization

NASA Astrophysics Data System (ADS)

Tjiputra, Jerry F.; Polzin, Dierk; Winguth, Arne M. E.

2007-03-01

An adjoint method is applied to a three-dimensional global ocean biogeochemical cycle model to optimize the ecosystem parameters on the basis of SeaWiFS surface chlorophyll observation. We showed with identical twin experiments that the model simulated chlorophyll concentration is sensitive to perturbation of phytoplankton and zooplankton exudation, herbivore egestion as fecal pellets, zooplankton grazing, and the assimilation efficiency parameters. The assimilation of SeaWiFS chlorophyll data significantly improved the prediction of chlorophyll concentration, especially in the high-latitude regions. Experiments that considered regional variations of parameters yielded a high seasonal variance of ecosystem parameters in the high latitudes, but a low variance in the tropical regions. These experiments indicate that the adjoint model is, despite the many uncertainties, generally capable to optimize sensitive parameters and carbon fluxes in the euphotic zone. The best fit regional parameters predict a global net primary production of 36 Pg C yr-1, which lies within the range suggested by Antoine et al. (1996). Additional constraints of nutrient data from the World Ocean Atlas showed further reduction in the model-data misfit and that assimilation with extensive data sets is necessary.

Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions

NASA Technical Reports Server (NTRS)

Akgun, Mehmet A.; Haftka, Raphael T.

2000-01-01

The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local and represents a small change in the stiffness matrix compared to the baseline (undamaged) structure. The exact solution to a slightly modified set of equations can be obtained from the baseline solution economically without actually solving the modified system.. Shennan-Morrison-Woodbury (SMW) formulas are matrix update formulas that allow this (Akgun et al., 1998b). SMW formulas were therefore used here to compute adjoint displacements for sensitivity computation and structural displacements in damaged configurations.

Multi-scale Sensitivity and Predictability of Hurricane Joaquin (2015) Illuminated Through Adjoint Studies

NASA Astrophysics Data System (ADS)

Doyle, J. D.; Holdaway, D.; Amerault, C. M.

2017-12-01

Hurricane Joaquin (2015) was a strong category 4 hurricane (maximum winds of 135 kts) that developed from an upper-level low over the western Atlantic and was noteworthy because of its large impact in the Bahamas, as well as the sinking of the cargo ship El Farroand loss of her 33 crew members. Joaquin initially moved southwest towards the Bahamas and rapidly intensified before sharply turning northeastward. Nearly all operational model forecasts failed to provide an accurate prediction of the rapid intensification and track, even at short lead times. As a result, the National Hurricane Center forecasted landfall in the mid-Atlantic, while in reality the storm moved well offshore. In this study, we utilize two adjoint modeling systems, the Navy COAMPS and the NASA GEOS-5, to investigate the role of initial condition errors that may have led to the relatively poor track and intensity predictions of Hurricane Joaquin. Adjoint models can provide valuable insight into the practical limitations of our ability to predict the path of tropical cyclones and their strength. An adjoint model can be used for the efficient and rigorous computation of numerical weather forecast sensitivity to changes in the initial state. The adjoint sensitivity diagnostics illustrate complex influences on the evolution of Joaquin that occur over a wide range of spatial scales. The sensitivity results highlight the importance of an upper-level trough to the northeast that provided the steering flow for the poorly-predicted southwesterly movement of the hurricane in its early phase. The steering flow and hurricane track are found to be very sensitive to relatively small changes in the initial state to the east-northeast of the hurricane. Additionally, the intensity prediction of Hurricane Joaquin is found to be very sensitive to the initial state moisture including highly structured regions around the storm and in remote regions as well. Hurricane Joaquin was observed in four NASA WB-57 research flights during the ONR Tropical Cyclone Intensity (TCI) experiment. The dropsondes that were deployed in regions of large initial state sensitivity are used to characterize the atmospheric properties of these sensitive regions. We will also quantify the impact of TCI dropsondes on COAMPS forecasts for select forecasts of Hurricane Joaquin.

Adjoint-Baed Optimal Control on the Pitch Angle of a Single-Bladed Vertical-Axis Wind Turbine

NASA Astrophysics Data System (ADS)

Tsai, Hsieh-Chen; Colonius, Tim

2017-11-01

Optimal control on the pitch angle of a NACA0018 single-bladed vertical-axis wind turbine (VAWT) is numerically investigated at a low Reynolds number of 1500. With fixed tip-speed ratio, the input power is minimized and mean tangential force is maximized over a specific time horizon. The immersed boundary method is used to simulate the two-dimensional, incompressible flow around a horizontal cross section of the VAWT. The problem is formulated as a PDE constrained optimization problem and an iterative solution is obtained using adjoint-based conjugate gradient methods. By the end of the longest control horizon examined, two controls end up with time-invariant pitch angles of about the same magnitude but with the opposite signs. The results show that both cases lead to a reduction in the input power but not necessarily an enhancement in the mean tangential force. These reductions in input power are due to the removal of a power-damaging phenomenon that occurs when a vortex pair is captured by the blade in the upwind-half region of a cycle. This project was supported by Caltech FLOWE center/Gordon and Betty Moore Foundation.

Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dekeyser, W., E-mail: Wouter.Dekeyser@kuleuven.be; Reiter, D.; Baelmans, M.

As magnetic confinement fusion progresses towards the development of first reactor-scale devices, computational tokamak divertor design is a topic of high priority. Presently, edge plasma codes are used in a forward approach, where magnetic field and divertor geometry are manually adjusted to meet design requirements. Due to the complex edge plasma flows and large number of design variables, this method is computationally very demanding. On the other hand, efficient optimization-based design strategies have been developed in computational aerodynamics and fluid mechanics. Such an optimization approach to divertor target shape design is elaborated in the present paper. A general formulation ofmore » the design problems is given, and conditions characterizing the optimal designs are formulated. Using a continuous adjoint framework, design sensitivities can be computed at a cost of only two edge plasma simulations, independent of the number of design variables. Furthermore, by using a one-shot method the entire optimization problem can be solved at an equivalent cost of only a few forward simulations. The methodology is applied to target shape design for uniform power load, in simplified edge plasma geometry.« less

A Hybrid Forward-Adjoint Data Assimilation Method for Reconstructing the Temporal Evolution of Mantle Dynamics

NASA Astrophysics Data System (ADS)

Zhou, Q.; Liu, L.

2017-12-01

Quantifying past mantle dynamic processes represents a major challenge in understanding the temporal evolution of the solid earth. Mantle convection modeling with data assimilation is one of the most powerful tools to investigate the dynamics of plate subduction and mantle convection. Although various data assimilation methods, both forward and inverse, have been created, these methods all have limitations in their capabilities to represent the real earth. Pure forward models tend to miss important mantle structures due to the incorrect initial condition and thus may lead to incorrect mantle evolution. In contrast, pure tomography-based models cannot effectively resolve the fine slab structure and would fail to predict important subduction-zone dynamic processes. Here we propose a hybrid data assimilation method that combines the unique power of the sequential and adjoint algorithms, which can properly capture the detailed evolution of the downgoing slab and the tomographically constrained mantle structures, respectively. We apply this new method to reconstructing mantle dynamics below the western U.S. while considering large lateral viscosity variations. By comparing this result with those from several existing data assimilation methods, we demonstrate that the hybrid modeling approach recovers the realistic 4-D mantle dynamics to the best.

Validation of a Wave Data Assimilation System Based on SWAN

NASA Astrophysics Data System (ADS)

Flampourisi, Stylianos; Veeramony, Jayaram; Orzech, Mark D.; Ngodock, Hans E.

2013-04-01

SWAN is one of the most broadly used models for wave predictions in the nearshore, with known and extensively studied limitations due to the physics and/or to the numerical implementation. In order to improve the performance of the model, a 4DVAR data assimilation system based on a tangent linear code and the corresponding adjoint from the numerical SWAN model has been developed at NRL(Orzech et. al., 2013), by implementing the methodology of Bennett 2002. The assimilation system takes into account the nonlinear triad and quadruplet interactions, depth-limited breaking, wind forcing, bottom friction and white-capping. Using conjugate gradient method, the assimilation system minimizes a quadratic penalty functional (which represents the overall error of the simulation) and generates the correction of the forward simulation in spatial, temporal and spectral domain. The weights are given to the output of the adjoint by calculating the covariance to an ensemble of forward simulations according to Evensen 2009. This presentation will focus on the extension of the system to a weak-constrainted data assimilation system and on the extensive validation of the system by using wave spectra for forcing, assimilation and validation, from FRF Duck, North Carolina, during August 2011. During this period, at the 17 m waverider buoy location, the wind speed was up to 35 m/s (due to Hurricane Irene) and the significant wave height varied from 0.5 m to 6 m and the peak period between 5 s and 18 s. In general, this study shows significant improvement of the integrated spectral properties, but the main benefit of assimilating the wave spectra (and not only their integrated properties) is that the accurate simulation of separated, in frequency and in direction, wave systems is possible even nearshore, where non-linear phenomena are dominant. The system is ready to be used for more precise reanalysis of the wave climate and climate variability, and determination of coastal hazards in regional or local scales, in case of available wave data. References: Orzech, M.D., J. Veeramony, and H.E. Ngodock, 2013: A variational assimilation system for nearshore wave modeling. J. Atm. & Oc. Tech., in press.

PROGRESS TOWARDS NEXT GENERATION, WAVEFORM BASED THREE-DIMENSIONAL MODELS AND METRICS TO IMPROVE NUCLEAR EXPLOSION MONITORING IN THE MIDDLE EAST

DOE Office of Scientific and Technical Information (OSTI.GOV)

Savage, B; Peter, D; Covellone, B

2009-07-02

Efforts to update current wave speed models of the Middle East require a thoroughly tested database of sources and recordings. Recordings of seismic waves traversing the region from Tibet to the Red Sea will be the principal metric in guiding improvements to the current wave speed model. Precise characterizations of the earthquakes, specifically depths and faulting mechanisms, are essential to avoid mapping source errors into the refined wave speed model. Errors associated with the source are manifested in amplitude and phase changes. Source depths and paths near nodal planes are particularly error prone as small changes may severely affect themore » resulting wavefield. Once sources are quantified, regions requiring refinement will be highlighted using adjoint tomography methods based on spectral element simulations [Komatitsch and Tromp (1999)]. An initial database of 250 regional Middle Eastern events from 1990-2007, was inverted for depth and focal mechanism using teleseismic arrivals [Kikuchi and Kanamori (1982)] and regional surface and body waves [Zhao and Helmberger (1994)]. From this initial database, we reinterpreted a large, well recorded subset of 201 events through a direct comparison between data and synthetics based upon a centroid moment tensor inversion [Liu et al. (2004)]. Evaluation was done using both a 1D reference model [Dziewonski and Anderson (1981)] at periods greater than 80 seconds and a 3D model [Kustowski et al. (2008)] at periods of 25 seconds and longer. The final source reinterpretations will be within the 3D model, as this is the initial starting point for the adjoint tomography. Transitioning from a 1D to 3D wave speed model shows dramatic improvements when comparisons are done at shorter periods, (25 s). Synthetics from the 1D model were created through mode summations while those from the 3D simulations were created using the spectral element method. To further assess errors in source depth and focal mechanism, comparisons between the three methods were made. These comparisons help to identify problematic stations and sources which may bias the final solution. Estimates of standard errors were generated for each event's source depth and focal mechanism to identify poorly constrained events. A final, well characterized set of sources and stations will be then used to iteratively improve the wave speed model of the Middle East. After a few iterations during the adjoint inversion process, the sources will be reexamined and relocated to further reduce mapping of source errors into structural features. Finally, efforts continue in developing the infrastructure required to 'quickly' generate event kernels at the n-th iteration and invert for a new, (n+1)-th, wave speed model of the Middle East. While development of the infrastructure proceeds, initial tests using a limited number of events shows the 3D model, while showing vast improvement compared to the 1D model, still requires substantial modifications. Employing our new, full source set and iterating the adjoint inversions at successively shorter periods will lead to significant changes and refined wave speed structures of the Middle East.« less

Application of Exactly Linearized Error Transport Equations to AIAA CFD Prediction Workshops

NASA Technical Reports Server (NTRS)

Derlaga, Joseph M.; Park, Michael A.; Rallabhandi, Sriram

2017-01-01

The computational fluid dynamics (CFD) prediction workshops sponsored by the AIAA have created invaluable opportunities in which to discuss the predictive capabilities of CFD in areas in which it has struggled, e.g., cruise drag, high-lift, and sonic boom pre diction. While there are many factors that contribute to disagreement between simulated and experimental results, such as modeling or discretization error, quantifying the errors contained in a simulation is important for those who make decisions based on the computational results. The linearized error transport equations (ETE) combined with a truncation error estimate is a method to quantify one source of errors. The ETE are implemented with a complex-step method to provide an exact linearization with minimal source code modifications to CFD and multidisciplinary analysis methods. The equivalency of adjoint and linearized ETE functional error correction is demonstrated. Uniformly refined grids from a series of AIAA prediction workshops demonstrate the utility of ETE for multidisciplinary analysis with a connection between estimated discretization error and (resolved or under-resolved) flow features.

The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alpay, Daniel, E-mail: dany@math.bgu.ac.il; Kimsey, David P., E-mail: dpkimsey@gmail.com; Colombo, Fabrizio, E-mail: fabrizio.colombo@polimi.it

In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The lack of a suitable notion ofmore » spectrum was a major obstruction to fully understand the spectral theorem for quaternionic normal operators. A prime motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti-self adjoint quaternionic operators which play a crucial role in the quaternionic quantum mechanics.« less

The Hartree Equation for Infinitely Many Particles I. Well-Posedness Theory

NASA Astrophysics Data System (ADS)

Lewin, Mathieu; Sabin, Julien

2015-02-01

We show local and global well-posedness results for the Hartree equation where γ is a bounded self-adjoint operator on , ρ γ ( x) = γ( x, x) and w is a smooth short-range interaction potential. The initial datum γ(0) is assumed to be a perturbation of a translation-invariant state γ f = f(-Δ) which describes a quantum system with an infinite number of particles, such as the Fermi sea at zero temperature, or the Fermi-Dirac and Bose-Einstein gases at positive temperature. Global well-posedness follows from the conservation of the relative (free) energy of the state γ( t), counted relatively to the stationary state γ f . We indeed use a general notion of relative entropy, which allows us to treat a wide class of stationary states f(-Δ). Our results are based on a Lieb-Thirring inequality at positive density and on a recent Strichartz inequality for orthonormal functions, which are both due to Frank, Lieb, Seiringer and the first author of this article.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raoult, Nina M.; Jupp, Tim E.; Cox, Peter M.

Land-surface models (LSMs) are crucial components of the Earth system models (ESMs) that are used to make coupled climate–carbon cycle projections for the 21st century. The Joint UK Land Environment Simulator (JULES) is the land-surface model used in the climate and weather forecast models of the UK Met Office. JULES is also extensively used offline as a land-surface impacts tool, forced with climatologies into the future. In this study, JULES is automatically differentiated with respect to JULES parameters using commercial software from FastOpt, resulting in an analytical gradient, or adjoint, of the model. Using this adjoint, the adJULES parameter estimationmore » system has been developed to search for locally optimum parameters by calibrating against observations. This paper describes adJULES in a data assimilation framework and demonstrates its ability to improve the model–data fit using eddy-covariance measurements of gross primary production (GPP) and latent heat (LE) fluxes. adJULES also has the ability to calibrate over multiple sites simultaneously. This feature is used to define new optimised parameter values for the five plant functional types (PFTs) in JULES. The optimised PFT-specific parameters improve the performance of JULES at over 85 % of the sites used in the study, at both the calibration and evaluation stages. Furthermore, the new improved parameters for JULES are presented along with the associated uncertainties for each parameter.« less

Land-surface parameter optimisation using data assimilation techniques: the adJULES system V1.0

NASA Astrophysics Data System (ADS)

Raoult, Nina M.; Jupp, Tim E.; Cox, Peter M.; Luke, Catherine M.

2016-08-01

Land-surface models (LSMs) are crucial components of the Earth system models (ESMs) that are used to make coupled climate-carbon cycle projections for the 21st century. The Joint UK Land Environment Simulator (JULES) is the land-surface model used in the climate and weather forecast models of the UK Met Office. JULES is also extensively used offline as a land-surface impacts tool, forced with climatologies into the future. In this study, JULES is automatically differentiated with respect to JULES parameters using commercial software from FastOpt, resulting in an analytical gradient, or adjoint, of the model. Using this adjoint, the adJULES parameter estimation system has been developed to search for locally optimum parameters by calibrating against observations. This paper describes adJULES in a data assimilation framework and demonstrates its ability to improve the model-data fit using eddy-covariance measurements of gross primary production (GPP) and latent heat (LE) fluxes. adJULES also has the ability to calibrate over multiple sites simultaneously. This feature is used to define new optimised parameter values for the five plant functional types (PFTs) in JULES. The optimised PFT-specific parameters improve the performance of JULES at over 85 % of the sites used in the study, at both the calibration and evaluation stages. The new improved parameters for JULES are presented along with the associated uncertainties for each parameter.

Relative Critical Points

NASA Astrophysics Data System (ADS)

Lewis, Debra

2013-05-01

Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic, Poisson, or variational - generating dynamical systems from such functions highlights the common features of their construction and analysis, and supports the construction of analogous functions in non-Hamiltonian settings. If the symmetry group is nonabelian, the functions are invariant only with respect to the isotropy subgroup of the given parameter value. Replacing the parametrized family of functions with a single function on the product manifold and extending the action using the (co)adjoint action on the algebra or its dual yields a fully invariant function. An invariant map can be used to reverse the usual perspective: rather than selecting a parametrized family of functions and finding their critical points, conditions under which functions will be critical on specific orbits, typically distinguished by isotropy class, can be derived. This strategy is illustrated using several well-known mechanical systems - the Lagrange top, the double spherical pendulum, the free rigid body, and the Riemann ellipsoids - and generalizations of these systems.

A Scalable, Parallel Approach for Multi-Point, High-Fidelity Aerostructural Optimization of Aircraft Configurations

NASA Astrophysics Data System (ADS)

Kenway, Gaetan K. W.

This thesis presents new tools and techniques developed to address the challenging problem of high-fidelity aerostructural optimization with respect to large numbers of design variables. A new mesh-movement scheme is developed that is both computationally efficient and sufficiently robust to accommodate large geometric design changes and aerostructural deformations. A fully coupled Newton-Krylov method is presented that accelerates the convergence of aerostructural systems and provides a 20% performance improvement over the traditional nonlinear block Gauss-Seidel approach and can handle more exible structures. A coupled adjoint method is used that efficiently computes derivatives for a gradient-based optimization algorithm. The implementation uses only machine accurate derivative techniques and is verified to yield fully consistent derivatives by comparing against the complex step method. The fully-coupled large-scale coupled adjoint solution method is shown to have 30% better performance than the segregated approach. The parallel scalability of the coupled adjoint technique is demonstrated on an Euler Computational Fluid Dynamics (CFD) model with more than 80 million state variables coupled to a detailed structural finite-element model of the wing with more than 1 million degrees of freedom. Multi-point high-fidelity aerostructural optimizations of a long-range wide-body, transonic transport aircraft configuration are performed using the developed techniques. The aerostructural analysis employs Euler CFD with a 2 million cell mesh and a structural finite element model with 300 000 DOF. Two design optimization problems are solved: one where takeoff gross weight is minimized, and another where fuel burn is minimized. Each optimization uses a multi-point formulation with 5 cruise conditions and 2 maneuver conditions. The optimization problems have 476 design variables are optimal results are obtained within 36 hours of wall time using 435 processors. The TOGW minimization results in a 4.2% reduction in TOGW with a 6.6% fuel burn reduction, while the fuel burn optimization resulted in a 11.2% fuel burn reduction with no change to the takeoff gross weight.

The efficiency of geophysical adjoint codes generated by automatic differentiation tools

NASA Astrophysics Data System (ADS)

Vlasenko, A. V.; Köhl, A.; Stammer, D.

2016-02-01

The accuracy of numerical models that describe complex physical or chemical processes depends on the choice of model parameters. Estimating an optimal set of parameters by optimization algorithms requires knowledge of the sensitivity of the process of interest to model parameters. Typically the sensitivity computation involves differentiation of the model, which can be performed by applying algorithmic differentiation (AD) tools to the underlying numerical code. However, existing AD tools differ substantially in design, legibility and computational efficiency. In this study we show that, for geophysical data assimilation problems of varying complexity, the performance of adjoint codes generated by the existing AD tools (i) Open_AD, (ii) Tapenade, (iii) NAGWare and (iv) Transformation of Algorithms in Fortran (TAF) can be vastly different. Based on simple test problems, we evaluate the efficiency of each AD tool with respect to computational speed, accuracy of the adjoint, the efficiency of memory usage, and the capability of each AD tool to handle modern FORTRAN 90-95 elements such as structures and pointers, which are new elements that either combine groups of variables or provide aliases to memory addresses, respectively. We show that, while operator overloading tools are the only ones suitable for modern codes written in object-oriented programming languages, their computational efficiency lags behind source transformation by orders of magnitude, rendering the application of these modern tools to practical assimilation problems prohibitive. In contrast, the application of source transformation tools appears to be the most efficient choice, allowing handling even large geophysical data assimilation problems. However, they can only be applied to numerical models written in earlier generations of programming languages. Our study indicates that applying existing AD tools to realistic geophysical problems faces limitations that urgently need to be solved to allow the continuous use of AD tools for solving geophysical problems on modern computer architectures.

Optimal control penalty finite elements - Applications to integrodifferential equations

NASA Astrophysics Data System (ADS)

Chung, T. J.

The application of the optimal-control/penalty finite-element method to the solution of integrodifferential equations in radiative-heat-transfer problems (Chung et al.; Chung and Kim, 1982) is discussed and illustrated. The nonself-adjointness of the convective terms in the governing equations is treated by utilizing optimal-control cost functions and employing penalty functions to constrain auxiliary equations which permit the reduction of second-order derivatives to first order. The OCPFE method is applied to combined-mode heat transfer by conduction, convection, and radiation, both without and with scattering and viscous dissipation; the results are presented graphically and compared to those obtained by other methods. The OCPFE method is shown to give good results in cases where standard Galerkin FE fail, and to facilitate the investigation of scattering and dissipation effects.

Quantum Markov semigroups constructed from quantum Bernoulli noises

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Caishi; Chen, Jinshu

2016-02-15

Quantum Bernoulli noises (QBNs) are the family of annihilation and creation operators acting on Bernoulli functionals, which can describe a two-level quantum system with infinitely many sites. In this paper, we consider the problem to construct quantum Markov semigroups (QMSs) directly from QBNs. We first establish several new theorems concerning QBNs. In particular, we define the number operator acting on Bernoulli functionals by using the canonical orthonormal basis, prove its self-adjoint property, and describe precisely its connections with QBN in a mathematically rigorous way. We then show the possibility to construct QMS directly from QBN. This is done by combiningmore » the general results on QMS with our new results on QBN obtained here. Finally, we examine some properties of QMS constructed from QBN.« less

Design of efficient stiffened shells of revolution

NASA Technical Reports Server (NTRS)

Majumder, D. K.; Thornton, W. A.

1976-01-01

A method to produce efficient piecewise uniform stiffened shells of revolution is presented. The approach uses a first order differential equation formulation for the shell prebuckling and buckling analyses and the necessary conditions for an optimum design are derived by a variational approach. A variety of local yielding and buckling constraints and the general buckling constraint are included in the design process. The local constraints are treated by means of an interior penalty function and the general buckling load is treated by means of an exterior penalty function. This allows the general buckling constraint to be included in the design process only when it is violated. The self-adjoint nature of the prebuckling and buckling formulations is used to reduce the computational effort. Results for four conical shells and one spherical shell are given.

Unitary evolution of the quantum Universe with a Brown-Kuchař dust

NASA Astrophysics Data System (ADS)

Maeda, Hideki

2015-12-01

We study the time evolution of a wave function for the spatially flat Friedmann-Lemaître-Robertson-Walker Universe governed by the Wheeler-DeWitt equation in both analytical and numerical methods. We consider a Brown-Kuchař dust as a matter field in order to introduce a ‘clock’ in quantum cosmology and adopt the Laplace-Beltrami operator-ordering. The Hamiltonian operator admits an infinite number of self-adjoint extensions corresponding to a one-parameter family of boundary conditions at the origin in the minisuperspace. For any value of the extension parameter in the boundary condition, the evolution of a wave function is unitary and the classical initial singularity is avoided and replaced by the big bounce in the quantum system. Exact wave functions show that the expectation value of the spatial volume of the Universe obeys the classical-time evolution in the late time but its variance diverges.

Towards full waveform ambient noise inversion

NASA Astrophysics Data System (ADS)

Sager, Korbinian; Ermert, Laura; Boehm, Christian; Fichtner, Andreas

2018-01-01

In this work we investigate fundamentals of a method—referred to as full waveform ambient noise inversion—that improves the resolution of tomographic images by extracting waveform information from interstation correlation functions that cannot be used without knowing the distribution of noise sources. The fundamental idea is to drop the principle of Green function retrieval and to establish correlation functions as self-consistent observables in seismology. This involves the following steps: (1) We introduce an operator-based formulation of the forward problem of computing correlation functions. It is valid for arbitrary distributions of noise sources in both space and frequency, and for any type of medium, including 3-D elastic, heterogeneous and attenuating media. In addition, the formulation allows us to keep the derivations independent of time and frequency domain and it facilitates the application of adjoint techniques, which we use to derive efficient expressions to compute first and also second derivatives. The latter are essential for a resolution analysis that accounts for intra- and interparameter trade-offs. (2) In a forward modelling study we investigate the effect of noise sources and structure on different observables. Traveltimes are hardly affected by heterogeneous noise source distributions. On the other hand, the amplitude asymmetry of correlations is at least to first order insensitive to unmodelled Earth structure. Energy and waveform differences are sensitive to both structure and the distribution of noise sources. (3) We design and implement an appropriate inversion scheme, where the extraction of waveform information is successively increased. We demonstrate that full waveform ambient noise inversion has the potential to go beyond ambient noise tomography based on Green function retrieval and to refine noise source location, which is essential for a better understanding of noise generation. Inherent trade-offs between source and structure are quantified using Hessian-vector products.

Towards Full-Waveform Ambient Noise Inversion

NASA Astrophysics Data System (ADS)

Sager, K.; Ermert, L. A.; Boehm, C.; Fichtner, A.

2016-12-01

Noise tomography usually works under the assumption that the inter-station ambient noise correlation is equal to a scaled version of the Green function between the two receivers. This assumption, however, is only met under specific conditions, e.g. wavefield diffusivity and equipartitioning, or the isotropic distribution of both mono- and dipolar uncorrelated noise sources. These assumptions are typically not satisfied in the Earth. This inconsistency inhibits the exploitation of the full waveform information contained in noise correlations in order to constrain Earth structure and noise generation. To overcome this limitation, we attempt to develop a method that consistently accounts for the distribution of noise sources, 3D heterogeneous Earth structure and the full seismic wave propagation physics. This is intended to improve the resolution of tomographic images, to refine noise source location, and thereby to contribute to a better understanding of noise generation. We introduce an operator-based formulation for the computation of correlation functions and apply the continuous adjoint method that allows us to compute first and second derivatives of misfit functionals with respect to source distribution and Earth structure efficiently. Based on these developments we design an inversion scheme using a 2D finite-difference code. To enable a joint inversion for noise sources and Earth structure, we investigate the following aspects: The capability of different misfit functionals to image wave speed anomalies and source distribution. Possible source-structure trade-offs, especially to what extent unresolvable structure can be mapped into the inverted noise source distribution and vice versa. In anticipation of real-data applications, we present an extension of the open-source waveform modelling and inversion package Salvus, which allows us to compute correlation functions in 3D media with heterogeneous noise sources at the surface.

Linearized inversion of multiple scattering seismic energy

NASA Astrophysics Data System (ADS)

Aldawood, Ali; Hoteit, Ibrahim; Zuberi, Mohammad

2014-05-01

Internal multiples deteriorate the quality of the migrated image obtained conventionally by imaging single scattering energy. So, imaging seismic data with the single-scattering assumption does not locate multiple bounces events in their actual subsurface positions. However, imaging internal multiples properly has the potential to enhance the migrated image because they illuminate zones in the subsurface that are poorly illuminated by single scattering energy such as nearly vertical faults. Standard migration of these multiples provides subsurface reflectivity distributions with low spatial resolution and migration artifacts due to the limited recording aperture, coarse sources and receivers sampling, and the band-limited nature of the source wavelet. The resultant image obtained by the adjoint operator is a smoothed depiction of the true subsurface reflectivity model and is heavily masked by migration artifacts and the source wavelet fingerprint that needs to be properly deconvolved. Hence, we proposed a linearized least-square inversion scheme to mitigate the effect of the migration artifacts, enhance the spatial resolution, and provide more accurate amplitude information when imaging internal multiples. The proposed algorithm uses the least-square image based on single-scattering assumption as a constraint to invert for the part of the image that is illuminated by internal scattering energy. Then, we posed the problem of imaging double-scattering energy as a least-square minimization problem that requires solving the normal equation of the following form: GTGv = GTd, (1) where G is a linearized forward modeling operator that predicts double-scattered seismic data. Also, GT is a linearized adjoint operator that image double-scattered seismic data. Gradient-based optimization algorithms solve this linear system. Hence, we used a quasi-Newton optimization technique to find the least-square minimizer. In this approach, an estimate of the Hessian matrix that contains curvature information is modified at every iteration by a low-rank update based on gradient changes at every step. At each iteration, the data residual is imaged using GT to determine the model update. Application of the linearized inversion to synthetic data to image a vertical fault plane demonstrate the effectiveness of this methodology to properly delineate the vertical fault plane and give better amplitude information than the standard migrated image using the adjoint operator that takes into account internal multiples. Thus, least-square imaging of multiple scattering enhances the spatial resolution of the events illuminated by internal scattering energy. It also deconvolves the source signature and helps remove the fingerprint of the acquisition geometry. The final image is obtained by the superposition of the least-square solution based on single scattering assumption and the least-square solution based on double scattering assumption.

A Least-Squares Transport Equation Compatible with Voids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, Jon; Peterson, Jacob; Morel, Jim

Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transportmore » equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S n formulation represents an excellent alternative to existing second-order S n transport formulations« less

The Spectral Shift Function and Spectral Flow

NASA Astrophysics Data System (ADS)

Azamov, N. A.; Carey, A. L.; Sukochev, F. A.

2007-11-01

At the 1974 International Congress, I. M. Singer proposed that eta invariants and hence spectral flow should be thought of as the integral of a one form. In the intervening years this idea has lead to many interesting developments in the study of both eta invariants and spectral flow. Using ideas of [24] Singer’s proposal was brought to an advanced level in [16] where a very general formula for spectral flow as the integral of a one form was produced in the framework of noncommutative geometry. This formula can be used for computing spectral flow in a general semifinite von Neumann algebra as described and reviewed in [5]. In the present paper we take the analytic approach to spectral flow much further by giving a large family of formulae for spectral flow between a pair of unbounded self-adjoint operators D and D + V with D having compact resolvent belonging to a general semifinite von Neumann algebra {mathcal{N}} and the perturbation V in {mathcal{N}} . In noncommutative geometry terms we remove summability hypotheses. This level of generality is made possible by introducing a new idea from [3]. There it was observed that M. G. Krein’s spectral shift function (in certain restricted cases with V trace class) computes spectral flow. The present paper extends Krein’s theory to the setting of semifinite spectral triples where D has compact resolvent belonging to {mathcal{N}} and V is any bounded self-adjoint operator in {mathcal{N}} . We give a definition of the spectral shift function under these hypotheses and show that it computes spectral flow. This is made possible by the understanding discovered in the present paper of the interplay between spectral shift function theory and the analytic theory of spectral flow. It is this interplay that enables us to take Singer’s idea much further to create a large class of one forms whose integrals calculate spectral flow. These advances depend critically on a new approach to the calculus of functions of non-commuting operators discovered in [3] which generalizes the double operator integral formalism of [8-10]. One surprising conclusion that follows from our results is that the Krein spectral shift function is computed, in certain circumstances, by the Atiyah-Patodi-Singer index theorem [2].

Application of Adjoint Method and Spectral-Element Method to Tomographic Inversion of Regional Seismological Structure Beneath Japanese Islands

NASA Astrophysics Data System (ADS)

Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.

2014-12-01

Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.

Burst wait time simulation of CALIBAN reactor at delayed super-critical state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humbert, P.; Authier, N.; Richard, B.

2012-07-01

In the past, the super prompt critical wait time probability distribution was measured on CALIBAN fast burst reactor [4]. Afterwards, these experiments were simulated with a very good agreement by solving the non-extinction probability equation [5]. Recently, the burst wait time probability distribution has been measured at CEA-Valduc on CALIBAN at different delayed super-critical states [6]. However, in the delayed super-critical case the non-extinction probability does not give access to the wait time distribution. In this case it is necessary to compute the time dependent evolution of the full neutron count number probability distribution. In this paper we present themore » point model deterministic method used to calculate the probability distribution of the wait time before a prescribed count level taking into account prompt neutrons and delayed neutron precursors. This method is based on the solution of the time dependent adjoint Kolmogorov master equations for the number of detections using the generating function methodology [8,9,10] and inverse discrete Fourier transforms. The obtained results are then compared to the measurements and Monte-Carlo calculations based on the algorithm presented in [7]. (authors)« less

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the monotone and stable discrete-analytical numerical schemes [1]-[3] conserving the positivity of the chemical substance concentrations and possessing the properties of energy and mass balance that are postulated in the general variational principle for integrated models. All algorithms for solution of transport, diffusion and transformation problems are direct (without iterations). The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References Penenko V., Tsvetova E. Discrete-analytical methods for the implementation of variational principles in environmental applications// Journal of computational and applied mathematics, 2009, v. 226, 319-330. Penenko A.V. Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods// Numerical Analysis and Applications, 2012, V. 5, pp 326-341. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models //Numerical Analysis and Applications, 2013 (in press).

An eigenvalue approach for the automatic scaling of unknowns in model-based reconstructions: Application to real-time phase-contrast flow MRI.

PubMed

Tan, Zhengguo; Hohage, Thorsten; Kalentev, Oleksandr; Joseph, Arun A; Wang, Xiaoqing; Voit, Dirk; Merboldt, K Dietmar; Frahm, Jens

2017-12-01

The purpose of this work is to develop an automatic method for the scaling of unknowns in model-based nonlinear inverse reconstructions and to evaluate its application to real-time phase-contrast (RT-PC) flow magnetic resonance imaging (MRI). Model-based MRI reconstructions of parametric maps which describe a physical or physiological function require the solution of a nonlinear inverse problem, because the list of unknowns in the extended MRI signal equation comprises multiple functional parameters and all coil sensitivity profiles. Iterative solutions therefore rely on an appropriate scaling of unknowns to numerically balance partial derivatives and regularization terms. The scaling of unknowns emerges as a self-adjoint and positive-definite matrix which is expressible by its maximal eigenvalue and solved by power iterations. The proposed method is applied to RT-PC flow MRI based on highly undersampled acquisitions. Experimental validations include numerical phantoms providing ground truth and a wide range of human studies in the ascending aorta, carotid arteries, deep veins during muscular exercise and cerebrospinal fluid during deep respiration. For RT-PC flow MRI, model-based reconstructions with automatic scaling not only offer velocity maps with high spatiotemporal acuity and much reduced phase noise, but also ensure fast convergence as well as accurate and precise velocities for all conditions tested, i.e. for different velocity ranges, vessel sizes and the simultaneous presence of signals with velocity aliasing. In summary, the proposed automatic scaling of unknowns in model-based MRI reconstructions yields quantitatively reliable velocities for RT-PC flow MRI in various experimental scenarios. Copyright © 2017 John Wiley & Sons, Ltd.

Theoretical Evaluation of the Maximum Work of Free-Piston Engine Generators

NASA Astrophysics Data System (ADS)

Kojima, Shinji

2017-01-01

Utilizing the adjoint equations that originate from the calculus of variations, we have calculated the maximum thermal efficiency that is theoretically attainable by free-piston engine generators considering the work loss due to friction and Joule heat. Based on the adjoint equations with seven dimensionless parameters, the trajectory of the piston, the histories of the electric current, the work done, and the two kinds of losses have been derived in analytic forms. Using these we have conducted parametric studies for the optimized Otto and Brayton cycles. The smallness of the pressure ratio of the Brayton cycle makes the net work done negative even when the duration of heat addition is optimized to give the maximum amount of heat addition. For the Otto cycle, the net work done is positive, and both types of losses relative to the gross work done become smaller with the larger compression ratio. Another remarkable feature of the optimized Brayton cycle is that the piston trajectory of the heat addition/disposal process is expressed by the same equation as that of an adiabatic process. The maximum thermal efficiency of any combination of isochoric and isobaric heat addition/disposal processes, such as the Sabathe cycle, may be deduced by applying the methods described here.

The coupling of the neutron transport application RATTLESNAKE to the nuclear fuels performance application BISON under the MOOSE framework

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gleicher, Frederick N.; Williamson, Richard L.; Ortensi, Javier

The MOOSE neutron transport application RATTLESNAKE was coupled to the fuels performance application BISON to provide a higher fidelity tool for fuel performance simulation. This project is motivated by the desire to couple a high fidelity core analysis program (based on the self-adjoint angular flux equations) to a high fidelity fuel performance program, both of which can simulate on unstructured meshes. RATTLESNAKE solves self-adjoint angular flux transport equation and provides a sub-pin level resolution of the multigroup neutron flux with resonance treatment during burnup or a fast transient. BISON solves the coupled thermomechanical equations for the fuel on a sub-millimetermore » scale. Both applications are able to solve their respective systems on aligned and unaligned unstructured finite element meshes. The power density and local burnup was transferred from RATTLESNAKE to BISON with the MOOSE Multiapp transfer system. Multiple depletion cases were run with one-way data transfer from RATTLESNAKE to BISON. The eigenvalues are shown to agree well with values obtained from the lattice physics code DRAGON. The one-way data transfer of power density is shown to agree with the power density obtained from an internal Lassman-style model in BISON.« less

A Minimum Fuel Based Estimator for Maneuver and Natrual Dynamics Reconstruction

NASA Astrophysics Data System (ADS)

Lubey, D.; Scheeres, D.

2013-09-01

The vast and growing population of objects in Earth orbit (active and defunct spacecraft, orbital debris, etc.) offers many unique challenges when it comes to tracking these objects and associating the resulting observations. Complicating these challenges are the inaccurate natural dynamical models of these objects, the active maneuvers of spacecraft that deviate them from their ballistic trajectories, and the fact that spacecraft are tracked and operated by separate agencies. Maneuver detection and reconstruction algorithms can help with each of these issues by estimating mismodeled and unmodeled dynamics through indirect observation of spacecraft. It also helps to verify the associations made by an object correlation algorithm or aid in making those associations, which is essential when tracking objects in orbit. The algorithm developed in this study applies an Optimal Control Problem (OCP) Distance Metric approach to the problems of Maneuver Reconstruction and Dynamics Estimation. This was first developed by Holzinger, Scheeres, and Alfriend (2011), with a subsequent study by Singh, Horwood, and Poore (2012). This method estimates the minimum fuel control policy rather than the state as a typical Kalman Filter would. This difference ensures that the states are connected through a given dynamical model and allows for automatic covariance manipulation, which can help to prevent filter saturation. Using a string of measurements (either verified or hypothesized to correlate with one another), the algorithm outputs a corresponding string of adjoint and state estimates with associated noise. Post-processing techniques are implemented, which when applied to the adjoint estimates can remove noise and expose unmodeled maneuvers and mismodeled natural dynamics. Specifically, the estimated controls are used to determine spacecraft dependent accelerations (atmospheric drag and solar radiation pressure) using an adapted form of the Optimal Control based natural dynamics estimation scheme developed by Lubey and Scheeres (2012). In order to allow for direct comparison, the estimator developed here was modeled after a typical Kalman Filter. The estimator forces the terminal state to lie on a manifold that satisfies the least squares with a priori information cost function, thus establishing a link with a typical Kalman filter. Terms are collected into a pseudo-Kalman Gain, which creates an equivalent form in the state estimates and covariances between the two estimators. While the two estimators share common roots, the inclusion of control in the Minimum Fuel Estimator gives it special properties. For instance, the inclusion of adjoint noise can help to automatically prevent filter saturation in a manner similar to a State Noise Compensation Algorithm. This property is quite important when considering dynamics mismodeling as filter saturation will cause estimate divergence for mismodeled systems. Additional properties and alternative forms of the estimator are also explored in this study. Several implementations of this estimator are given in this paper. It is applied to LEO, GEO, and GTO orbits with drag and SRP mismodeling. The inclusion of unmodeled maneuvers is also considered. These numerical simulations verify the mathematical properties of this estimator, and demonstrate the advantages that this estimator has over typical Kalman Filters.

Aerothermodynamic shape optimization of hypersonic blunt bodies

NASA Astrophysics Data System (ADS)

Eyi, Sinan; Yumuşak, Mine

2015-07-01

The aim of this study is to develop a reliable and efficient design tool that can be used in hypersonic flows. The flow analysis is based on the axisymmetric Euler/Navier-Stokes and finite-rate chemical reaction equations. The equations are coupled simultaneously and solved implicitly using Newton's method. The Jacobian matrix is evaluated analytically. A gradient-based numerical optimization is used. The adjoint method is utilized for sensitivity calculations. The objective of the design is to generate a hypersonic blunt geometry that produces the minimum drag with low aerodynamic heating. Bezier curves are used for geometry parameterization. The performances of the design optimization method are demonstrated for different hypersonic flow conditions.

Elliptic complexes over C∗-algebras of compact operators

NASA Astrophysics Data System (ADS)

Krýsl, Svatopluk

2016-03-01

For a C∗-algebra A of compact operators and a compact manifold M, we prove that the Hodge theory holds for A-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective A-Hilbert bundles over M. For these C∗-algebras and manifolds, we get a topological isomorphism between the cohomology groups of an A-elliptic complex and the space of harmonic elements of the complex. Consequently, the cohomology groups appear to be finitely generated projective C∗-Hilbert modules and especially, Banach spaces. We also prove that in the category of Hilbert A-modules and continuous adjointable Hilbert A-module homomorphisms, the property of a complex of being self-adjoint parametrix possessing characterizes the complexes of Hodge type.

Land-surface parameter optimisation using data assimilation techniques: the adJULES system V1.0

DOE PAGES

Raoult, Nina M.; Jupp, Tim E.; Cox, Peter M.; ...

2016-08-25

Land-surface models (LSMs) are crucial components of the Earth system models (ESMs) that are used to make coupled climate–carbon cycle projections for the 21st century. The Joint UK Land Environment Simulator (JULES) is the land-surface model used in the climate and weather forecast models of the UK Met Office. JULES is also extensively used offline as a land-surface impacts tool, forced with climatologies into the future. In this study, JULES is automatically differentiated with respect to JULES parameters using commercial software from FastOpt, resulting in an analytical gradient, or adjoint, of the model. Using this adjoint, the adJULES parameter estimationmore » system has been developed to search for locally optimum parameters by calibrating against observations. This paper describes adJULES in a data assimilation framework and demonstrates its ability to improve the model–data fit using eddy-covariance measurements of gross primary production (GPP) and latent heat (LE) fluxes. adJULES also has the ability to calibrate over multiple sites simultaneously. This feature is used to define new optimised parameter values for the five plant functional types (PFTs) in JULES. The optimised PFT-specific parameters improve the performance of JULES at over 85 % of the sites used in the study, at both the calibration and evaluation stages. Furthermore, the new improved parameters for JULES are presented along with the associated uncertainties for each parameter.« less

PRODUCTION OF SOUND BY UNSTEADY THROTTLING OF FLOW INTO A RESONANT CAVITY, WITH APPLICATION TO VOICED SPEECH

PubMed Central

Howe, M. S.; McGowan, R. S.

2011-01-01

An analysis is made of the sound generated by the time-dependent throttling of a nominally steady stream of air through a small orifice into a flow-through resonant cavity. This is exemplified by the production of voiced speech, where air from the lungs enters the vocal tract through the glottis at a time variable volume flow rate Q(t) controlled by oscillations of the glottis cross-section. Voicing theory has hitherto determined Q from a heuristic, reduced complexity ‘Fant’ differential equation (G. Fant, Acoustic Theory of Speech Production, 1960). A new self-consistent, integro-differential form of this equation is derived in this paper using the theory of aerodynamic sound, with full account taken of the back-reaction of the resonant tract on the glottal flux Q. The theory involves an aeroacoustic Green’s function (G) for flow-surface interactions in a time-dependent glottis, so making the problem non-self-adjoint. In complex problems of this type it is not usually possible to obtain G in an explicit analytic form. The principal objective of the paper is to show how the Fant equation can still be derived in such cases from a consideration of the equation of aerodynamic sound and from the adjoint of the equation governing G in the neighbourhood of the ‘throttle’. The theory is illustrated by application to the canonical problem of throttled flow into a Helmholtz resonator. PMID:21666824

Airfoil Design Using a Coupled Euler and Integral Boundary Layer Method with Adjoint Based Sensitivities

NASA Technical Reports Server (NTRS)

Edwards, S.; Reuther, J.; Chattot, J. J.

1997-01-01

The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjunct approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speed.

A fast finite-difference algorithm for topology optimization of permanent magnets

NASA Astrophysics Data System (ADS)

Abert, Claas; Huber, Christian; Bruckner, Florian; Vogler, Christoph; Wautischer, Gregor; Suess, Dieter

2017-09-01

We present a finite-difference method for the topology optimization of permanent magnets that is based on the fast-Fourier-transform (FFT) accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and uses an adjoint method for the gradient computation. Comparison to various state-of-the-art finite-element implementations shows a superior performance and accuracy. Moreover, the presented method is very flexible and easy to implement due to various preexisting FFT stray-field implementations that can be used.

Numerical solution of inverse scattering for near-field optics.

PubMed

Bao, Gang; Li, Peijun

2007-06-01

A novel regularized recursive linearization method is developed for a two-dimensional inverse medium scattering problem that arises in near-field optics, which reconstructs the scatterer of an inhomogeneous medium located on a substrate from data accessible through photon scanning tunneling microscopy experiments. Based on multiple frequency scattering data, the method starts from the Born approximation corresponding to weak scattering at a low frequency, and each update is obtained by continuation on the wavenumber from solutions of one forward problem and one adjoint problem of the Helmholtz equation.

The Scaling of Broadband Shock-Associated Noise with Increasing Temperature

NASA Technical Reports Server (NTRS)

Miller, Steven A.

2012-01-01

A physical explanation for the saturation of broadband shock-associated noise (BBSAN) intensity with increasing jet stagnation temperature has eluded investigators. An explanation is proposed for this phenomenon with the use of an acoustic analogy. For this purpose the acoustic analogy of Morris and Miller is examined. To isolate the relevant physics, the scaling of BBSAN at the peak intensity level at the sideline ( = 90 degrees) observer location is examined. Scaling terms are isolated from the acoustic analogy and the result is compared using a convergent nozzle with the experiments of Bridges and Brown and using a convergent-divergent nozzle with the experiments of Kuo, McLaughlin, and Morris at four nozzle pressure ratios in increments of total temperature ratios from one to four. The equivalent source within the framework of the acoustic analogy for BBSAN is based on local field quantities at shock wave shear layer interactions. The equivalent source combined with accurate calculations of the propagation of sound through the jet shear layer, using an adjoint vector Green s function solver of the linearized Euler equations, allows for predictions that retain the scaling with respect to stagnation pressure and allows for the accurate saturation of BBSAN with increasing stagnation temperature. This is a minor change to the source model relative to the previously developed models. The full development of the scaling term is shown. The sources and vector Green s function solver are informed by steady Reynolds-Averaged Navier-Stokes solutions. These solutions are examined as a function of stagnation temperature at the first shock wave shear layer interaction. It is discovered that saturation of BBSAN with increasing jet stagnation temperature occurs due to a balance between the amplification of the sound propagation through the shear layer and the source term scaling.A physical explanation for the saturation of broadband shock-associated noise (BBSAN) intensity with increasing jet stagnation temperature has eluded investigators. An explanation is proposed for this phenomenon with the use of an acoustic analogy. For this purpose the acoustic analogy of Morris and Miller is examined. To isolate the relevant physics, the scaling of BBSAN at the peak intensity level at the sideline psi = 90 degrees) observer location is examined. Scaling terms are isolated from the acoustic analogy and the result is compared using a convergent nozzle with the experiments of Bridges and Brown and using a convergent-divergent nozzle with the experiments of Kuo, McLaughlin, and Morris at four nozzle pressure ratios in increments of total temperature ratios from one to four. The equivalent source within the framework of the acoustic analogy for BBSAN is based on local field quantities at shock wave shear layer interactions. The equivalent source combined with accurate calculations of the propagation of sound through the jet shear layer, using an adjoint vector Green s function solver of the linearized Euler equations, allows for predictions that retain the scaling with respect to stagnation pressure and allows for the accurate saturation of BBSAN with increasing stagnation temperature. This is a minor change to the source model relative to the previously developed models. The full development of the scaling term is shown. The sources and vector Green s function solver are informed by steady Reynolds-Averaged Navier-Stokes solutions. These solutions are examined as a function of stagnation temperature at the first shock wave shear layer interaction. It is discovered that saturation of BBSAN with increasing jet stagnation temperature occurs due to a balance between the amplification of the sound propagation through the shear layer and the source term scaling.

Objective-function hybridization in adjoint seismic tomography

NASA Astrophysics Data System (ADS)

Yuan, Yanhua O.; Bozdaǧ, Ebru; Simons, Frederik J.; Gao, Fuchun

2017-04-01

Seismic tomography is at the threshold of a new era of massive data sets. Improving the resolution and accuracy of the estimated Earth structure by assimilating as much information as possible from every seismogram, remains a challenge. We propose the use of the "exponentiated phase'', a type of measurement that robustly captures the information contained in the variation of phase with time in the seismogram. We explore its performance in both conventional and double-difference (Yuan, Simons & Tromp, Geophys. J. Intern, 2016) adjoint seismic tomography. We introduce a hybrid approach to combine different objective functions, taking advantage of both conventional and our new measurements. We initially focus on phase measurements in global tomography. Cross-correlation measurements are generally tailored by window selection algorithms, such as FLEXWIN, to balance amplitude differences between seismic phases. However, within selection windows, such measurements still favor the larger-amplitude phases. It is also difficult to select all usable portions of the seismogram in an optimal way, such that much information may be lost, particularly the scattered waves. Time-continuous phase measurements, which associate a time shift with each point in time, have the potential to extract information from every wiggle in the seismogram without cutting it into small pieces. One such type of measurement is the instantaneous phase (Bozdaǧ, Trampert & Tromp, Geophys. J. Intern, 2011), which thus far has not been implemented in realistic seismic-tomography experiments, given how difficult the computation of phase can sometimes be. The exponentiated phase, on the other hand, is computed on the basis of the normalized analytic signal, does not need an explicit measure of phase, and is thus much easier to implement, and more practical for real-world applications. Both types of measurements carry comparable structural information when direct measurements of the phase are not wrapped. To deal with cycle skips, we use the exponentiated phase to take into account relatively small-magnitude scattered waves at long periods, while using cross-correlation measurements on windows determined by FLEXWIN to select distinct body-wave arrivals without complicating measurements due to non-linearities at short periods. We present synthetic experiments to show how exponentiated-phase, cross-correlation measurements, and their hybridization affect tomographic results. We demonstrate the use of hybrid measurements on teleseismic seismograms, in which surface waves are prominent, for continental and global seismic imaging. It is clear that the exponentiated-phase measurements behave well and provide a better representation of the smaller phases in the adjoint sources required for the computation of the misfit gradient. The combination of two different types of phase measurements in a hybrid approach moves us towards using all of the available information in a data set, addressing data quality and measurement challenges simultaneously, while negligibly affecting computation time.

Large-Scale Optimization for Bayesian Inference in Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Willcox, Karen; Marzouk, Youssef

2013-11-12

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT--Sandia component of themore » SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas--Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as ``reduce then sample'' and ``sample then reduce.'' In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

Final Report: Large-Scale Optimization for Bayesian Inference in Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghattas, Omar

2013-10-15

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimiza- tion) Project focuses on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimiza- tion and inversion methods. Our research is directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. Our efforts are integrated in the context of a challenging testbed problem that considers subsurface reacting flow and transport. The MIT component of the SAGUAROmore » Project addresses the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas-Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to- observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

Adjoint tomography and centroid-moment tensor inversion of the Kanto region, Japan

NASA Astrophysics Data System (ADS)

Miyoshi, T.

2017-12-01

A three-dimensional seismic wave speed model in the Kanto region of Japan was developed using adjoint tomography based on large computing. Starting with a model based on previous travel time tomographic results, we inverted the waveforms obtained at seismic broadband stations from 140 local earthquakes in the Kanto region to obtain the P- and S-wave speeds Vp and Vs. The synthetic displacements were calculated using the spectral element method (SEM; e.g. Komatitsch and Tromp 1999; Peter et al. 2011) in which the Kanto region was parameterized using 16 million grid points. The model parameters Vp and Vs were updated iteratively by Newton's method using the misfit and Hessian kernels until the misfit between the observed and synthetic waveforms was minimized. The proposed model reveals several anomalous areas with extremely low Vs values in comparison with those of the initial model. The synthetic waveforms obtained using the newly proposed model for the selected earthquakes show better fit than the initial model to the observed waveforms in different period ranges within 5-30 s. In the present study, all centroid times of the source solutions were determined using time shifts based on cross correlation to prevent high computing resources before the structural inversion. Additionally, parameters of centroid-moment solutions were fully determined using the SEM assuming the 3D structure (e.g. Liu et al. 2004). As a preliminary result, new solutions were basically same as their initial solutions. This may indicate that the 3D structure is not effective for the source estimation. Acknowledgements: This study was supported by JSPS KAKENHI Grant Number 16K21699.

Sources and processes contributing to nitrogen deposition: an adjoint model analysis applied to biodiversity hotspots worldwide.

PubMed

Paulot, Fabien; Jacob, Daniel J; Henze, Daven K

2013-04-02

Anthropogenic enrichment of reactive nitrogen (Nr) deposition is an ecological concern. We use the adjoint of a global 3-D chemical transport model (GEOS-Chem) to identify the sources and processes that control Nr deposition to an ensemble of biodiversity hotspots worldwide and two U.S. national parks (Cuyahoga and Rocky Mountain). We find that anthropogenic sources dominate deposition at all continental sites and are mainly regional (less than 1000 km) in origin. In Hawaii, Nr supply is controlled by oceanic emissions of ammonia (50%) and anthropogenic sources (50%), with important contributions from Asia and North America. Nr deposition is also sensitive in complicated ways to emissions of SO2, which affect Nr gas-aerosol partitioning, and of volatile organic compounds (VOCs), which affect oxidant concentrations and produce organic nitrate reservoirs. For example, VOC emissions generally inhibit deposition of locally emitted NOx but significantly increase Nr deposition downwind. However, in polluted boreal regions, anthropogenic VOC emissions can promote Nr deposition in winter. Uncertainties in chemical rate constants for OH + NO2 and NO2 hydrolysis also complicate the determination of source-receptor relationships for polluted sites in winter. Application of our adjoint sensitivities to the representative concentration pathways (RCPs) scenarios for 2010-2050 indicates that future decreases in Nr deposition due to NOx emission controls will be offset by concurrent increases in ammonia emissions from agriculture.

Top-down estimate of dust emissions through integration of MODIS and MISR aerosol retrievals with the GEOS-Chem adjoint model

NASA Astrophysics Data System (ADS)

Wang, Jun; Xu, Xiaoguang; Henze, Daven K.; Zeng, Jing; Ji, Qiang; Tsay, Si-Chee; Huang, Jianping

2012-04-01

Predicting the influences of dust on atmospheric composition, climate, and human health requires accurate knowledge of dust emissions, but large uncertainties persist in quantifying mineral sources. This study presents a new method for combined use of satellite-measured radiances and inverse modeling to spatially constrain the amount and location of dust emissions. The technique is illustrated with a case study in May 2008; the dust emissions in Taklimakan and Gobi deserts are spatially optimized using the GEOS-Chem chemical transport model and its adjoint constrained by aerosol optical depth (AOD) that are derived over the downwind dark-surface region in China from MODIS (Moderate Resolution Imaging Spectroradiometer) reflectance with the aerosol single scattering properties consistent with GEOS-chem. The adjoint inverse modeling yields an overall 51% decrease in prior dust emissions estimated by GEOS-Chem over the Taklimakan-Gobi area, with more significant reductions south of the Gobi Desert. The model simulation with optimized dust emissions shows much better agreement with independent observations from MISR (Multi-angle Imaging SpectroRadiometer) AOD and MODIS Deep Blue AOD over the dust source region and surface PM10 concentrations. The technique of this study can be applied to global multi-sensor remote sensing data for constraining dust emissions at various temporal and spatial scales, and hence improving the quantification of dust effects on climate, air quality, and human health.

Efficient checkpointing schemes for depletion perturbation solutions on memory-limited architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stripling, H. F.; Adams, M. L.; Hawkins, W. D.

2013-07-01

We describe a methodology for decreasing the memory footprint and machine I/O load associated with the need to access a forward solution during an adjoint solve. Specifically, we are interested in the depletion perturbation equations, where terms in the adjoint Bateman and transport equations depend on the forward flux solution. Checkpointing is the procedure of storing snapshots of the forward solution to disk and using these snapshots to recompute the parts of the forward solution that are necessary for the adjoint solve. For large problems, however, the storage cost of just a few copies of an angular flux vector canmore » exceed the available RAM on the host machine. We propose a methodology that does not checkpoint the angular flux vector; instead, we write and store converged source moments, which are typically of a much lower dimension than the angular flux solution. This reduces the memory footprint and I/O load of the problem, but requires that we perform single sweeps to reconstruct flux vectors on demand. We argue that this trade-off is exactly the kind of algorithm that will scale on advanced, memory-limited architectures. We analyze the cost, in terms of FLOPS and memory footprint, of five checkpointing schemes. We also provide computational results that support the analysis and show that the memory-for-work trade off does improve time to solution. (authors)« less

Top-down Estimate of Dust Emissions Through Integration of MODIS and MISR Aerosol Retrievals With the Geos-chem Adjoint Model

NASA Technical Reports Server (NTRS)

Wang, Jun; Xu, Xiaoguang; Henze, Daven K.; Zeng, Jing; Ji, Qiang; Tsay, Si-Chee; Huang, Jianping

2012-01-01

Predicting the influences of dust on atmospheric composition, climate, and human health requires accurate knowledge of dust emissions, but large uncertainties persist in quantifying mineral sources. This study presents a new method for combined use of satellite-measured radiances and inverse modeling to spatially constrain the amount and location of dust emissions. The technique is illustrated with a case study in May 2008; the dust emissions in Taklimakan and Gobi deserts are spatially optimized using the GEOSChem chemical transport model and its adjoint constrained by aerosol optical depth (AOD) that are derived over the downwind dark-surface region in China from MODIS (Moderate Resolution Imaging Spectroradiometer) reflectance with the aerosol single scattering properties consistent with GEOS-chem. The adjoint inverse modeling yields an overall 51% decrease in prior dust emissions estimated by GEOS-Chem over the Taklimakan-Gobi area, with more significant reductions south of the Gobi Desert. The model simulation with optimized dust emissions shows much better agreement with independent observations from MISR (Multi-angle Imaging SpectroRadiometer) AOD and MODIS Deep Blue AOD over the dust source region and surface PM10 concentrations. The technique of this study can be applied to global multi-sensor remote sensing data for constraining dust emissions at various temporal and spatial scales, and hence improving the quantification of dust effects on climate, air quality, and human health.

Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kent, James

2015-01-01

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

A variational data assimilation system for the range dependent acoustic model using the representer method: Theoretical derivations.

PubMed

Ngodock, Hans; Carrier, Matthew; Fabre, Josette; Zingarelli, Robert; Souopgui, Innocent

2017-07-01

This study presents the theoretical framework for variational data assimilation of acoustic pressure observations into an acoustic propagation model, namely, the range dependent acoustic model (RAM). RAM uses the split-step Padé algorithm to solve the parabolic equation. The assimilation consists of minimizing a weighted least squares cost function that includes discrepancies between the model solution and the observations. The minimization process, which uses the principle of variations, requires the derivation of the tangent linear and adjoint models of the RAM. The mathematical derivations are presented here, and, for the sake of brevity, a companion study presents the numerical implementation and results from the assimilation simulated acoustic pressure observations.

A string realisation of Ω-deformed Abelian N =2* theory

NASA Astrophysics Data System (ADS)

Angelantonj, Carlo; Antoniadis, Ignatios; Samsonyan, Marine

2017-10-01

The N =2* supersymmetric gauge theory is a massive deformation of N = 4, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-)Abelian N =2* theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual N = 2 chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the two-parameter Ω-background, in agreement with a recent proposal.