Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

NASA Astrophysics Data System (ADS)

Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

2010-12-01

Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

DOE PAGES

Shen, Qiuyang; Wu, Xuqing; Chen, Jiefu; ...

2017-11-20

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthalmore » resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.« less

Decomposing Large Inverse Problems with an Augmented Lagrangian Approach: Application to Joint Inversion of Body-Wave Travel Times and Surface-Wave Dispersion Measurements

NASA Astrophysics Data System (ADS)

Reiter, D. T.; Rodi, W. L.

2015-12-01

Constructing 3D Earth models through the joint inversion of large geophysical data sets presents numerous theoretical and practical challenges, especially when diverse types of data and model parameters are involved. Among the challenges are the computational complexity associated with large data and model vectors and the need to unify differing model parameterizations, forward modeling methods and regularization schemes within a common inversion framework. The challenges can be addressed in part by decomposing the inverse problem into smaller, simpler inverse problems that can be solved separately, providing one knows how to merge the separate inversion results into an optimal solution of the full problem. We have formulated an approach to the decomposition of large inverse problems based on the augmented Lagrangian technique from optimization theory. As commonly done, we define a solution to the full inverse problem as the Earth model minimizing an objective function motivated, for example, by a Bayesian inference formulation. Our decomposition approach recasts the minimization problem equivalently as the minimization of component objective functions, corresponding to specified data subsets, subject to the constraints that the minimizing models be equal. A standard optimization algorithm solves the resulting constrained minimization problems by alternating between the separate solution of the component problems and the updating of Lagrange multipliers that serve to steer the individual solution models toward a common model solving the full problem. We are applying our inversion method to the reconstruction of the·crust and upper-mantle seismic velocity structure across Eurasia.· Data for the inversion comprise a large set of P and S body-wave travel times·and fundamental and first-higher mode Rayleigh-wave group velocities.

Inverse problems in the design, modeling and testing of engineering systems

NASA Technical Reports Server (NTRS)

Alifanov, Oleg M.

1991-01-01

Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

PubMed

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

Joint Geophysical Inversion With Multi-Objective Global Optimization Methods

NASA Astrophysics Data System (ADS)

Lelievre, P. G.; Bijani, R.; Farquharson, C. G.

2015-12-01

Pareto multi-objective global optimization (PMOGO) methods generate a suite of solutions that minimize multiple objectives (e.g. data misfits and regularization terms) in a Pareto-optimal sense. Providing a suite of models, as opposed to a single model that minimizes a weighted sum of objectives, allows a more complete assessment of the possibilities and avoids the often difficult choice of how to weight each objective. We are applying PMOGO methods to three classes of inverse problems. The first class are standard mesh-based problems where the physical property values in each cell are treated as continuous variables. The second class of problems are also mesh-based but cells can only take discrete physical property values corresponding to known or assumed rock units. In the third class we consider a fundamentally different type of inversion in which a model comprises wireframe surfaces representing contacts between rock units; the physical properties of each rock unit remain fixed while the inversion controls the position of the contact surfaces via control nodes. This third class of problem is essentially a geometry inversion, which can be used to recover the unknown geometry of a target body or to investigate the viability of a proposed Earth model. Joint inversion is greatly simplified for the latter two problem classes because no additional mathematical coupling measure is required in the objective function. PMOGO methods can solve numerically complicated problems that could not be solved with standard descent-based local minimization methods. This includes the latter two classes of problems mentioned above. There are significant increases in the computational requirements when PMOGO methods are used but these can be ameliorated using parallelization and problem dimension reduction strategies.

The inverse Wiener polarity index problem for chemical trees.

PubMed

Du, Zhibin; Ali, Akbar

2018-01-01

The Wiener polarity number (which, nowadays, known as the Wiener polarity index and usually denoted by Wp) was devised by the chemist Harold Wiener, for predicting the boiling points of alkanes. The index Wp of chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices (carbon atoms) at distance 3. The inverse problems based on some well-known topological indices have already been addressed in the literature. The solution of such inverse problems may be helpful in speeding up the discovery of lead compounds having the desired properties. This paper is devoted to solving a stronger version of the inverse problem based on Wiener polarity index for chemical trees. More precisely, it is proved that for every integer t ∈ {n - 3, n - 2,…,3n - 16, 3n - 15}, n ≥ 6, there exists an n-vertex chemical tree T such that Wp(T) = t.

Approximation of the ruin probability using the scaled Laplace transform inversion

PubMed Central

Mnatsakanov, Robert M.; Sarkisian, Khachatur; Hakobyan, Artak

2015-01-01

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen–Weideman–Schmelzer and maximum entropy methods are presented via a simulation study. PMID:26752796

Cross hole GPR traveltime inversion using a fast and accurate neural network as a forward model

NASA Astrophysics Data System (ADS)

Mejer Hansen, Thomas

2017-04-01

Probabilistic formulated inverse problems can be solved using Monte Carlo based sampling methods. In principle both advanced prior information, such as based on geostatistics, and complex non-linear forward physical models can be considered. However, in practice these methods can be associated with huge computational costs that in practice limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error, that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival travel time inversion of cross hole ground-penetrating radar (GPR) data. An accurate forward model, based on 2D full-waveform modeling followed by automatic travel time picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the full forward model, and considerably faster, and more accurate, than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of the types of inverse problems that can be solved using non-linear Monte Carlo sampling techniques.

Solving Inverse Kinematics of Robot Manipulators by Means of Meta-Heuristic Optimisation

NASA Astrophysics Data System (ADS)

Wichapong, Kritsada; Bureerat, Sujin; Pholdee, Nantiwat

2018-05-01

This paper presents the use of meta-heuristic algorithms (MHs) for solving inverse kinematics of robot manipulators based on using forward kinematic. Design variables are joint angular displacements used to move a robot end-effector to the target in the Cartesian space while the design problem is posed to minimize error between target points and the positions of the robot end-effector. The problem is said to be a dynamic problem as the target points always changed by a robot user. Several well established MHs are used to solve the problem and the results obtained from using different meta-heuristics are compared based on the end-effector error and searching speed of the algorithms. From the study, the best performer will be obtained for setting as the baseline for future development of MH-based inverse kinematic solving.

NLSE: Parameter-Based Inversion Algorithm

NASA Astrophysics Data System (ADS)

Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Aldrin, John C.; Knopp, Jeremy S.

Chapter 11 introduced us to the notion of an inverse problem and gave us some examples of the value of this idea to the solution of realistic industrial problems. The basic inversion algorithm described in Chap. 11 was based upon the Gauss-Newton theory of nonlinear least-squares estimation and is called NLSE in this book. In this chapter we will develop the mathematical background of this theory more fully, because this algorithm will be the foundation of inverse methods and their applications during the remainder of this book. We hope, thereby, to introduce the reader to the application of sophisticated mathematical concepts to engineering practice without introducing excessive mathematical sophistication.

Fractional Gaussian model in global optimization

NASA Astrophysics Data System (ADS)

Dimri, V. P.; Srivastava, R. P.

2009-12-01

Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.

The attitude inversion method of geostationary satellites based on unscented particle filter

NASA Astrophysics Data System (ADS)

Du, Xiaoping; Wang, Yang; Hu, Heng; Gou, Ruixin; Liu, Hao

2018-04-01

The attitude information of geostationary satellites is difficult to be obtained since they are presented in non-resolved images on the ground observation equipment in space object surveillance. In this paper, an attitude inversion method for geostationary satellite based on Unscented Particle Filter (UPF) and ground photometric data is presented. The inversion algorithm based on UPF is proposed aiming at the strong non-linear feature in the photometric data inversion for satellite attitude, which combines the advantage of Unscented Kalman Filter (UKF) and Particle Filter (PF). This update method improves the particle selection based on the idea of UKF to redesign the importance density function. Moreover, it uses the RMS-UKF to partially correct the prediction covariance matrix, which improves the applicability of the attitude inversion method in view of UKF and the particle degradation and dilution of the attitude inversion method based on PF. This paper describes the main principles and steps of algorithm in detail, correctness, accuracy, stability and applicability of the method are verified by simulation experiment and scaling experiment in the end. The results show that the proposed method can effectively solve the problem of particle degradation and depletion in the attitude inversion method on account of PF, and the problem that UKF is not suitable for the strong non-linear attitude inversion. However, the inversion accuracy is obviously superior to UKF and PF, in addition, in the case of the inversion with large attitude error that can inverse the attitude with small particles and high precision.

Computational structures for robotic computations

NASA Technical Reports Server (NTRS)

Lee, C. S. G.; Chang, P. R.

1987-01-01

The computational problem of inverse kinematics and inverse dynamics of robot manipulators by taking advantage of parallelism and pipelining architectures is discussed. For the computation of inverse kinematic position solution, a maximum pipelined CORDIC architecture has been designed based on a functional decomposition of the closed-form joint equations. For the inverse dynamics computation, an efficient p-fold parallel algorithm to overcome the recurrence problem of the Newton-Euler equations of motion to achieve the time lower bound of O(log sub 2 n) has also been developed.

Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique

NASA Astrophysics Data System (ADS)

Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi

2013-09-01

According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.

Inverse solutions for electrical impedance tomography based on conjugate gradients methods

NASA Astrophysics Data System (ADS)

Wang, M.

2002-01-01

A multistep inverse solution for two-dimensional electric field distribution is developed to deal with the nonlinear inverse problem of electric field distribution in relation to its boundary condition and the problem of divergence due to errors introduced by the ill-conditioned sensitivity matrix and the noise produced by electrode modelling and instruments. This solution is based on a normalized linear approximation method where the change in mutual impedance is derived from the sensitivity theorem and a method of error vector decomposition. This paper presents an algebraic solution of the linear equations at each inverse step, using a generalized conjugate gradients method. Limiting the number of iterations in the generalized conjugate gradients method controls the artificial errors introduced by the assumption of linearity and the ill-conditioned sensitivity matrix. The solution of the nonlinear problem is approached using a multistep inversion. This paper also reviews the mathematical and physical definitions of the sensitivity back-projection algorithm based on the sensitivity theorem. Simulations and discussion based on the multistep algorithm, the sensitivity coefficient back-projection method and the Newton-Raphson method are given. Examples of imaging gas-liquid mixing and a human hand in brine are presented.

Performance impact of mutation operators of a subpopulation-based genetic algorithm for multi-robot task allocation problems.

PubMed

Liu, Chun; Kroll, Andreas

2016-01-01

Multi-robot task allocation determines the task sequence and distribution for a group of robots in multi-robot systems, which is one of constrained combinatorial optimization problems and more complex in case of cooperative tasks because they introduce additional spatial and temporal constraints. To solve multi-robot task allocation problems with cooperative tasks efficiently, a subpopulation-based genetic algorithm, a crossover-free genetic algorithm employing mutation operators and elitism selection in each subpopulation, is developed in this paper. Moreover, the impact of mutation operators (swap, insertion, inversion, displacement, and their various combinations) is analyzed when solving several industrial plant inspection problems. The experimental results show that: (1) the proposed genetic algorithm can obtain better solutions than the tested binary tournament genetic algorithm with partially mapped crossover; (2) inversion mutation performs better than other tested mutation operators when solving problems without cooperative tasks, and the swap-inversion combination performs better than other tested mutation operators/combinations when solving problems with cooperative tasks. As it is difficult to produce all desired effects with a single mutation operator, using multiple mutation operators (including both inversion and swap) is suggested when solving similar combinatorial optimization problems.

A direct method for nonlinear ill-posed problems

NASA Astrophysics Data System (ADS)

Lakhal, A.

2018-02-01

We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.

Gravity inversion of a fault by Particle swarm optimization (PSO).

PubMed

Toushmalani, Reza

2013-01-01

Particle swarm optimization is a heuristic global optimization method and also an optimization algorithm, which is based on swarm intelligence. It comes from the research on the bird and fish flock movement behavior. In this paper we introduce and use this method in gravity inverse problem. We discuss the solution for the inverse problem of determining the shape of a fault whose gravity anomaly is known. Application of the proposed algorithm to this problem has proven its capability to deal with difficult optimization problems. The technique proved to work efficiently when tested to a number of models.

An ambiguity of information content and error in an ill-posed satellite inversion

NASA Astrophysics Data System (ADS)

Koner, Prabhat

According to Rodgers (2000, stochastic approach), the averaging kernel (AK) is the representational matrix to understand the information content in a scholastic inversion. On the other hand, in deterministic approach this is referred to as model resolution matrix (MRM, Menke 1989). The analysis of AK/MRM can only give some understanding of how much regularization is imposed on the inverse problem. The trace of the AK/MRM matrix, which is the so-called degree of freedom from signal (DFS; stochastic) or degree of freedom in retrieval (DFR; deterministic). There are no physical/mathematical explanations in the literature: why the trace of the matrix is a valid form to calculate this quantity? We will present an ambiguity between information and error using a real life problem of SST retrieval from GOES13. The stochastic information content calculation is based on the linear assumption. The validity of such mathematics in satellite inversion will be questioned because it is based on the nonlinear radiative transfer and ill-conditioned inverse problems. References: Menke, W., 1989: Geophysical data analysis: discrete inverse theory. San Diego academic press. Rodgers, C.D., 2000: Inverse methods for atmospheric soundings: theory and practice. Singapore :World Scientific.

The inverse electroencephalography pipeline

NASA Astrophysics Data System (ADS)

Weinstein, David Michael

The inverse electroencephalography (EEG) problem is defined as determining which regions of the brain are active based on remote measurements recorded with scalp EEG electrodes. An accurate solution to this problem would benefit both fundamental neuroscience research and clinical neuroscience applications. However, constructing accurate patient-specific inverse EEG solutions requires complex modeling, simulation, and visualization algorithms, and to date only a few systems have been developed that provide such capabilities. In this dissertation, a computational system for generating and investigating patient-specific inverse EEG solutions is introduced, and the requirements for each stage of this Inverse EEG Pipeline are defined and discussed. While the requirements of many of the stages are satisfied with existing algorithms, others have motivated research into novel modeling and simulation methods. The principal technical results of this work include novel surface-based volume modeling techniques, an efficient construction for the EEG lead field, and the Open Source release of the Inverse EEG Pipeline software for use by the bioelectric field research community. In this work, the Inverse EEG Pipeline is applied to three research problems in neurology: comparing focal and distributed source imaging algorithms; separating measurements into independent activation components for multifocal epilepsy; and localizing the cortical activity that produces the P300 effect in schizophrenia.

Restart Operator Meta-heuristics for a Problem-Oriented Evolutionary Strategies Algorithm in Inverse Mathematical MISO Modelling Problem Solving

NASA Astrophysics Data System (ADS)

Ryzhikov, I. S.; Semenkin, E. S.

2017-02-01

This study is focused on solving an inverse mathematical modelling problem for dynamical systems based on observation data and control inputs. The mathematical model is being searched in the form of a linear differential equation, which determines the system with multiple inputs and a single output, and a vector of the initial point coordinates. The described problem is complex and multimodal and for this reason the proposed evolutionary-based optimization technique, which is oriented on a dynamical system identification problem, was applied. To improve its performance an algorithm restart operator was implemented.

Research on inverse, hybrid and optimization problems in engineering sciences with emphasis on turbomachine aerodynamics: Review of Chinese advances

NASA Technical Reports Server (NTRS)

Liu, Gao-Lian

1991-01-01

Advances in inverse design and optimization theory in engineering fields in China are presented. Two original approaches, the image-space approach and the variational approach, are discussed in terms of turbomachine aerodynamic inverse design. Other areas of research in turbomachine aerodynamic inverse design include the improved mean-streamline (stream surface) method and optimization theory based on optimal control. Among the additional engineering fields discussed are the following: the inverse problem of heat conduction, free-surface flow, variational cogeneration of optimal grid and flow field, and optimal meshing theory of gears.

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

The neural network approximation method for solving multidimensional nonlinear inverse problems of geophysics

NASA Astrophysics Data System (ADS)

Shimelevich, M. I.; Obornev, E. A.; Obornev, I. E.; Rodionov, E. A.

2017-07-01

The iterative approximation neural network method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The inverse problem is solved in the class of grid (block) models of the medium on a regularized parameterization grid. The construction principle of this grid relies on using the calculated values of the continuity modulus of the inverse operator and its modifications determining the degree of ambiguity of the solutions. The method provides approximate solutions of inverse problems with the maximal degree of detail given the specified degree of ambiguity with the total number of the sought parameters n × 103 of the medium. The a priori and a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the three-dimensional (3D) inversion of the synthesized 2D areal geoelectrical (audio magnetotelluric sounding, AMTS) data corresponding to the schematic model of a kimberlite pipe.

A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line

NASA Astrophysics Data System (ADS)

Its, A.; Sukhanov, V.

2016-05-01

The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.

Black hole algorithm for determining model parameter in self-potential data

NASA Astrophysics Data System (ADS)

Sungkono; Warnana, Dwa Desa

2018-01-01

Analysis of self-potential (SP) data is increasingly popular in geophysical method due to its relevance in many cases. However, the inversion of SP data is often highly nonlinear. Consequently, local search algorithms commonly based on gradient approaches have often failed to find the global optimum solution in nonlinear problems. Black hole algorithm (BHA) was proposed as a solution to such problems. As the name suggests, the algorithm was constructed based on the black hole phenomena. This paper investigates the application of BHA to solve inversions of field and synthetic self-potential (SP) data. The inversion results show that BHA accurately determines model parameters and model uncertainty. This indicates that BHA is highly potential as an innovative approach for SP data inversion.

Moving from pixel to object scale when inverting radiative transfer models for quantitative estimation of biophysical variables in vegetation (Invited)

NASA Astrophysics Data System (ADS)

Atzberger, C.

2013-12-01

The robust and accurate retrieval of vegetation biophysical variables using RTM is seriously hampered by the ill-posedness of the inverse problem. The contribution presents our object-based inversion approach and evaluate it against measured data. The proposed method takes advantage of the fact that nearby pixels are generally more similar than those at a larger distance. For example, within a given vegetation patch, nearby pixels often share similar leaf angular distributions. This leads to spectral co-variations in the n-dimensional spectral features space, which can be used for regularization purposes. Using a set of leaf area index (LAI) measurements (n=26) acquired over alfalfa, sugar beet and garlic crops of the Barrax test site (Spain), it is demonstrated that the proposed regularization using neighbourhood information yields more accurate results compared to the traditional pixel-based inversion. Principle of the ill-posed inverse problem and the proposed solution illustrated in the red-nIR feature space using (PROSAIL). [A] spectral trajectory ('soil trajectory') obtained for one leaf angle (ALA) and one soil brightness (αsoil), when LAI varies between 0 and 10, [B] 'soil trajectories' for 5 soil brightness values and three leaf angles, [C] ill-posed inverse problem: different combinations of ALA × αsoil yield an identical crossing point, [D] object-based RTM inversion; only one 'soil trajectory' fits all nine pixelswithin a gliding (3×3) window. The black dots (plus the rectangle=central pixel) represent the hypothetical position of nine pixels within a 3×3 (gliding) window. Assuming that over short distances (× 1 pixel) variations in soil brightness can be neglected, the proposed object-based inversion searches for one common set of ALA × αsoil so that the resulting 'soil trajectory' best fits the nine measured pixels. Ground measured vs. retrieved LAI values for three crops. Left: proposed object-based approach. Right: pixel-based inversion

A multi-frequency iterative imaging method for discontinuous inverse medium problem

NASA Astrophysics Data System (ADS)

Zhang, Lei; Feng, Lixin

2018-06-01

The inverse medium problem with discontinuous refractive index is a kind of challenging inverse problem. We employ the primal dual theory and fast solution of integral equations, and propose a new iterative imaging method. The selection criteria of regularization parameter is given by the method of generalized cross-validation. Based on multi-frequency measurements of the scattered field, a recursive linearization algorithm has been presented with respect to the frequency from low to high. We also discuss the initial guess selection strategy by semi-analytical approaches. Numerical experiments are presented to show the effectiveness of the proposed method.

Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks

NASA Astrophysics Data System (ADS)

Jiang, Fei-Bo; Dai, Qian-Wei; Dong, Li

2016-06-01

Conventional artificial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network (PBNN) nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter α k , which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

NASA Astrophysics Data System (ADS)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Rapid processing of data based on high-performance algorithms for solving inverse problems and 3D-simulation of the tsunami and earthquakes

NASA Astrophysics Data System (ADS)

Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.

2012-04-01

We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to create technology «no frost», realizing a steady stream of direct and inverse problems: solving the direct problem, the visualization and comparison with observed data, to solve the inverse problem (correction of the model parameters). The main objective of further work is the creation of a workstation operating emergency tool that could be used by an emergency duty person in real time.

Geophysical approaches to inverse problems: A methodological comparison. Part 1: A Posteriori approach

NASA Technical Reports Server (NTRS)

Seidman, T. I.; Munteanu, M. J.

1979-01-01

The relationships of a variety of general computational methods (and variances) for treating illposed problems such as geophysical inverse problems are considered. Differences in approach and interpretation based on varying assumptions as to, e.g., the nature of measurement uncertainties are discussed along with the factors to be considered in selecting an approach. The reliability of the results of such computation is addressed.

Space structures insulating material's thermophysical and radiation properties estimation

NASA Astrophysics Data System (ADS)

Nenarokomov, A. V.; Alifanov, O. M.; Titov, D. M.

2007-11-01

In many practical situations in aerospace technology it is impossible to measure directly such properties of analyzed materials (for example, composites) as thermal and radiation characteristics. The only way that can often be used to overcome these difficulties is indirect measurements. This type of measurement is usually formulated as the solution of inverse heat transfer problems. Such problems are ill-posed in mathematical sense and their main feature shows itself in the solution instabilities. That is why special regularizing methods are needed to solve them. The experimental methods of identification of the mathematical models of heat transfer based on solving the inverse problems are one of the modern effective solving manners. The objective of this paper is to estimate thermal and radiation properties of advanced materials using the approach based on inverse methods.

Query-based learning for aerospace applications.

PubMed

Saad, E W; Choi, J J; Vian, J L; Wunsch, D C Ii

2003-01-01

Models of real-world applications often include a large number of parameters with a wide dynamic range, which contributes to the difficulties of neural network training. Creating the training data set for such applications becomes costly, if not impossible. In order to overcome the challenge, one can employ an active learning technique known as query-based learning (QBL) to add performance-critical data to the training set during the learning phase, thereby efficiently improving the overall learning/generalization. The performance-critical data can be obtained using an inverse mapping called network inversion (discrete network inversion and continuous network inversion) followed by oracle query. This paper investigates the use of both inversion techniques for QBL learning, and introduces an original heuristic to select the inversion target values for continuous network inversion method. Efficiency and generalization was further enhanced by employing node decoupled extended Kalman filter (NDEKF) training and a causality index (CI) as a means to reduce the input search dimensionality. The benefits of the overall QBL approach are experimentally demonstrated in two aerospace applications: a classification problem with large input space and a control distribution problem.

Time-reversal and Bayesian inversion

NASA Astrophysics Data System (ADS)

Debski, Wojciech

2017-04-01

Probabilistic inversion technique is superior to the classical optimization-based approach in all but one aspects. It requires quite exhaustive computations which prohibit its use in huge size inverse problems like global seismic tomography or waveform inversion to name a few. The advantages of the approach are, however, so appealing that there is an ongoing continuous afford to make the large inverse task as mentioned above manageable with the probabilistic inverse approach. One of the perspective possibility to achieve this goal relays on exploring the internal symmetry of the seismological modeling problems in hand - a time reversal and reciprocity invariance. This two basic properties of the elastic wave equation when incorporating into the probabilistic inversion schemata open a new horizons for Bayesian inversion. In this presentation we discuss the time reversal symmetry property, its mathematical aspects and propose how to combine it with the probabilistic inverse theory into a compact, fast inversion algorithm. We illustrate the proposed idea with the newly developed location algorithm TRMLOC and discuss its efficiency when applied to mining induced seismic data.

A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

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

Li, Jinglai, E-mail: jinglaili@sjtu.edu.cn; Lin, Guang, E-mail: lin491@purdue.edu; Computational Sciences and Mathematics Division, Pacific Northwest National Laboratory, Richland, WA 99352

2015-09-01

In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by threemore » steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.« less

EIT image reconstruction based on a hybrid FE-EFG forward method and the complete-electrode model.

PubMed

Hadinia, M; Jafari, R; Soleimani, M

2016-06-01

This paper presents the application of the hybrid finite element-element free Galerkin (FE-EFG) method for the forward and inverse problems of electrical impedance tomography (EIT). The proposed method is based on the complete electrode model. Finite element (FE) and element-free Galerkin (EFG) methods are accurate numerical techniques. However, the FE technique has meshing task problems and the EFG method is computationally expensive. In this paper, the hybrid FE-EFG method is applied to take both advantages of FE and EFG methods, the complete electrode model of the forward problem is solved, and an iterative regularized Gauss-Newton method is adopted to solve the inverse problem. The proposed method is applied to compute Jacobian in the inverse problem. Utilizing 2D circular homogenous models, the numerical results are validated with analytical and experimental results and the performance of the hybrid FE-EFG method compared with the FE method is illustrated. Results of image reconstruction are presented for a human chest experimental phantom.

A new approach to integrate GPU-based Monte Carlo simulation into inverse treatment plan optimization for proton therapy.

PubMed

Li, Yongbao; Tian, Zhen; Song, Ting; Wu, Zhaoxia; Liu, Yaqiang; Jiang, Steve; Jia, Xun

2017-01-07

Monte Carlo (MC)-based spot dose calculation is highly desired for inverse treatment planning in proton therapy because of its accuracy. Recent studies on biological optimization have also indicated the use of MC methods to compute relevant quantities of interest, e.g. linear energy transfer. Although GPU-based MC engines have been developed to address inverse optimization problems, their efficiency still needs to be improved. Also, the use of a large number of GPUs in MC calculation is not favorable for clinical applications. The previously proposed adaptive particle sampling (APS) method can improve the efficiency of MC-based inverse optimization by using the computationally expensive MC simulation more effectively. This method is more efficient than the conventional approach that performs spot dose calculation and optimization in two sequential steps. In this paper, we propose a computational library to perform MC-based spot dose calculation on GPU with the APS scheme. The implemented APS method performs a non-uniform sampling of the particles from pencil beam spots during the optimization process, favoring those from the high intensity spots. The library also conducts two computationally intensive matrix-vector operations frequently used when solving an optimization problem. This library design allows a streamlined integration of the MC-based spot dose calculation into an existing proton therapy inverse planning process. We tested the developed library in a typical inverse optimization system with four patient cases. The library achieved the targeted functions by supporting inverse planning in various proton therapy schemes, e.g. single field uniform dose, 3D intensity modulated proton therapy, and distal edge tracking. The efficiency was 41.6  ±  15.3% higher than the use of a GPU-based MC package in a conventional calculation scheme. The total computation time ranged between 2 and 50 min on a single GPU card depending on the problem size.

A new approach to integrate GPU-based Monte Carlo simulation into inverse treatment plan optimization for proton therapy

NASA Astrophysics Data System (ADS)

Li, Yongbao; Tian, Zhen; Song, Ting; Wu, Zhaoxia; Liu, Yaqiang; Jiang, Steve; Jia, Xun

2017-01-01

Monte Carlo (MC)-based spot dose calculation is highly desired for inverse treatment planning in proton therapy because of its accuracy. Recent studies on biological optimization have also indicated the use of MC methods to compute relevant quantities of interest, e.g. linear energy transfer. Although GPU-based MC engines have been developed to address inverse optimization problems, their efficiency still needs to be improved. Also, the use of a large number of GPUs in MC calculation is not favorable for clinical applications. The previously proposed adaptive particle sampling (APS) method can improve the efficiency of MC-based inverse optimization by using the computationally expensive MC simulation more effectively. This method is more efficient than the conventional approach that performs spot dose calculation and optimization in two sequential steps. In this paper, we propose a computational library to perform MC-based spot dose calculation on GPU with the APS scheme. The implemented APS method performs a non-uniform sampling of the particles from pencil beam spots during the optimization process, favoring those from the high intensity spots. The library also conducts two computationally intensive matrix-vector operations frequently used when solving an optimization problem. This library design allows a streamlined integration of the MC-based spot dose calculation into an existing proton therapy inverse planning process. We tested the developed library in a typical inverse optimization system with four patient cases. The library achieved the targeted functions by supporting inverse planning in various proton therapy schemes, e.g. single field uniform dose, 3D intensity modulated proton therapy, and distal edge tracking. The efficiency was 41.6  ±  15.3% higher than the use of a GPU-based MC package in a conventional calculation scheme. The total computation time ranged between 2 and 50 min on a single GPU card depending on the problem size.

A New Approach to Integrate GPU-based Monte Carlo Simulation into Inverse Treatment Plan Optimization for Proton Therapy

PubMed Central

Li, Yongbao; Tian, Zhen; Song, Ting; Wu, Zhaoxia; Liu, Yaqiang; Jiang, Steve; Jia, Xun

2016-01-01

Monte Carlo (MC)-based spot dose calculation is highly desired for inverse treatment planning in proton therapy because of its accuracy. Recent studies on biological optimization have also indicated the use of MC methods to compute relevant quantities of interest, e.g. linear energy transfer. Although GPU-based MC engines have been developed to address inverse optimization problems, their efficiency still needs to be improved. Also, the use of a large number of GPUs in MC calculation is not favorable for clinical applications. The previously proposed adaptive particle sampling (APS) method can improve the efficiency of MC-based inverse optimization by using the computationally expensive MC simulation more effectively. This method is more efficient than the conventional approach that performs spot dose calculation and optimization in two sequential steps. In this paper, we propose a computational library to perform MC-based spot dose calculation on GPU with the APS scheme. The implemented APS method performs a non-uniform sampling of the particles from pencil beam spots during the optimization process, favoring those from the high intensity spots. The library also conducts two computationally intensive matrix-vector operations frequently used when solving an optimization problem. This library design allows a streamlined integration of the MC-based spot dose calculation into an existing proton therapy inverse planning process. We tested the developed library in a typical inverse optimization system with four patient cases. The library achieved the targeted functions by supporting inverse planning in various proton therapy schemes, e.g. single field uniform dose, 3D intensity modulated proton therapy, and distal edge tracking. The efficiency was 41.6±15.3% higher than the use of a GPU-based MC package in a conventional calculation scheme. The total computation time ranged between 2 and 50 min on a single GPU card depending on the problem size. PMID:27991456

Estimating uncertainty of Full Waveform Inversion with Ensemble-based methods

NASA Astrophysics Data System (ADS)

Thurin, J.; Brossier, R.; Métivier, L.

2017-12-01

Uncertainty estimation is one key feature of tomographic applications for robust interpretation. However, this information is often missing in the frame of large scale linearized inversions, and only the results at convergence are shown, despite the ill-posed nature of the problem. This issue is common in the Full Waveform Inversion community.While few methodologies have already been proposed in the literature, standard FWI workflows do not include any systematic uncertainty quantifications methods yet, but often try to assess the result's quality through cross-comparison with other results from seismic or comparison with other geophysical data. With the development of large seismic networks/surveys, the increase in computational power and the more and more systematic application of FWI, it is crucial to tackle this problem and to propose robust and affordable workflows, in order to address the uncertainty quantification problem faced for near surface targets, crustal exploration, as well as regional and global scales.In this work (Thurin et al., 2017a,b), we propose an approach which takes advantage of the Ensemble Transform Kalman Filter (ETKF) proposed by Bishop et al., (2001), in order to estimate a low-rank approximation of the posterior covariance matrix of the FWI problem, allowing us to evaluate some uncertainty information of the solution. Instead of solving the FWI problem through a Bayesian inversion with the ETKF, we chose to combine a conventional FWI, based on local optimization, and the ETKF strategies. This scheme allows combining the efficiency of local optimization for solving large scale inverse problems and make the sampling of the local solution space possible thanks to its embarrassingly parallel property. References:Bishop, C. H., Etherton, B. J. and Majumdar, S. J., 2001. Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Monthly weather review, 129(3), 420-436.Thurin, J., Brossier, R. and Métivier, L. 2017,a.: Ensemble-Based Uncertainty Estimation in Full Waveform Inversion. 79th EAGE Conference and Exhibition 2017, (12 - 15 June, 2017)Thurin, J., Brossier, R. and Métivier, L. 2017,b.: An Ensemble-Transform Kalman Filter - Full Waveform Inversion scheme for Uncertainty estimation; SEG Technical Program Expanded Abstracts 2012

Inverse problems and optimal experiment design in unsteady heat transfer processes identification

NASA Technical Reports Server (NTRS)

Artyukhin, Eugene A.

1991-01-01

Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.

Low frequency full waveform seismic inversion within a tree based Bayesian framework

NASA Astrophysics Data System (ADS)

Ray, Anandaroop; Kaplan, Sam; Washbourne, John; Albertin, Uwe

2018-01-01

Limited illumination, insufficient offset, noisy data and poor starting models can pose challenges for seismic full waveform inversion. We present an application of a tree based Bayesian inversion scheme which attempts to mitigate these problems by accounting for data uncertainty while using a mildly informative prior about subsurface structure. We sample the resulting posterior model distribution of compressional velocity using a trans-dimensional (trans-D) or Reversible Jump Markov chain Monte Carlo method in the wavelet transform domain of velocity. This allows us to attain rapid convergence to a stationary distribution of posterior models while requiring a limited number of wavelet coefficients to define a sampled model. Two synthetic, low frequency, noisy data examples are provided. The first example is a simple reflection + transmission inverse problem, and the second uses a scaled version of the Marmousi velocity model, dominated by reflections. Both examples are initially started from a semi-infinite half-space with incorrect background velocity. We find that the trans-D tree based approach together with parallel tempering for navigating rugged likelihood (i.e. misfit) topography provides a promising, easily generalized method for solving large-scale geophysical inverse problems which are difficult to optimize, but where the true model contains a hierarchy of features at multiple scales.

Inversion of particle-size distribution from angular light-scattering data with genetic algorithms.

PubMed

Ye, M; Wang, S; Lu, Y; Hu, T; Zhu, Z; Xu, Y

1999-04-20

A stochastic inverse technique based on a genetic algorithm (GA) to invert particle-size distribution from angular light-scattering data is developed. This inverse technique is independent of any given a priori information of particle-size distribution. Numerical tests show that this technique can be successfully applied to inverse problems with high stability in the presence of random noise and low susceptibility to the shape of distributions. It has also been shown that the GA-based inverse technique is more efficient in use of computing time than the inverse Monte Carlo method recently developed by Ligon et al. [Appl. Opt. 35, 4297 (1996)].

MATLAB Simulation of Gradient-Based Neural Network for Online Matrix Inversion

NASA Astrophysics Data System (ADS)

Zhang, Yunong; Chen, Ke; Ma, Weimu; Li, Xiao-Dong

This paper investigates the simulation of a gradient-based recurrent neural network for online solution of the matrix-inverse problem. Several important techniques are employed as follows to simulate such a neural system. 1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector-differential-equation (VDE); i.e., finally, a standard ordinary-differential-equation (ODE) is obtained. 2) MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem. 3) In addition to various implementation errors, different kinds of activation functions are simulated to show the characteristics of such a neural network. Simulation results substantiate the theoretical analysis and efficacy of the gradient-based neural network for online constant matrix inversion.

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.

Determination of thermophysical characteristics of solid materials by electrical modelling of the solutions to the inverse problems in nonsteady heat conduction

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Krivoshei, F. A.

1985-01-01

The solution of the inverse problem of nonsteady heat conduction is discussed, based on finding the coefficient of the heat conduction and the coefficient of specific volumetric heat capacity. These findings are included in the equation used for the electrical model of this phenomenon.

Noether's Theorem and its Inverse of Birkhoffian System in Event Space Based on Herglotz Variational Problem

NASA Astrophysics Data System (ADS)

Tian, X.; Zhang, Y.

2018-03-01

Herglotz variational principle, in which the functional is defined by a differential equation, generalizes the classical ones defining the functional by an integral. The principle gives a variational principle description of nonconservative systems even when the Lagrangian is independent of time. This paper focuses on studying the Noether's theorem and its inverse of a Birkhoffian system in event space based on the Herglotz variational problem. Firstly, according to the Herglotz variational principle of a Birkhoffian system, the principle of a Birkhoffian system in event space is established. Secondly, its parametric equations and two basic formulae for the variation of Pfaff-Herglotz action of a Birkhoffian system in event space are obtained. Furthermore, the definition and criteria of Noether symmetry of the Birkhoffian system in event space based on the Herglotz variational problem are given. Then, according to the relationship between the Noether symmetry and conserved quantity, the Noether's theorem is derived. Under classical conditions, Noether's theorem of a Birkhoffian system in event space based on the Herglotz variational problem reduces to the classical ones. In addition, Noether's inverse theorem of the Birkhoffian system in event space based on the Herglotz variational problem is also obtained. In the end of the paper, an example is given to illustrate the application of the results.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Irving, J.; Koepke, C.; Elsheikh, A. H.

2017-12-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward process model linking subsurface parameters to measured data, which is typically assumed to be known perfectly in the inversion procedure. However, in order to make the stochastic solution of the inverse problem computationally tractable using, for example, Markov-chain-Monte-Carlo (MCMC) methods, fast approximations of the forward model are commonly employed. This introduces model error into the problem, which has the potential to significantly bias posterior statistics and hamper data integration efforts if not properly accounted for. Here, we present a new methodology for addressing the issue of model error in Bayesian solutions to hydrogeophysical inverse problems that is geared towards the common case where these errors cannot be effectively characterized globally through some parametric statistical distribution or locally based on interpolation between a small number of computed realizations. Rather than focusing on the construction of a global or local error model, we instead work towards identification of the model-error component of the residual through a projection-based approach. In this regard, pairs of approximate and detailed model runs are stored in a dictionary that grows at a specified rate during the MCMC inversion procedure. At each iteration, a local model-error basis is constructed for the current test set of model parameters using the K-nearest neighbour entries in the dictionary, which is then used to separate the model error from the other error sources before computing the likelihood of the proposed set of model parameters. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar traveltime data for three different subsurface parameterizations of varying complexity. The synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed in the inversion procedure. In each case, the developed model-error approach enables to remove posterior bias and obtain a more realistic characterization of uncertainty.

Optimization of the Inverse Algorithm for Estimating the Optical Properties of Biological Materials Using Spatially-resolved Diffuse Reflectance Technique

USDA-ARS?s Scientific Manuscript database

Determination of the optical properties from intact biological materials based on diffusion approximation theory is a complicated inverse problem, and it requires proper implementation of inverse algorithm, instrumentation, and experiment. This work was aimed at optimizing the procedure of estimatin...

Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Wu, Jianping; Geng, Xianguo

2017-12-01

The inverse scattering transform of the coupled modified Korteweg-de Vries equation is studied by the Riemann-Hilbert approach. In the direct scattering process, the spectral analysis of the Lax pair is performed, from which a Riemann-Hilbert problem is established for the equation. In the inverse scattering process, by solving Riemann-Hilbert problems corresponding to the reflectionless cases, three types of multi-soliton solutions are obtained. The multi-soliton classification is based on the zero structures of the Riemann-Hilbert problem. In addition, some figures are given to illustrate the soliton characteristics of the coupled modified Korteweg-de Vries equation.

Distorted Born iterative T-matrix method for inversion of CSEM data in anisotropic media

NASA Astrophysics Data System (ADS)

Jakobsen, Morten; Tveit, Svenn

2018-05-01

We present a direct iterative solutions to the nonlinear controlled-source electromagnetic (CSEM) inversion problem in the frequency domain, which is based on a volume integral equation formulation of the forward modelling problem in anisotropic conductive media. Our vectorial nonlinear inverse scattering approach effectively replaces an ill-posed nonlinear inverse problem with a series of linear ill-posed inverse problems, for which there already exist efficient (regularized) solution methods. The solution update the dyadic Green's function's from the source to the scattering-volume and from the scattering-volume to the receivers, after each iteration. The T-matrix approach of multiple scattering theory is used for efficient updating of all dyadic Green's functions after each linearized inversion step. This means that we have developed a T-matrix variant of the Distorted Born Iterative (DBI) method, which is often used in the acoustic and electromagnetic (medical) imaging communities as an alternative to contrast-source inversion. The main advantage of using the T-matrix approach in this context, is that it eliminates the need to perform a full forward simulation at each iteration of the DBI method, which is known to be consistent with the Gauss-Newton method. The T-matrix allows for a natural domain decomposition, since in the sense that a large model can be decomposed into an arbitrary number of domains that can be treated independently and in parallel. The T-matrix we use for efficient model updating is also independent of the source-receiver configuration, which could be an advantage when performing fast-repeat modelling and time-lapse inversion. The T-matrix is also compatible with the use of modern renormalization methods that can potentially help us to reduce the sensitivity of the CSEM inversion results on the starting model. To illustrate the performance and potential of our T-matrix variant of the DBI method for CSEM inversion, we performed a numerical experiments based on synthetic CSEM data associated with 2D VTI and 3D orthorombic model inversions. The results of our numerical experiment suggest that the DBIT method for inversion of CSEM data in anisotropic media is both accurate and efficient.

Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of X-ray reflection and scattering

NASA Astrophysics Data System (ADS)

Khachaturov, R. V.

2014-06-01

A mathematical model of X-ray reflection and scattering by multilayered nanostructures in the quasi-optical approximation is proposed. X-ray propagation and the electric field distribution inside the multilayered structure are considered with allowance for refraction, which is taken into account via the second derivative with respect to the depth of the structure. This model is used to demonstrate the possibility of solving inverse problems in order to determine the characteristics of irregularities not only over the depth (as in the one-dimensional problem) but also over the length of the structure. An approximate combinatorial method for system decomposition and composition is proposed for solving the inverse problems.

Metamodel-based inverse method for parameter identification: elastic-plastic damage model

NASA Astrophysics Data System (ADS)

Huang, Changwu; El Hami, Abdelkhalak; Radi, Bouchaïb

2017-04-01

This article proposed a metamodel-based inverse method for material parameter identification and applies it to elastic-plastic damage model parameter identification. An elastic-plastic damage model is presented and implemented in numerical simulation. The metamodel-based inverse method is proposed in order to overcome the disadvantage in computational cost of the inverse method. In the metamodel-based inverse method, a Kriging metamodel is constructed based on the experimental design in order to model the relationship between material parameters and the objective function values in the inverse problem, and then the optimization procedure is executed by the use of a metamodel. The applications of the presented material model and proposed parameter identification method in the standard A 2017-T4 tensile test prove that the presented elastic-plastic damage model is adequate to describe the material's mechanical behaviour and that the proposed metamodel-based inverse method not only enhances the efficiency of parameter identification but also gives reliable results.

Model based inversion of ultrasound data in composites

NASA Astrophysics Data System (ADS)

Roberts, R. A.

2018-04-01

Work is reported on model-based defect characterization in CFRP composites. The work utilizes computational models of ultrasound interaction with defects in composites, to determine 1) the measured signal dependence on material and defect properties (forward problem), and 2) an assessment of defect properties from analysis of measured ultrasound signals (inverse problem). Work is reported on model implementation for inspection of CFRP laminates containing multi-ply impact-induced delamination, in laminates displaying irregular surface geometry (roughness), as well as internal elastic heterogeneity (varying fiber density, porosity). Inversion of ultrasound data is demonstrated showing the quantitative extraction of delamination geometry and surface transmissivity. Additionally, data inversion is demonstrated for determination of surface roughness and internal heterogeneity, and the influence of these features on delamination characterization is examined. Estimation of porosity volume fraction is demonstrated when internal heterogeneity is attributed to porosity.

A geostatistical approach to the change-of-support problem and variable-support data fusion in spatial analysis

NASA Astrophysics Data System (ADS)

Wang, Jun; Wang, Yang; Zeng, Hui

2016-01-01

A key issue to address in synthesizing spatial data with variable-support in spatial analysis and modeling is the change-of-support problem. We present an approach for solving the change-of-support and variable-support data fusion problems. This approach is based on geostatistical inverse modeling that explicitly accounts for differences in spatial support. The inverse model is applied here to produce both the best predictions of a target support and prediction uncertainties, based on one or more measurements, while honoring measurements. Spatial data covering large geographic areas often exhibit spatial nonstationarity and can lead to computational challenge due to the large data size. We developed a local-window geostatistical inverse modeling approach to accommodate these issues of spatial nonstationarity and alleviate computational burden. We conducted experiments using synthetic and real-world raster data. Synthetic data were generated and aggregated to multiple supports and downscaled back to the original support to analyze the accuracy of spatial predictions and the correctness of prediction uncertainties. Similar experiments were conducted for real-world raster data. Real-world data with variable-support were statistically fused to produce single-support predictions and associated uncertainties. The modeling results demonstrate that geostatistical inverse modeling can produce accurate predictions and associated prediction uncertainties. It is shown that the local-window geostatistical inverse modeling approach suggested offers a practical way to solve the well-known change-of-support problem and variable-support data fusion problem in spatial analysis and modeling.

Hessian Schatten-norm regularization for linear inverse problems.

PubMed

Lefkimmiatis, Stamatios; Ward, John Paul; Unser, Michael

2013-05-01

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which are computed at every pixel of the image. They can be viewed as second-order extensions of the popular total-variation (TV) semi-norm since they satisfy the same invariance properties. Meanwhile, by taking advantage of second-order derivatives, they avoid the staircase effect, a common artifact of TV-based reconstructions, and perform well for a wide range of applications. To solve the corresponding optimization problems, we propose an algorithm that is based on a primal-dual formulation. A fundamental ingredient of this algorithm is the projection of matrices onto Schatten norm balls of arbitrary radius. This operation is performed efficiently based on a direct link we provide between vector projections onto lq norm balls and matrix projections onto Schatten norm balls. Finally, we demonstrate the effectiveness of the proposed methods through experimental results on several inverse imaging problems with real and simulated data.

Numerical solution of 2D-vector tomography problem using the method of approximate inverse

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

Svetov, Ivan; Maltseva, Svetlana; Polyakova, Anna

2016-08-10

We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.

Density-to-Potential Inversions to Guide Development of Exchange-Correlation Approximations at Finite Temperature

NASA Astrophysics Data System (ADS)

Jensen, Daniel; Wasserman, Adam; Baczewski, Andrew

The construction of approximations to the exchange-correlation potential for warm dense matter (WDM) is a topic of significant recent interest. In this work, we study the inverse problem of Kohn-Sham (KS) DFT as a means of guiding functional design at zero temperature and in WDM. Whereas the forward problem solves the KS equations to produce a density from a specified exchange-correlation potential, the inverse problem seeks to construct the exchange-correlation potential from specified densities. These two problems require different computational methods and convergence criteria despite sharing the same mathematical equations. We present two new inversion methods based on constrained variational and PDE-constrained optimization methods. We adapt these methods to finite temperature calculations to reveal the exchange-correlation potential's temperature dependence in WDM-relevant conditions. The different inversion methods presented are applied to both non-interacting and interacting model systems for comparison. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Security Administration under contract DE-AC04-94.

Reconstruction of local perturbations in periodic surfaces

NASA Astrophysics Data System (ADS)

Lechleiter, Armin; Zhang, Ruming

2018-03-01

This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce quasi-periodic fields in one periodic cell, are no longer available. Based on the Floquet-Bloch transform, a numerical method has been developed to solve the direct problem, that leads to a possibility to design an algorithm for the inverse problem. The numerical method introduced in this paper contains two steps. The first step is initialization, that is to locate the support of the perturbation by a simple method. This step reduces the inverse problem in an infinite domain into one periodic cell. The second step is to apply the Newton-CG method to solve the associated optimization problem. The perturbation is then approximated by a finite spline basis. Numerical examples are given at the end of this paper, showing the efficiency of the numerical method.

Preview-Based Stable-Inversion for Output Tracking

NASA Technical Reports Server (NTRS)

Zou, Qing-Ze; Devasia, Santosh

1999-01-01

Stable Inversion techniques can be used to achieve high-accuracy output tracking. However, for nonminimum phase systems, the inverse is non-causal - hence the inverse has to be pre-computed using a pre-specified desired-output trajectory. This requirement for pre-specification of the desired output restricts the use of inversion-based approaches to trajectory planning problems (for nonminimum phase systems). In the present article, it is shown that preview information of the desired output can be used to achieve online inversion-based output tracking of linear systems. The amount of preview-time needed is quantified in terms of the tracking error and the internal dynamics of the system (zeros of the system). The methodology is applied to the online output tracking of a flexible structure and experimental results are presented.

Discrete Inverse and State Estimation Problems

NASA Astrophysics Data System (ADS)

Wunsch, Carl

2006-06-01

The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines. This book addresses these problems using examples taken from geophysical fluid dynamics. It focuses on discrete formulations, both static and time-varying, known variously as inverse, state estimation or data assimilation problems. Starting with fundamental algebraic and statistical ideas, the book guides the reader through a range of inference tools including the singular value decomposition, Gauss-Markov and minimum variance estimates, Kalman filters and related smoothers, and adjoint (Lagrange multiplier) methods. The final chapters discuss a variety of practical applications to geophysical flow problems. Discrete Inverse and State Estimation Problems is an ideal introduction to the topic for graduate students and researchers in oceanography, meteorology, climate dynamics, and geophysical fluid dynamics. It is also accessible to a wider scientific audience; the only prerequisite is an understanding of linear algebra. Provides a comprehensive introduction to discrete methods of inference from incomplete information Based upon 25 years of practical experience using real data and models Develops sequential and whole-domain analysis methods from simple least-squares Contains many examples and problems, and web-based support through MIT opencourseware

Acoustic Inversion in Optoacoustic Tomography: A Review

PubMed Central

Rosenthal, Amir; Ntziachristos, Vasilis; Razansky, Daniel

2013-01-01

Optoacoustic tomography enables volumetric imaging with optical contrast in biological tissue at depths beyond the optical mean free path by the use of optical excitation and acoustic detection. The hybrid nature of optoacoustic tomography gives rise to two distinct inverse problems: The optical inverse problem, related to the propagation of the excitation light in tissue, and the acoustic inverse problem, which deals with the propagation and detection of the generated acoustic waves. Since the two inverse problems have different physical underpinnings and are governed by different types of equations, they are often treated independently as unrelated problems. From an imaging standpoint, the acoustic inverse problem relates to forming an image from the measured acoustic data, whereas the optical inverse problem relates to quantifying the formed image. This review focuses on the acoustic aspects of optoacoustic tomography, specifically acoustic reconstruction algorithms and imaging-system practicalities. As these two aspects are intimately linked, and no silver bullet exists in the path towards high-performance imaging, we adopt a holistic approach in our review and discuss the many links between the two aspects. Four classes of reconstruction algorithms are reviewed: time-domain (so called back-projection) formulae, frequency-domain formulae, time-reversal algorithms, and model-based algorithms. These algorithms are discussed in the context of the various acoustic detectors and detection surfaces which are commonly used in experimental studies. We further discuss the effects of non-ideal imaging scenarios on the quality of reconstruction and review methods that can mitigate these effects. Namely, we consider the cases of finite detector aperture, limited-view tomography, spatial under-sampling of the acoustic signals, and acoustic heterogeneities and losses. PMID:24772060

Perturbational and nonperturbational inversion of Rayleigh-wave velocities

USGS Publications Warehouse

Haney, Matt; Tsai, Victor C.

2017-01-01

The inversion of Rayleigh-wave dispersion curves is a classic geophysical inverse problem. We have developed a set of MATLAB codes that performs forward modeling and inversion of Rayleigh-wave phase or group velocity measurements. We describe two different methods of inversion: a perturbational method based on finite elements and a nonperturbational method based on the recently developed Dix-type relation for Rayleigh waves. In practice, the nonperturbational method can be used to provide a good starting model that can be iteratively improved with the perturbational method. Although the perturbational method is well-known, we solve the forward problem using an eigenvalue/eigenvector solver instead of the conventional approach of root finding. Features of the codes include the ability to handle any mix of phase or group velocity measurements, combinations of modes of any order, the presence of a surface water layer, computation of partial derivatives due to changes in material properties and layer boundaries, and the implementation of an automatic grid of layers that is optimally suited for the depth sensitivity of Rayleigh waves.

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

The inverse problem of refraction travel times, part II: Quantifying refraction nonuniqueness using a three-layer model

USGS Publications Warehouse

Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.

2005-01-01

This paper is the second of a set of two papers in which we study the inverse refraction problem. The first paper, "Types of Geophysical Nonuniqueness through Minimization," studies and classifies the types of nonuniqueness that exist when solving inverse problems depending on the participation of a priori information required to obtain reliable solutions of inverse geophysical problems. In view of the classification developed, in this paper we study the type of nonuniqueness associated with the inverse refraction problem. An approach for obtaining a realistic solution to the inverse refraction problem is offered in a third paper that is in preparation. The nonuniqueness of the inverse refraction problem is examined by using a simple three-layer model. Like many other inverse geophysical problems, the inverse refraction problem does not have a unique solution. Conventionally, nonuniqueness is considered to be a result of insufficient data and/or error in the data, for any fixed number of model parameters. This study illustrates that even for overdetermined and error free data, nonlinear inverse refraction problems exhibit exact-data nonuniqueness, which further complicates the problem of nonuniqueness. By evaluating the nonuniqueness of the inverse refraction problem, this paper targets the improvement of refraction inversion algorithms, and as a result, the achievement of more realistic solutions. The nonuniqueness of the inverse refraction problem is examined initially by using a simple three-layer model. The observations and conclusions of the three-layer model nonuniqueness study are used to evaluate the nonuniqueness of more complicated n-layer models and multi-parameter cell models such as in refraction tomography. For any fixed number of model parameters, the inverse refraction problem exhibits continuous ranges of exact-data nonuniqueness. Such an unfavorable type of nonuniqueness can be uniquely solved only by providing abundant a priori information. Insufficient a priori information during the inversion is the reason why refraction methods often may not produce desired results or even fail. This work also demonstrates that the application of the smoothing constraints, typical when solving ill-posed inverse problems, has a dual and contradictory role when applied to the ill-posed inverse problem of refraction travel times. This observation indicates that smoothing constraints may play such a two-fold role when applied to other inverse problems. Other factors that contribute to inverse-refraction-problem nonuniqueness are also considered, including indeterminacy, statistical data-error distribution, numerical error and instability, finite data, and model parameters. ?? Birkha??user Verlag, Basel, 2005.

Absolute mass scale calibration in the inverse problem of the physical theory of fireballs.

NASA Astrophysics Data System (ADS)

Kalenichenko, V. V.

A method of the absolute mass scale calibration is suggested for solving the inverse problem of the physical theory of fireballs. The method is based on the data on the masses of the fallen meteorites whose fireballs have been photographed in their flight. The method may be applied to those fireballs whose bodies have not experienced considerable fragmentation during their destruction in the atmosphere and have kept their form well enough. Statistical analysis of the inverse problem solution for a sufficiently representative sample makes it possible to separate a subsample of such fireballs. The data on the Lost City and Innisfree meteorites are used to obtain calibration coefficients.

An inverse finance problem for estimation of the volatility

NASA Astrophysics Data System (ADS)

Neisy, A.; Salmani, K.

2013-01-01

Black-Scholes model, as a base model for pricing in derivatives markets has some deficiencies, such as ignoring market jumps, and considering market volatility as a constant factor. In this article, we introduce a pricing model for European-Options under jump-diffusion underlying asset. Then, using some appropriate numerical methods we try to solve this model with integral term, and terms including derivative. Finally, considering volatility as an unknown parameter, we try to estimate it by using our proposed model. For the purpose of estimating volatility, in this article, we utilize inverse problem, in which inverse problem model is first defined, and then volatility is estimated using minimization function with Tikhonov regularization.

Improved resistivity imaging of groundwater solute plumes using POD-based inversion

NASA Astrophysics Data System (ADS)

Oware, E. K.; Moysey, S. M.; Khan, T.

2012-12-01

We propose a new approach for enforcing physics-based regularization in electrical resistivity imaging (ERI) problems. The approach utilizes a basis-constrained inversion where an optimal set of basis vectors is extracted from training data by Proper Orthogonal Decomposition (POD). The key aspect of the approach is that Monte Carlo simulation of flow and transport is used to generate a training dataset, thereby intrinsically capturing the physics of the underlying flow and transport models in a non-parametric form. POD allows for these training data to be projected onto a subspace of the original domain, resulting in the extraction of a basis for the inversion that captures characteristics of the groundwater flow and transport system, while simultaneously allowing for dimensionality reduction of the original problem in the projected space We use two different synthetic transport scenarios in heterogeneous media to illustrate how the POD-based inversion compares with standard Tikhonov and coupled inversion. The first scenario had a single source zone leading to a unimodal solute plume (synthetic #1), whereas, the second scenario had two source zones that produced a bimodal plume (synthetic #2). For both coupled inversion and the POD approach, the conceptual flow and transport model used considered only a single source zone for both scenarios. Results were compared based on multiple metrics (concentration root-mean square error (RMSE), peak concentration, and total solute mass). In addition, results for POD inversion based on 3 different data densities (120, 300, and 560 data points) and varying number of selected basis images (100, 300, and 500) were compared. For synthetic #1, we found that all three methods provided qualitatively reasonable reproduction of the true plume. Quantitatively, the POD inversion performed best overall for each metric considered. Moreover, since synthetic #1 was consistent with the conceptual transport model, a small number of basis vectors (100) contained enough a priori information to constrain the inversion. Increasing the amount of data or number of selected basis images did not translate into significant improvement in imaging results. For synthetic #2, the RMSE and error in total mass were lowest for the POD inversion. However, the peak concentration was significantly overestimated by the POD approach. Regardless, the POD-based inversion was the only technique that could capture the bimodality of the plume in the reconstructed image, thus providing critical information that could be used to reconceptualize the transport problem. We also found that, in the case of synthetic #2, increasing the number of resistivity measurements and the number of selected basis vectors allowed for significant improvements in the reconstructed images.

Controlling bridging and pinching with pixel-based mask for inverse lithography

NASA Astrophysics Data System (ADS)

Kobelkov, Sergey; Tritchkov, Alexander; Han, JiWan

2016-03-01

Inverse Lithography Technology (ILT) has become a viable computational lithography candidate in recent years as it can produce mask output that results in process latitude and CD control in the fab that is hard to match with conventional OPC/SRAF insertion approaches. An approach to solving the inverse lithography problem as a nonlinear, constrained minimization problem over a domain mask pixels was suggested in the paper by Y. Granik "Fast pixel-based mask optimization for inverse lithography" in 2006. The present paper extends this method to satisfy bridging and pinching constraints imposed on print contours. Namely, there are suggested objective functions expressing penalty for constraints violations, and their minimization with gradient descent methods is considered. This approach has been tested with an ILT-based Local Printability Enhancement (LPTM) tool in an automated flow to eliminate hotspots that can be present on the full chip after conventional SRAF placement/OPC and has been applied in 14nm, 10nm node production, single and multiple-patterning flows.

Inverse transport problems in quantitative PAT for molecular imaging

NASA Astrophysics Data System (ADS)

Ren, Kui; Zhang, Rongting; Zhong, Yimin

2015-12-01

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in Ren K and Zhao H (2013 SIAM J. Imaging Sci. 6 2024-49) on the same problem but in the diffusive regime.

Model-based elastography: a survey of approaches to the inverse elasticity problem

PubMed Central

Doyley, M M

2012-01-01

Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This article reviews current approaches to elastography in three areas — quasi-static, harmonic, and transient — and describes inversion schemes for each elastographic imaging approach. Approaches include: first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials; and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper’s objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic, and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the transient behavior of soft tissue; and (3) developing better test procedures to evaluate the performance of modulus elastograms. PMID:22222839

The Modularized Software Package ASKI - Full Waveform Inversion Based on Waveform Sensitivity Kernels Utilizing External Seismic Wave Propagation Codes

NASA Astrophysics Data System (ADS)

Schumacher, F.; Friederich, W.

2015-12-01

We present the modularized software package ASKI which is a flexible and extendable toolbox for seismic full waveform inversion (FWI) as well as sensitivity or resolution analysis operating on the sensitivity matrix. It utilizes established wave propagation codes for solving the forward problem and offers an alternative to the monolithic, unflexible and hard-to-modify codes that have typically been written for solving inverse problems. It is available under the GPL at www.rub.de/aski. The Gauss-Newton FWI method for 3D-heterogeneous elastic earth models is based on waveform sensitivity kernels and can be applied to inverse problems at various spatial scales in both Cartesian and spherical geometries. The kernels are derived in the frequency domain from Born scattering theory as the Fréchet derivatives of linearized full waveform data functionals, quantifying the influence of elastic earth model parameters on the particular waveform data values. As an important innovation, we keep two independent spatial descriptions of the earth model - one for solving the forward problem and one representing the inverted model updates. Thereby we account for the independent needs of spatial model resolution of forward and inverse problem, respectively. Due to pre-integration of the kernels over the (in general much coarser) inversion grid, storage requirements for the sensitivity kernels are dramatically reduced.ASKI can be flexibly extended to other forward codes by providing it with specific interface routines that contain knowledge about forward code-specific file formats and auxiliary information provided by the new forward code. In order to sustain flexibility, the ASKI tools must communicate via file output/input, thus large storage capacities need to be accessible in a convenient way. Storing the complete sensitivity matrix to file, however, permits the scientist full manual control over each step in a customized procedure of sensitivity/resolution analysis and full waveform inversion.

The inverse problem of refraction travel times, part I: Types of Geophysical Nonuniqueness through Minimization

USGS Publications Warehouse

Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.; Park, C.B.

2005-01-01

In a set of two papers we study the inverse problem of refraction travel times. The purpose of this work is to use the study as a basis for development of more sophisticated methods for finding more reliable solutions to the inverse problem of refraction travel times, which is known to be nonunique. The first paper, "Types of Geophysical Nonuniqueness through Minimization," emphasizes the existence of different forms of nonuniqueness in the realm of inverse geophysical problems. Each type of nonuniqueness requires a different type and amount of a priori information to acquire a reliable solution. Based on such coupling, a nonuniqueness classification is designed. Therefore, since most inverse geophysical problems are nonunique, each inverse problem must be studied to define what type of nonuniqueness it belongs to and thus determine what type of a priori information is necessary to find a realistic solution. The second paper, "Quantifying Refraction Nonuniqueness Using a Three-layer Model," serves as an example of such an approach. However, its main purpose is to provide a better understanding of the inverse refraction problem by studying the type of nonuniqueness it possesses. An approach for obtaining a realistic solution to the inverse refraction problem is planned to be offered in a third paper that is in preparation. The main goal of this paper is to redefine the existing generalized notion of nonuniqueness and a priori information by offering a classified, discriminate structure. Nonuniqueness is often encountered when trying to solve inverse problems. However, possible nonuniqueness diversity is typically neglected and nonuniqueness is regarded as a whole, as an unpleasant "black box" and is approached in the same manner by applying smoothing constraints, damping constraints with respect to the solution increment and, rarely, damping constraints with respect to some sparse reference information about the true parameters. In practice, when solving geophysical problems different types of nonuniqueness exist, and thus there are different ways to solve the problems. Nonuniqueness is usually regarded as due to data error, assuming the true geology is acceptably approximated by simple mathematical models. Compounding the nonlinear problems, geophysical applications routinely exhibit exact-data nonuniqueness even for models with very few parameters adding to the nonuniqueness due to data error. While nonuniqueness variations have been defined earlier, they have not been linked to specific use of a priori information necessary to resolve each case. Four types of nonuniqueness, typical for minimization problems are defined with the corresponding methods for inclusion of a priori information to find a realistic solution without resorting to a non-discriminative approach. The above-developed stand-alone classification is expected to be helpful when solving any geophysical inverse problems. ?? Birkha??user Verlag, Basel, 2005.

Inverse kinematic-based robot control

NASA Technical Reports Server (NTRS)

Wolovich, W. A.; Flueckiger, K. F.

1987-01-01

A fundamental problem which must be resolved in virtually all non-trivial robotic operations is the well-known inverse kinematic question. More specifically, most of the tasks which robots are called upon to perform are specified in Cartesian (x,y,z) space, such as simple tracking along one or more straight line paths or following a specified surfacer with compliant force sensors and/or visual feedback. In all cases, control is actually implemented through coordinated motion of the various links which comprise the manipulator; i.e., in link space. As a consequence, the control computer of every sophisticated anthropomorphic robot must contain provisions for solving the inverse kinematic problem which, in the case of simple, non-redundant position control, involves the determination of the first three link angles, theta sub 1, theta sub 2, and theta sub 3, which produce a desired wrist origin position P sub xw, P sub yw, and P sub zw at the end of link 3 relative to some fixed base frame. Researchers outline a new inverse kinematic solution and demonstrate its potential via some recent computer simulations. They also compare it to current inverse kinematic methods and outline some of the remaining problems which will be addressed in order to render it fully operational. Also discussed are a number of practical consequences of this technique beyond its obvious use in solving the inverse kinematic question.

Atmospheric inverse modeling via sparse reconstruction

NASA Astrophysics Data System (ADS)

Hase, Nils; Miller, Scot M.; Maaß, Peter; Notholt, Justus; Palm, Mathias; Warneke, Thorsten

2017-10-01

Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

Children's Understanding of the Relation between Addition and Subtraction: Inversion, Identity, and Decomposition.

ERIC Educational Resources Information Center

Bryant, Peter; Rendu, Alison; Christie, Clare

1999-01-01

Examined whether 5- and 6-year-olds understand that addition and subtraction cancel each other and whether this understanding is based on identity or quantity of addend and subtrahend. Found that children used inversion principle. Six- to eight-year-olds also used inversion and decomposition to solve a + b - (B+1) problems. Concluded that…

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Effective one-dimensional approach to the source reconstruction problem of three-dimensional inverse optoacoustics

NASA Astrophysics Data System (ADS)

Stritzel, J.; Melchert, O.; Wollweber, M.; Roth, B.

2017-09-01

The direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three-dimensional (3D) wave equation for an initial acoustic stress profile. In contrast, the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider an effectively 1D approach, based on the assumption of a Gaussian transverse irradiation source profile and plane acoustic waves, in which the effects of acoustic diffraction are described in terms of a linear integral equation. The respective inverse problem along the beam axis can be cast into a Volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity as well as the limits of the inversion scheme via numerical experiments, with parameters geared toward actual optoacoustic problem instances. The considered inversion input consists of synthetic data, obtained in terms of the effectively 1D approach, and, more generally, a solution of the 3D optoacoustic wave equation. Finally, we also analyze the effect of noise and different detector-to-sample distances on the optoacoustic signal and the reconstructed pressure profiles.

The inverse problem of acoustic wave scattering by an air-saturated poroelastic cylinder.

PubMed

Ogam, Erick; Fellah, Z E A; Baki, Paul

2013-03-01

The efficient use of plastic foams in a diverse range of structural applications like in noise reduction, cushioning, and sleeping mattresses requires detailed characterization of their permeability and deformation (load-bearing) behavior. The elastic moduli and airflow resistance properties of foams are often measured using two separate techniques, one employing mechanical vibration methods and the other, flow rates of fluids based on fluid mechanics technology, respectively. A multi-parameter inverse acoustic scattering problem to recover airflow resistivity (AR) and mechanical properties of an air-saturated foam cylinder is solved. A wave-fluid saturated poroelastic structure interaction model based on the modified Biot theory and plane-wave decomposition using orthogonal cylindrical functions is employed to solve the inverse problem. The solutions to the inverse problem are obtained by constructing the objective functional given by the total square of the difference between predictions from the model and scattered acoustic field data acquired in an anechoic chamber. The value of the recovered AR is in good agreement with that of a slab sample cut from the cylinder and characterized using a method employing low frequency transmitted and reflected acoustic waves in a long waveguide developed by Fellah et al. [Rev. Sci. Instrum. 78(11), 114902 (2007)].

Bayesian inference in geomagnetism

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.

Parts-based geophysical inversion with application to water flooding interface detection and geological facies detection

NASA Astrophysics Data System (ADS)

Zhang, Junwei

I built parts-based and manifold based mathematical learning model for the geophysical inverse problem and I applied this approach to two problems. One is related to the detection of the oil-water encroachment front during the water flooding of an oil reservoir. In this application, I propose a new 4D inversion approach based on the Gauss-Newton approach to invert time-lapse cross-well resistance data. The goal of this study is to image the position of the oil-water encroachment front in a heterogeneous clayey sand reservoir. This approach is based on explicitly connecting the change of resistivity to the petrophysical properties controlling the position of the front (porosity and permeability) and to the saturation of the water phase through a petrophysical resistivity model accounting for bulk and surface conductivity contributions and saturation. The distributions of the permeability and porosity are also inverted using the time-lapse resistivity data in order to better reconstruct the position of the oil water encroachment front. In our synthetic test case, we get a better position of the front with the by-products of porosity and permeability inferences near the flow trajectory and close to the wells. The numerical simulations show that the position of the front is recovered well but the distribution of the recovered porosity and permeability is only fair. A comparison with a commercial code based on a classical Gauss-Newton approach with no information provided by the two-phase flow model fails to recover the position of the front. The new approach could be also used for the time-lapse monitoring of various processes in both geothermal fields and oil and gas reservoirs using a combination of geophysical methods. A paper has been published in Geophysical Journal International on this topic and I am the first author of this paper. The second application is related to the detection of geological facies boundaries and their deforation to satisfy to geophysica data and prior distributions. We pose the geophysical inverse problem in terms of Gaussian random fields with mean functions controlled by petrophysical relationships and covariance functions controlled by a prior geological cross-section, including the definition of spatial boundaries for the geological facies. The petrophysical relationship problem is formulated as a regression problem upon each facies. The inversion is performed in a Bayesian framework. We demonstrate the usefulness of this strategy using a first synthetic case study, performing a joint inversion of gravity and galvanometric resistivity data with the stations all located at the ground surface. The joint inversion is used to recover the density and resistivity distributions of the subsurface. In a second step, we consider the possibility that the facies boundaries are deformable and their shapes are inverted as well. We use the level set approach to deform the facies boundaries preserving prior topological properties of the facies throughout the inversion. With the additional help of prior facies petrophysical relationships, topological characteristic of each facies, we make posterior inference about multiple geophysical tomograms based on their corresponding geophysical data misfits. The result of the inversion technique is encouraging when applied to a second synthetic case study, showing that we can recover the heterogeneities inside the facies, the mean values for the petrophysical properties, and, to some extent, the facies boundaries. A paper has been submitted to Geophysics on this topic and I am the first author of this paper. During this thesis, I also worked on the time lapse inversion problem of gravity data in collaboration with Marios Karaoulis and a paper was published in Geophysical Journal international on this topic. I also worked on the time-lapse inversion of cross-well geophysical data (seismic and resistivity) using both a structural approach named the cross-gradient approach and a petrophysical approach. A paper was published in Geophysics on this topic.

Object-based inversion of crosswell radar tomography data to monitor vegetable oil injection experiments

USGS Publications Warehouse

Lane, John W.; Day-Lewis, Frederick D.; Versteeg, Roelof J.; Casey, Clifton C.

2004-01-01

Crosswell radar methods can be used to dynamically image ground-water flow and mass transport associated with tracer tests, hydraulic tests, and natural physical processes, for improved characterization of preferential flow paths and complex aquifer heterogeneity. Unfortunately, because the raypath coverage of the interwell region is limited by the borehole geometry, the tomographic inverse problem is typically underdetermined, and tomograms may contain artifacts such as spurious blurring or streaking that confuse interpretation.We implement object-based inversion (using a constrained, non-linear, least-squares algorithm) to improve results from pixel-based inversion approaches that utilize regularization criteria, such as damping or smoothness. Our approach requires pre- and post-injection travel-time data. Parameterization of the image plane comprises a small number of objects rather than a large number of pixels, resulting in an overdetermined problem that reduces the need for prior information. The nature and geometry of the objects are based on hydrologic insight into aquifer characteristics, the nature of the experiment, and the planned use of the geophysical results.The object-based inversion is demonstrated using synthetic and crosswell radar field data acquired during vegetable-oil injection experiments at a site in Fridley, Minnesota. The region where oil has displaced ground water is discretized as a stack of rectangles of variable horizontal extents. The inversion provides the geometry of the affected region and an estimate of the radar slowness change for each rectangle. Applying petrophysical models to these results and porosity from neutron logs, we estimate the vegetable-oil emulsion saturation in various layers.Using synthetic- and field-data examples, object-based inversion is shown to be an effective strategy for inverting crosswell radar tomography data acquired to monitor the emplacement of vegetable-oil emulsions. A principal advantage of object-based inversion is that it yields images that hydrologists and engineers can easily interpret and use for model calibration.

Recursive inversion of externally defined linear systems

NASA Technical Reports Server (NTRS)

Bach, Ralph E., Jr.; Baram, Yoram

1988-01-01

The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problems of system identification and compensation.

Determination of unknown coefficient in a non-linear elliptic problem related to the elastoplastic torsion of a bar

NASA Astrophysics Data System (ADS)

Hasanov, Alemdar; Erdem, Arzu

2008-08-01

The inverse problem of determining the unknown coefficient of the non-linear differential equation of torsional creep is studied. The unknown coefficient g = g({xi}2) depends on the gradient{xi} : = |{nabla}u| of the solution u(x), x [isin] {Omega} [sub] Rn, of the direct problem. It is proved that this gradient is bounded in C-norm. This permits one to choose the natural class of admissible coefficients for the considered inverse problem. The continuity in the norm of the Sobolev space H1({Omega}) of the solution u(x;g) of the direct problem with respect to the unknown coefficient g = g({xi}2) is obtained in the following sense: ||u(x;g) - u(x;gm)||1 [->] 0 when gm({eta}) [->] g({eta}) point-wise as m [->] {infty}. Based on these results, the existence of a quasi-solution of the inverse problem in the considered class of admissible coefficients is obtained. Numerical examples related to determination of the unknown coefficient are presented.

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

ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

NASA Astrophysics Data System (ADS)

Růžek, B.; Kolář, P.

2009-04-01

Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good performance of the algorithm. Both versions and documentation are available on Internet and anybody can download them. The goal of this presentation is to offer the algorithm and computer codes for anybody interested in the solution to inverse problems.

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.

Direct Estimation of Optical Parameters From Photoacoustic Time Series in Quantitative Photoacoustic Tomography.

PubMed

Pulkkinen, Aki; Cox, Ben T; Arridge, Simon R; Goh, Hwan; Kaipio, Jari P; Tarvainen, Tanja

2016-11-01

Estimation of optical absorption and scattering of a target is an inverse problem associated with quantitative photoacoustic tomography. Conventionally, the problem is expressed as two folded. First, images of initial pressure distribution created by absorption of a light pulse are formed based on acoustic boundary measurements. Then, the optical properties are determined based on these photoacoustic images. The optical stage of the inverse problem can thus suffer from, for example, artefacts caused by the acoustic stage. These could be caused by imperfections in the acoustic measurement setting, of which an example is a limited view acoustic measurement geometry. In this work, the forward model of quantitative photoacoustic tomography is treated as a coupled acoustic and optical model and the inverse problem is solved by using a Bayesian approach. Spatial distribution of the optical properties of the imaged target are estimated directly from the photoacoustic time series in varying acoustic detection and optical illumination configurations. It is numerically demonstrated, that estimation of optical properties of the imaged target is feasible in limited view acoustic detection setting.

Inversion method based on stochastic optimization for particle sizing.

PubMed

Sánchez-Escobar, Juan Jaime; Barbosa-Santillán, Liliana Ibeth; Vargas-Ubera, Javier; Aguilar-Valdés, Félix

2016-08-01

A stochastic inverse method is presented based on a hybrid evolutionary optimization algorithm (HEOA) to retrieve a monomodal particle-size distribution (PSD) from the angular distribution of scattered light. By solving an optimization problem, the HEOA (with the Fraunhofer approximation) retrieves the PSD from an intensity pattern generated by Mie theory. The analyzed light-scattering pattern can be attributed to unimodal normal, gamma, or lognormal distribution of spherical particles covering the interval of modal size parameters 46≤α≤150. The HEOA ensures convergence to the near-optimal solution during the optimization of a real-valued objective function by combining the advantages of a multimember evolution strategy and locally weighted linear regression. The numerical results show that our HEOA can be satisfactorily applied to solve the inverse light-scattering problem.

Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method

NASA Astrophysics Data System (ADS)

Alekseev, G.; Tokhtina, A.; Soboleva, O.

2017-10-01

Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields - electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.

Inverse problem of radiofrequency sounding of ionosphere

NASA Astrophysics Data System (ADS)

Velichko, E. N.; Yu. Grishentsev, A.; Korobeynikov, A. G.

2016-01-01

An algorithm for the solution of the inverse problem of vertical ionosphere sounding and a mathematical model of noise filtering are presented. An automated system for processing and analysis of spectrograms of vertical ionosphere sounding based on our algorithm is described. It is shown that the algorithm we suggest has a rather high efficiency. This is supported by the data obtained at the ionospheric stations of the so-called “AIS-M” type.

Variational approach to direct and inverse problems of atmospheric pollution studies

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

2016-04-01

We present the development of a variational approach for solving interrelated problems of atmospheric hydrodynamics and chemistry concerning air pollution transport and transformations. The proposed approach allows us to carry out complex studies of different-scale physical and chemical processes using the methods of direct and inverse modeling [1-3]. We formulate the problems of risk/vulnerability and uncertainty assessment, sensitivity studies, variational data assimilation procedures [4], etc. A computational technology of constructing consistent mathematical models and methods of their numerical implementation is based on the variational principle in the weak constraint formulation specifically designed to account for uncertainties in models and observations. Algorithms for direct and inverse modeling are designed with the use of global and local adjoint problems. Implementing the idea of adjoint integrating factors provides unconditionally monotone and stable discrete-analytic approximations for convection-diffusion-reaction problems [5,6]. The general framework is applied to the direct and inverse problems for the models of transport and transformation of pollutants in Siberian and Arctic regions. The work has been partially supported by the RFBR grant 14-01-00125 and RAS Presidium Program I.33P. References: 1. V. Penenko, A.Baklanov, E. Tsvetova and A. Mahura . Direct and inverse problems in a variational concept of environmental modeling //Pure and Applied Geoph.(2012) v.169: 447-465. 2. V. V. Penenko, E. A. Tsvetova, and A. V. Penenko Development of variational approach for direct and inverse problems of atmospheric hydrodynamics and chemistry, Izvestiya, Atmospheric and Oceanic Physics, 2015, Vol. 51, No. 3, p. 311-319, DOI: 10.1134/S0001433815030093. 3. V.V. Penenko, E.A. Tsvetova, A.V. Penenko. Methods based on the joint use of models and observational data in the framework of variational approach to forecasting weather and atmospheric composition quality// Russian meteorology and hydrology, V. 40, Issue: 6, Pages: 365-373, DOI: 10.3103/S1068373915060023. 4. A.V. Penenko and V.V. Penenko. Direct data assimilation method for convection-diffusion models based on splitting scheme. Computational technologies, 19(4):69-83, 2014. 5. 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, Pages 2240-2256, DOI:10.1016/j.camwa.2014.04.004 6. 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, DOI 10.1134/S199542391303004X

Recursive inversion of externally defined linear systems by FIR filters

NASA Technical Reports Server (NTRS)

Bach, Ralph E., Jr.; Baram, Yoram

1989-01-01

The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least-squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problem of system identification and compensation.

Sensitivity computation of the ell1 minimization problem and its application to dictionary design of ill-posed problems

NASA Astrophysics Data System (ADS)

Horesh, L.; Haber, E.

2009-09-01

The ell1 minimization problem has been studied extensively in the past few years. Recently, there has been a growing interest in its application for inverse problems. Most studies have concentrated in devising ways for sparse representation of a solution using a given prototype dictionary. Very few studies have addressed the more challenging problem of optimal dictionary construction, and even these were primarily devoted to the simplistic sparse coding application. In this paper, sensitivity analysis of the inverse solution with respect to the dictionary is presented. This analysis reveals some of the salient features and intrinsic difficulties which are associated with the dictionary design problem. Equipped with these insights, we propose an optimization strategy that alleviates these hurdles while utilizing the derived sensitivity relations for the design of a locally optimal dictionary. Our optimality criterion is based on local minimization of the Bayesian risk, given a set of training models. We present a mathematical formulation and an algorithmic framework to achieve this goal. The proposed framework offers the design of dictionaries for inverse problems that incorporate non-trivial, non-injective observation operators, where the data and the recovered parameters may reside in different spaces. We test our algorithm and show that it yields improved dictionaries for a diverse set of inverse problems in geophysics and medical imaging.

Development of a Preventive HIV Vaccine Requires Solving Inverse Problems Which Is Unattainable by Rational Vaccine Design

PubMed Central

Van Regenmortel, Marc H. V.

2018-01-01

Hypotheses and theories are essential constituents of the scientific method. Many vaccinologists are unaware that the problems they try to solve are mostly inverse problems that consist in imagining what could bring about a desired outcome. An inverse problem starts with the result and tries to guess what are the multiple causes that could have produced it. Compared to the usual direct scientific problems that start with the causes and derive or calculate the results using deductive reasoning and known mechanisms, solving an inverse problem uses a less reliable inductive approach and requires the development of a theoretical model that may have different solutions or none at all. Unsuccessful attempts to solve inverse problems in HIV vaccinology by reductionist methods, systems biology and structure-based reverse vaccinology are described. The popular strategy known as rational vaccine design is unable to solve the multiple inverse problems faced by HIV vaccine developers. The term “rational” is derived from “rational drug design” which uses the 3D structure of a biological target for designing molecules that will selectively bind to it and inhibit its biological activity. In vaccine design, however, the word “rational” simply means that the investigator is concentrating on parts of the system for which molecular information is available. The economist and Nobel laureate Herbert Simon introduced the concept of “bounded rationality” to explain why the complexity of the world economic system makes it impossible, for instance, to predict an event like the financial crash of 2007–2008. Humans always operate under unavoidable constraints such as insufficient information, a limited capacity to process huge amounts of data and a limited amount of time available to reach a decision. Such limitations always prevent us from achieving the complete understanding and optimization of a complex system that would be needed to achieve a truly rational design process. This is why the complexity of the human immune system prevents us from rationally designing an HIV vaccine by solving inverse problems. PMID:29387066

A MATLAB implementation of the minimum relative entropy method for linear inverse problems

NASA Astrophysics Data System (ADS)

Neupauer, Roseanna M.; Borchers, Brian

2001-08-01

The minimum relative entropy (MRE) method can be used to solve linear inverse problems of the form Gm= d, where m is a vector of unknown model parameters and d is a vector of measured data. The MRE method treats the elements of m as random variables, and obtains a multivariate probability density function for m. The probability density function is constrained by prior information about the upper and lower bounds of m, a prior expected value of m, and the measured data. The solution of the inverse problem is the expected value of m, based on the derived probability density function. We present a MATLAB implementation of the MRE method. Several numerical issues arise in the implementation of the MRE method and are discussed here. We present the source history reconstruction problem from groundwater hydrology as an example of the MRE implementation.

The inverse problem: Ocean tides derived from earth tide observations

NASA Technical Reports Server (NTRS)

Kuo, J. T.

1978-01-01

Indirect mapping ocean tides by means of land and island-based tidal gravity measurements is presented. The inverse scheme of linear programming is used for indirect mapping of ocean tides. Open ocean tides were measured by the numerical integration of Laplace's tidal equations.

Two-dimensional probabilistic inversion of plane-wave electromagnetic data: methodology, model constraints and joint inversion with electrical resistivity data

NASA Astrophysics Data System (ADS)

Rosas-Carbajal, Marina; Linde, Niklas; Kalscheuer, Thomas; Vrugt, Jasper A.

2014-03-01

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.

A MATLAB based 3D modeling and inversion code for MT data

NASA Astrophysics Data System (ADS)

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

2017-07-01

The development of a MATLAB based computer code, AP3DMT, for modeling and inversion of 3D Magnetotelluric (MT) data is presented. The code comprises two independent components: grid generator code and modeling/inversion code. The grid generator code performs model discretization and acts as an interface by generating various I/O files. The inversion code performs core computations in modular form - forward modeling, data functionals, sensitivity computations and regularization. These modules can be readily extended to other similar inverse problems like Controlled-Source EM (CSEM). The modular structure of the code provides a framework useful for implementation of new applications and inversion algorithms. The use of MATLAB and its libraries makes it more compact and user friendly. The code has been validated on several published models. To demonstrate its versatility and capabilities the results of inversion for two complex models are presented.

Acoustic and elastic waveform inversion best practices

NASA Astrophysics Data System (ADS)

Modrak, Ryan T.

Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence, one or two test cases are not enough to reliably inform such decisions. We identify best practices instead using two global, one regional and four near-surface acoustic test problems. To obtain meaningful quantitative comparisons, we carry out hundreds acoustic inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that L-BFGS provides computational savings over nonlinear conjugate gradient methods in a wide variety of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization, and total variation regularization are effective in different contexts. Besides these issues, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details have a strong effect on computational cost, regardless of the chosen material parameterization or nonlinear optimization algorithm. Building on the acoustic inversion results, we carry out elastic experiments with four test problems, three objective functions, and four material parameterizations. The choice of parameterization for isotropic elastic media is found to be more complicated than previous studies suggests, with "wavespeed-like'' parameters performing well with phase-based objective functions and Lame parameters performing well with amplitude-based objective functions. Reliability and efficiency can be even harder to achieve in transversely isotropic elastic inversions because rotation angle parameters describing fast-axis direction are difficult to recover. Using Voigt or Chen-Tromp parameters avoids the need to include rotation angles explicitly and provides an effective strategy for anisotropic inversion. The need for flexible and portable workflow management tools for seismic inversion also poses a major challenge. In a final chapter, the software used to the carry out the above experiments is described and instructions for reproducing experimental results are given.

An Adaptive ANOVA-based PCKF for High-Dimensional Nonlinear Inverse Modeling

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

LI, Weixuan; Lin, Guang; Zhang, Dongxiao

2014-02-01

The probabilistic collocation-based Kalman filter (PCKF) is a recently developed approach for solving inverse problems. It resembles the ensemble Kalman filter (EnKF) in every aspect—except that it represents and propagates model uncertainty by polynomial chaos expansion (PCE) instead of an ensemble of model realizations. Previous studies have shown PCKF is a more efficient alternative to EnKF for many data assimilation problems. However, the accuracy and efficiency of PCKF depends on an appropriate truncation of the PCE series. Having more polynomial chaos bases in the expansion helps to capture uncertainty more accurately but increases computational cost. Bases selection is particularly importantmore » for high-dimensional stochastic problems because the number of polynomial chaos bases required to represent model uncertainty grows dramatically as the number of input parameters (random dimensions) increases. In classic PCKF algorithms, the PCE bases are pre-set based on users’ experience. Also, for sequential data assimilation problems, the bases kept in PCE expression remain unchanged in different Kalman filter loops, which could limit the accuracy and computational efficiency of classic PCKF algorithms. To address this issue, we present a new algorithm that adaptively selects PCE bases for different problems and automatically adjusts the number of bases in different Kalman filter loops. The algorithm is based on adaptive functional ANOVA (analysis of variance) decomposition, which approximates a high-dimensional function with the summation of a set of low-dimensional functions. Thus, instead of expanding the original model into PCE, we implement the PCE expansion on these low-dimensional functions, which is much less costly. We also propose a new adaptive criterion for ANOVA that is more suited for solving inverse problems. The new algorithm is tested with different examples and demonstrated great effectiveness in comparison with non-adaptive PCKF and EnKF algorithms.« less

Identification of subsurface structures using electromagnetic data and shape priors

NASA Astrophysics Data System (ADS)

Tveit, Svenn; Bakr, Shaaban A.; Lien, Martha; Mannseth, Trond

2015-03-01

We consider the inverse problem of identifying large-scale subsurface structures using the controlled source electromagnetic method. To identify structures in the subsurface where the contrast in electric conductivity can be small, regularization is needed to bias the solution towards preserving structural information. We propose to combine two approaches for regularization of the inverse problem. In the first approach we utilize a model-based, reduced, composite representation of the electric conductivity that is highly flexible, even for a moderate number of degrees of freedom. With a low number of parameters, the inverse problem is efficiently solved using a standard, second-order gradient-based optimization algorithm. Further regularization is obtained using structural prior information, available, e.g., from interpreted seismic data. The reduced conductivity representation is suitable for incorporation of structural prior information. Such prior information cannot, however, be accurately modeled with a gaussian distribution. To alleviate this, we incorporate the structural information using shape priors. The shape prior technique requires the choice of kernel function, which is application dependent. We argue for using the conditionally positive definite kernel which is shown to have computational advantages over the commonly applied gaussian kernel for our problem. Numerical experiments on various test cases show that the methodology is able to identify fairly complex subsurface electric conductivity distributions while preserving structural prior information during the inversion.

Round-off errors in cutting plane algorithms based on the revised simplex procedure

NASA Technical Reports Server (NTRS)

Moore, J. E.

1973-01-01

This report statistically analyzes computational round-off errors associated with the cutting plane approach to solving linear integer programming problems. Cutting plane methods require that the inverse of a sequence of matrices be computed. The problem basically reduces to one of minimizing round-off errors in the sequence of inverses. Two procedures for minimizing this problem are presented, and their influence on error accumulation is statistically analyzed. One procedure employs a very small tolerance factor to round computed values to zero. The other procedure is a numerical analysis technique for reinverting or improving the approximate inverse of a matrix. The results indicated that round-off accumulation can be effectively minimized by employing a tolerance factor which reflects the number of significant digits carried for each calculation and by applying the reinversion procedure once to each computed inverse. If 18 significant digits plus an exponent are carried for each variable during computations, then a tolerance value of 0.1 x 10 to the minus 12th power is reasonable.

Simultaneous source and attenuation reconstruction in SPECT using ballistic and single scattering data

NASA Astrophysics Data System (ADS)

Courdurier, M.; Monard, F.; Osses, A.; Romero, F.

2015-09-01

In medical single-photon emission computed tomography (SPECT) imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first-order scattering measurements and assuming a very specific scattering regime. The problem is modeled using the radiative transfer equation by means of an explicit non-linear operator that gives the ballistic and scattering measurements as a function of the radioactive source and attenuation distributions. First, by differentiating this non-linear operator we obtain a linearized inverse problem. Then, under regularity hypothesis for the source distribution and attenuation map and considering small attenuations, we rigorously prove that the linear operator is invertible and we compute its inverse explicitly. This allows proof of local uniqueness for the non-linear inverse problem. Finally, using the previous inversion result for the linear operator, we propose a new type of iterative algorithm for simultaneous source and attenuation recovery for SPECT based on the Neumann series and a Newton-Raphson algorithm.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Köpke, Corinna; Irving, James; Elsheikh, Ahmed H.

2018-06-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward model linking subsurface physical properties to measured data, which is typically assumed to be perfectly known in the inversion procedure. However, to make the stochastic solution of the inverse problem computationally tractable using methods such as Markov-chain-Monte-Carlo (MCMC), fast approximations of the forward model are commonly employed. This gives rise to model error, which has the potential to significantly bias posterior statistics if not properly accounted for. Here, we present a new methodology for dealing with the model error arising from the use of approximate forward solvers in Bayesian solutions to hydrogeophysical inverse problems. Our approach is geared towards the common case where this error cannot be (i) effectively characterized through some parametric statistical distribution; or (ii) estimated by interpolating between a small number of computed model-error realizations. To this end, we focus on identification and removal of the model-error component of the residual during MCMC using a projection-based approach, whereby the orthogonal basis employed for the projection is derived in each iteration from the K-nearest-neighboring entries in a model-error dictionary. The latter is constructed during the inversion and grows at a specified rate as the iterations proceed. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar travel-time data considering three different subsurface parameterizations of varying complexity. Synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed for their inversion. In each case, our developed approach enables us to remove posterior bias and obtain a more realistic characterization of uncertainty.

Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

NASA Astrophysics Data System (ADS)

Zhou, Xin

1990-03-01

For the direct-inverse scattering transform of the time dependent Schrödinger equation, rigorous results are obtained based on an opertor-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution.

Adults' understanding of inversion concepts: how does performance on addition and subtraction inversion problems compare to performance on multiplication and division inversion problems?

PubMed

Robinson, Katherine M; Ninowski, Jerilyn E

2003-12-01

Problems of the form a + b - b have been used to assess conceptual understanding of the relationship between addition and subtraction. No study has investigated the same relationship between multiplication and division on problems of the form d x e / e. In both types of inversion problems, no calculation is required if the inverse relationship between the operations is understood. Adult participants solved addition/subtraction and multiplication/division inversion (e.g., 9 x 22 / 22) and standard (e.g., 2 + 27 - 28) problems. Participants started to use the inversion strategy earlier and more frequently on addition/subtraction problems. Participants took longer to solve both types of multiplication/division problems. Overall, conceptual understanding of the relationship between multiplication and division was not as strong as that between addition and subtraction. One explanation for this difference in performance is that the operation of division is more weakly represented and understood than the other operations and that this weakness affects performance on problems of the form d x e / e.

Identification of groundwater flow parameters using reciprocal data from hydraulic interference tests

NASA Astrophysics Data System (ADS)

Marinoni, Marianna; Delay, Frederick; Ackerer, Philippe; Riva, Monica; Guadagnini, Alberto

2016-08-01

We investigate the effect of considering reciprocal drawdown curves for the characterization of hydraulic properties of aquifer systems through inverse modeling based on interference well testing. Reciprocity implies that drawdown observed in a well B when pumping takes place from well A should strictly coincide with the drawdown observed in A when pumping in B with the same flow rate as in A. In this context, a critical point related to applications of hydraulic tomography is the assessment of the number of available independent drawdown data and their impact on the solution of the inverse problem. The issue arises when inverse modeling relies upon mathematical formulations of the classical single-continuum approach to flow in porous media grounded on Darcy's law. In these cases, introducing reciprocal drawdown curves in the database of an inverse problem is equivalent to duplicate some information, to a certain extent. We present a theoretical analysis of the way a Least-Square objective function and a Levenberg-Marquardt minimization algorithm are affected by the introduction of reciprocal information in the inverse problem. We also investigate the way these reciprocal data, eventually corrupted by measurement errors, influence model parameter identification in terms of: (a) the convergence of the inverse model, (b) the optimal values of parameter estimates, and (c) the associated estimation uncertainty. Our theoretical findings are exemplified through a suite of computational examples focused on block-heterogeneous systems with increased complexity level. We find that the introduction of noisy reciprocal information in the objective function of the inverse problem has a very limited influence on the optimal parameter estimates. Convergence of the inverse problem improves when adding diverse (nonreciprocal) drawdown series, but does not improve when reciprocal information is added to condition the flow model. The uncertainty on optimal parameter estimates is influenced by the strength of measurement errors and it is not significantly diminished or increased by adding noisy reciprocal information.

Large-scale inverse model analyses employing fast randomized data reduction

NASA Astrophysics Data System (ADS)

Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel; Vesselinov, Velimir V.; Bui-Thanh, Tan

2017-08-01

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called "sketching" matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

Sparsity-based acoustic inversion in cross-sectional multiscale optoacoustic imaging.

PubMed

Han, Yiyong; Tzoumas, Stratis; Nunes, Antonio; Ntziachristos, Vasilis; Rosenthal, Amir

2015-09-01

With recent advancement in hardware of optoacoustic imaging systems, highly detailed cross-sectional images may be acquired at a single laser shot, thus eliminating motion artifacts. Nonetheless, other sources of artifacts remain due to signal distortion or out-of-plane signals. The purpose of image reconstruction algorithms is to obtain the most accurate images from noisy, distorted projection data. In this paper, the authors use the model-based approach for acoustic inversion, combined with a sparsity-based inversion procedure. Specifically, a cost function is used that includes the L1 norm of the image in sparse representation and a total variation (TV) term. The optimization problem is solved by a numerically efficient implementation of a nonlinear gradient descent algorithm. TV-L1 model-based inversion is tested in the cross section geometry for numerically generated data as well as for in vivo experimental data from an adult mouse. In all cases, model-based TV-L1 inversion showed a better performance over the conventional Tikhonov regularization, TV inversion, and L1 inversion. In the numerical examples, the images reconstructed with TV-L1 inversion were quantitatively more similar to the originating images. In the experimental examples, TV-L1 inversion yielded sharper images and weaker streak artifact. The results herein show that TV-L1 inversion is capable of improving the quality of highly detailed, multiscale optoacoustic images obtained in vivo using cross-sectional imaging systems. As a result of its high fidelity, model-based TV-L1 inversion may be considered as the new standard for image reconstruction in cross-sectional imaging.

Remarks on a financial inverse problem by means of Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Cuomo, Salvatore; Di Somma, Vittorio; Sica, Federica

2017-10-01

Estimating the price of a barrier option is a typical inverse problem. In this paper we present a numerical and statistical framework for a market with risk-free interest rate and a risk asset, described by a Geometric Brownian Motion (GBM). After approximating the risk asset with a numerical method, we find the final option price by following an approach based on sequential Monte Carlo methods. All theoretical results are applied to the case of an option whose underlying is a real stock.

Lithological and Surface Geometry Joint Inversions Using Multi-Objective Global Optimization Methods

NASA Astrophysics Data System (ADS)

Lelièvre, Peter; Bijani, Rodrigo; Farquharson, Colin

2016-04-01

Geologists' interpretations about the Earth typically involve distinct rock units with contacts (interfaces) between them. In contrast, standard minimum-structure geophysical inversions are performed on meshes of space-filling cells (typically prisms or tetrahedra) and recover smoothly varying physical property distributions that are inconsistent with typical geological interpretations. There are several approaches through which mesh-based minimum-structure geophysical inversion can help recover models with some of the desired characteristics. However, a more effective strategy may be to consider two fundamentally different types of inversions: lithological and surface geometry inversions. A major advantage of these two inversion approaches is that joint inversion of multiple types of geophysical data is greatly simplified. In a lithological inversion, the subsurface is discretized into a mesh and each cell contains a particular rock type. A lithological model must be translated to a physical property model before geophysical data simulation. Each lithology may map to discrete property values or there may be some a priori probability density function associated with the mapping. Through this mapping, lithological inverse problems limit the parameter domain and consequently reduce the non-uniqueness from that presented by standard mesh-based inversions that allow physical property values on continuous ranges. Furthermore, joint inversion is greatly simplified because no additional mathematical coupling measure is required in the objective function to link multiple physical property models. In a surface geometry inversion, the model comprises wireframe surfaces representing contacts between rock units. This parameterization is then fully consistent with Earth models built by geologists, which in 3D typically comprise wireframe contact surfaces of tessellated triangles. As for the lithological case, the physical properties of the units lying between the contact surfaces are set to a priori values. The inversion is tasked with calculating the geometry of the contact surfaces instead of some piecewise distribution of properties in a mesh. Again, no coupling measure is required and joint inversion is simplified. Both of these inverse problems involve high nonlinearity and discontinuous or non-obtainable derivatives. They can also involve the existence of multiple minima. Hence, one can not apply the standard descent-based local minimization methods used to solve typical minimum-structure inversions. Instead, we are applying Pareto multi-objective global optimization (PMOGO) methods, which generate a suite of solutions that minimize multiple objectives (e.g. data misfits and regularization terms) in a Pareto-optimal sense. Providing a suite of models, as opposed to a single model that minimizes a weighted sum of objectives, allows a more complete assessment of the possibilities and avoids the often difficult choice of how to weight each objective. While there are definite advantages to PMOGO joint inversion approaches, the methods come with significantly increased computational requirements. We are researching various strategies to ameliorate these computational issues including parallelization and problem dimension reduction.

Comparison of Optimal Design Methods in Inverse Problems

PubMed Central

Banks, H. T.; Holm, Kathleen; Kappel, Franz

2011-01-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29]. PMID:21857762

Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra.

PubMed

Fu, Zhongtao; Yang, Wenyu; Yang, Zhen

2013-08-01

In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

Inverse source problems in elastodynamics

NASA Astrophysics Data System (ADS)

Bao, Gang; Hu, Guanghui; Kian, Yavar; Yin, Tao

2018-04-01

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain approaches to show uniqueness in determining the spatial function from wave fields on a large sphere over a finite time interval. The stability estimate of the temporal function from the data of one receiver and the uniqueness result using partial boundary data are proved. Our arguments rely heavily on the use of the Fourier transform, which motivates inversion schemes that can be easily implemented. A Landweber iterative algorithm for recovering the spatial function and a non-iterative inversion scheme based on the uniqueness proof for recovering the temporal function are proposed. Numerical examples are demonstrated in both two and three dimensions.

The Lanchester square-law model extended to a (2,2) conflict

NASA Astrophysics Data System (ADS)

Colegrave, R. K.; Hyde, J. M.

1993-01-01

A natural extension of the Lanchester (1,1) square-law model is the (M,N) linear model in which M forces oppose N forces with constant attrition rates. The (2,2) model is treated from both direct and inverse viewpoints. The inverse problem means that the model is to be fitted to a minimum number of observed force levels, i.e. the attrition rates are to be found from the initial force levels together with the levels observed at two subsequent times. An approach based on Hamiltonian dynamics has enabled the authors to derive a procedure for solving the inverse problem, which is readily computerized. Conflicts in which participants unexpectedly rally or weaken must be excluded.

Children's Understanding of the Arithmetic Concepts of Inversion and Associativity

ERIC Educational Resources Information Center

Robinson, Katherine M.; Ninowski, Jerilyn E.; Gray, Melissa L.

2006-01-01

Previous studies have shown that even preschoolers can solve inversion problems of the form a + b - b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e [divided by] e was also examined. Grade 6 and 8 students solved inversion problems of both types as well…

EDITORIAL: Introduction to the special issue on electromagnetic inverse problems: emerging methods and novel applications Introduction to the special issue on electromagnetic inverse problems: emerging methods and novel applications

NASA Astrophysics Data System (ADS)

Dorn, O.; Lesselier, D.

2010-07-01

Inverse problems in electromagnetics have a long history and have stimulated exciting research over many decades. New applications and solution methods are still emerging, providing a rich source of challenging topics for further investigation. The purpose of this special issue is to combine descriptions of several such developments that are expected to have the potential to fundamentally fuel new research, and to provide an overview of novel methods and applications for electromagnetic inverse problems. There have been several special sections published in Inverse Problems over the last decade addressing fully, or partly, electromagnetic inverse problems. Examples are: Electromagnetic imaging and inversion of the Earth's subsurface (Guest Editors: D Lesselier and T Habashy) October 2000 Testing inversion algorithms against experimental data (Guest Editors: K Belkebir and M Saillard) December 2001 Electromagnetic and ultrasonic nondestructive evaluation (Guest Editors: D Lesselier and J Bowler) December 2002 Electromagnetic characterization of buried obstacles (Guest Editors: D Lesselier and W C Chew) December 2004 Testing inversion algorithms against experimental data: inhomogeneous targets (Guest Editors: K Belkebir and M Saillard) December 2005 Testing inversion algorithms against experimental data: 3D targets (Guest Editors: A Litman and L Crocco) February 2009 In a certain sense, the current issue can be understood as a continuation of this series of special sections on electromagnetic inverse problems. On the other hand, its focus is intended to be more general than previous ones. Instead of trying to cover a well-defined, somewhat specialized research topic as completely as possible, this issue aims to show the broad range of techniques and applications that are relevant to electromagnetic imaging nowadays, which may serve as a source of inspiration and encouragement for all those entering this active and rapidly developing research area. Also, the construction of this special issue is likely to have been different from preceding ones. In addition to the invitations sent to specific research groups involved in electromagnetic inverse problems, the Guest Editors also solicited recommendations, from a large number of experts, of potential authors who were thereupon encouraged to contribute. Moreover, an open call for contributions was published on the homepage of Inverse Problems in order to attract as wide a scope of contributions as possible. This special issue's attempt at generality might also define its limitations: by no means could this collection of papers be exhaustive or complete, and as Guest Editors we are well aware that many exciting topics and potential contributions will be missing. This, however, also determines its very special flavor: besides addressing electromagnetic inverse problems in a broad sense, there were only a few restrictions on the contributions considered for this section. One requirement was plausible evidence of either novelty or the emergent nature of the technique or application described, judged mainly by the referees, and in some cases by the Guest Editors. The technical quality of the contributions always remained a stringent condition of acceptance, final adjudication (possibly questionable either way, not always positive) being made in most cases once a thorough revision process had been carried out. Therefore, we hope that the final result presented here constitutes an interesting collection of novel ideas and applications, properly refereed and edited, which will find its own readership and which can stimulate significant new research in the topics represented. Overall, as Guest Editors, we feel quite fortunate to have obtained such a strong response to the call for this issue and to have a really wide-ranging collection of high-quality contributions which, indeed, can be read from the first to the last page with sustained enthusiasm. A large number of applications and techniques is represented, overall via 16 contributions with 45 authors in total. This shows, in our opinion, that electromagnetic imaging and inversion remain amongst the most challenging and active research areas in applied inverse problems today. Below, we give a brief overview of the contributions included in this issue, ordered alphabetically by the surname of the leading author. 1. The complexity of handling potential randomness of the source in an inverse scattering problem is not minor, and the literature is far from being replete in this configuration. The contribution by G Bao, S N Chow, P Li and H Zhou, `Numerical solution of an inverse medium scattering problem with a stochastic source', exemplifies how to hybridize Wiener chaos expansion with a recursive linearization method in order to solve the stochastic problem as a set of decoupled deterministic ones. 2. In cases where the forward problem is expensive to evaluate, database methods might become a reliable method of choice, while enabling one to deliver more information on the inversion itself. The contribution by S Bilicz, M Lambert and Sz Gyimóthy, `Kriging-based generation of optimal databases as forward and inverse surrogate models', describes such a technique which uses kriging for constructing an efficient database with the goal of achieving an equidistant distribution of points in the measurement space. 3. Anisotropy remains a considerable challenge in electromagnetic imaging, which is tackled in the contribution by F Cakoni, D Colton, P Monk and J Sun, `The inverse electromagnetic scattering problem for anisotropic media', via the fact that transmission eigenvalues can be retrieved from a far-field scattering pattern, yielding, in particular, lower and upper bounds of the index of refraction of the unknown (dielectric anisotropic) scatterer. 4. So-called subspace optimization methods (SOM) have attracted a lot of interest recently in many fields. The contribution by X Chen, `Subspace-based optimization method for inverse scattering problems with an inhomogeneous background medium', illustrates how to address a realistic situation in which the medium containing the unknown obstacles is not homogeneous, via blending a properly developed SOM with a finite-element approach to the required Green's functions. 5. H Egger, M Hanke, C Schneider, J Schöberl and S Zaglmayr, in their contribution `Adjoint-based sampling methods for electromagnetic scattering', show how to efficiently develop sampling methods without explicit knowledge of the dyadic Green's function once an adjoint problem has been solved at much lower computational cost. This is demonstrated by examples in demanding propagative and diffusive situations. 6. Passive sensor arrays can be employed to image reflectors from ambient noise via proper migration of cross-correlation matrices into their embedding medium. This is investigated, and resolution, in particular, is considered in detail, as a function of the characteristics of the sensor array and those of the noise, in the contribution by J Garnier and G Papanicolaou, `Resolution analysis for imaging with noise'. 7. A direct reconstruction technique based on the conformal mapping theorem is proposed and investigated in depth in the contribution by H Haddar and R Kress, `Conformal mapping and impedance tomography'. This paper expands on previous work, with inclusions in homogeneous media, convergence results, and numerical illustrations. 8. The contribution by T Hohage and S Langer, `Acceleration techniques for regularized Newton methods applied to electromagnetic inverse medium scattering problems', focuses on a spectral preconditioner intended to accelerate regularized Newton methods as employed for the retrieval of a local inhomogeneity in a three-dimensional vector electromagnetic case, while also illustrating the implementation of a Lepskiĭ-type stopping rule outsmarting a traditional discrepancy principle. 9. Geophysical applications are a rich source of practically relevant inverse problems. The contribution by M Li, A Abubakar and T Habashy, `Application of a two-and-a-half dimensional model-based algorithm to crosswell electromagnetic data inversion', deals with a model-based inversion technique for electromagnetic imaging which addresses novel challenges such as multi-physics inversion, and incorporation of prior knowledge, such as in hydrocarbon recovery. 10. Non-stationary inverse problems, considered as a special class of Bayesian inverse problems, are framed via an orthogonal decomposition representation in the contribution by A Lipponen, A Seppänen and J P Kaipio, `Reduced order estimation of nonstationary flows with electrical impedance tomography'. The goal is to simultaneously estimate, from electrical impedance tomography data, certain characteristics of the Navier--Stokes fluid flow model together with time-varying concentration distribution. 11. Non-iterative imaging methods of thin, penetrable cracks, based on asymptotic expansion of the scattering amplitude and analysis of the multi-static response matrix, are discussed in the contribution by W-K Park, `On the imaging of thin dielectric inclusions buried within a half-space', completing, for a shallow burial case at multiple frequencies, the direct imaging of small obstacles (here, along their transverse dimension), MUSIC and non-MUSIC type indicator functions being used for that purpose. 12. The contribution by R Potthast, `A study on orthogonality sampling' envisages quick localization and shaping of obstacles from (portions of) far-field scattering patterns collected at one or more time-harmonic frequencies, via the simple calculation (and summation) of scalar products between those patterns and a test function. This is numerically exemplified for Neumann/Dirichlet boundary conditions and homogeneous/heterogeneous embedding media. 13. The contribution by J D Shea, P Kosmas, B D Van Veen and S C Hagness, `Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms', aims at microwave medical imaging, namely the early detection of breast cancer. The use of contrast enhancing agents is discussed in detail and a number of reconstructions in three-dimensional geometry of realistic numerical breast phantoms are presented. 14. The contribution by D A Subbarayappa and V Isakov, `Increasing stability of the continuation for the Maxwell system', discusses enhanced log-type stability results for continuation of solutions of the time-harmonic Maxwell system, adding a fresh chapter to the interesting story of the study of the Cauchy problem for PDE. 15. In their contribution, `Recent developments of a monotonicity imaging method for magnetic induction tomography in the small skin-depth regime', A Tamburrino, S Ventre and G Rubinacci extend the recently developed monotonicity method toward the application of magnetic induction tomography in order to map surface-breaking defects affecting a damaged metal component. 16. The contribution by F Viani, P Rocca, M Benedetti, G Oliveri and A Massa, `Electromagnetic passive localization and tracking of moving targets in a WSN-infrastructured environment', contributes to what could still be seen as a niche problem, yet both useful in terms of applications, e.g., security, and challenging in terms of methodologies and experiments, in particular, in view of the complexity of environments in which this endeavor is to take place and the variability of the wireless sensor networks employed. To conclude, we would like to thank the able and tireless work of Kate Watt and Zoë Crossman, as past and present Publishers of the Journal, on what was definitely a long and exciting journey (sometimes a little discouraging when reports were not arriving, or authors were late, or Guest Editors overwhelmed) that started from a thorough discussion at the `Manchester workshop on electromagnetic inverse problems' held mid-June 2009, between Kate Watt and the Guest Editors. We gratefully acknowledge the fact that W W Symes gave us his full backing to carry out this special issue and that A K Louis completed it successfully. Last, but not least, the staff of Inverse Problems should be thanked, since they work together to make it a premier journal.

A minimal dissipation type-based classification in irreversible thermodynamics and microeconomics

NASA Astrophysics Data System (ADS)

Tsirlin, A. M.; Kazakov, V.; Kolinko, N. A.

2003-10-01

We formulate the problem of finding classes of kinetic dependencies in irreversible thermodynamic and microeconomic systems for which minimal dissipation processes belong to the same type. We show that this problem is an inverse optimal control problem and solve it. The commonality of this problem in irreversible thermodynamics and microeconomics is emphasized.

Model based defect characterization in composites

NASA Astrophysics Data System (ADS)

Roberts, R.; Holland, S.

2017-02-01

Work is reported on model-based defect characterization in CFRP composites. The work utilizes computational models of the interaction of NDE probing energy fields (ultrasound and thermography), to determine 1) the measured signal dependence on material and defect properties (forward problem), and 2) an assessment of performance-critical defect properties from analysis of measured NDE signals (inverse problem). Work is reported on model implementation for inspection of CFRP laminates containing multi-ply impact-induced delamination, with application in this paper focusing on ultrasound. A companion paper in these proceedings summarizes corresponding activity in thermography. Inversion of ultrasound data is demonstrated showing the quantitative extraction of damage properties.

A general approach to regularizing inverse problems with regional data using Slepian wavelets

NASA Astrophysics Data System (ADS)

Michel, Volker; Simons, Frederik J.

2017-12-01

Slepian functions are orthogonal function systems that live on subdomains (for example, geographical regions on the Earth’s surface, or bandlimited portions of the entire spectrum). They have been firmly established as a useful tool for the synthesis and analysis of localized (concentrated or confined) signals, and for the modeling and inversion of noise-contaminated data that are only regionally available or only of regional interest. In this paper, we consider a general abstract setup for inverse problems represented by a linear and compact operator between Hilbert spaces with a known singular-value decomposition (svd). In practice, such an svd is often only given for the case of a global expansion of the data (e.g. on the whole sphere) but not for regional data distributions. We show that, in either case, Slepian functions (associated to an arbitrarily prescribed region and the given compact operator) can be determined and applied to construct a regularization for the ill-posed regional inverse problem. Moreover, we describe an algorithm for constructing the Slepian basis via an algebraic eigenvalue problem. The obtained Slepian functions can be used to derive an svd for the combination of the regionalizing projection and the compact operator. As a result, standard regularization techniques relying on a known svd become applicable also to those inverse problems where the data are regionally given only. In particular, wavelet-based multiscale techniques can be used. An example for the latter case is elaborated theoretically and tested on two synthetic numerical examples.

The 2-D magnetotelluric inverse problem solved with optimization

NASA Astrophysics Data System (ADS)

van Beusekom, Ashley E.; Parker, Robert L.; Bank, Randolph E.; Gill, Philip E.; Constable, Steven

2011-02-01

The practical 2-D magnetotelluric inverse problem seeks to determine the shallow-Earth conductivity structure using finite and uncertain data collected on the ground surface. We present an approach based on using PLTMG (Piecewise Linear Triangular MultiGrid), a special-purpose code for optimization with second-order partial differential equation (PDE) constraints. At each frequency, the electromagnetic field and conductivity are treated as unknowns in an optimization problem in which the data misfit is minimized subject to constraints that include Maxwell's equations and the boundary conditions. Within this framework it is straightforward to accommodate upper and lower bounds or other conditions on the conductivity. In addition, as the underlying inverse problem is ill-posed, constraints may be used to apply various kinds of regularization. We discuss some of the advantages and difficulties associated with using PDE-constrained optimization as the basis for solving large-scale nonlinear geophysical inverse problems. Combined transverse electric and transverse magnetic complex admittances from the COPROD2 data are inverted. First, we invert penalizing size and roughness giving solutions that are similar to those found previously. In a second example, conventional regularization is replaced by a technique that imposes upper and lower bounds on the model. In both examples the data misfit is better than that obtained previously, without any increase in model complexity.

Three-dimensional Gravity Inversion with a New Gradient Scheme on Unstructured Grids

NASA Astrophysics Data System (ADS)

Sun, S.; Yin, C.; Gao, X.; Liu, Y.; Zhang, B.

2017-12-01

Stabilized gradient-based methods have been proved to be efficient for inverse problems. Based on these methods, setting gradient close to zero can effectively minimize the objective function. Thus the gradient of objective function determines the inversion results. By analyzing the cause of poor resolution on depth in gradient-based gravity inversion methods, we find that imposing depth weighting functional in conventional gradient can improve the depth resolution to some extent. However, the improvement is affected by the regularization parameter and the effect of the regularization term becomes smaller with increasing depth (shown as Figure 1 (a)). In this paper, we propose a new gradient scheme for gravity inversion by introducing a weighted model vector. The new gradient can improve the depth resolution more efficiently, which is independent of the regularization parameter, and the effect of regularization term will not be weakened when depth increases. Besides, fuzzy c-means clustering method and smooth operator are both used as regularization terms to yield an internal consecutive inverse model with sharp boundaries (Sun and Li, 2015). We have tested our new gradient scheme with unstructured grids on synthetic data to illustrate the effectiveness of the algorithm. Gravity forward modeling with unstructured grids is based on the algorithm proposed by Okbe (1979). We use a linear conjugate gradient inversion scheme to solve the inversion problem. The numerical experiments show a great improvement in depth resolution compared with regular gradient scheme, and the inverse model is compact at all depths (shown as Figure 1 (b)). AcknowledgeThis research is supported by Key Program of National Natural Science Foundation of China (41530320), China Natural Science Foundation for Young Scientists (41404093), and Key National Research Project of China (2016YFC0303100, 2017YFC0601900). ReferencesSun J, Li Y. 2015. Multidomain petrophysically constrained inversion and geology differentiation using guided fuzzy c-means clustering. Geophysics, 80(4): ID1-ID18. Okabe M. 1979. Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies. Geophysics, 44(4), 730-741.

Inverse transport calculations in optical imaging with subspace optimization algorithms

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

Ding, Tian, E-mail: tding@math.utexas.edu; Ren, Kui, E-mail: ren@math.utexas.edu

2014-09-15

Inverse boundary value problems for the radiative transport equation play an important role in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid progress in the mathematical theory and numerical computation of these inverse problems in recent years, developing robust and efficient reconstruction algorithms remains a challenging task and an active research topic. We propose here a robust reconstruction method that is based on subspace minimization techniques. The method splits the unknown transport solution (or a functional of it) into low-frequency and high-frequency components, and uses singular value decomposition to analyticallymore » recover part of low-frequency information. Minimization is then applied to recover part of the high-frequency components of the unknowns. We present some numerical simulations with synthetic data to demonstrate the performance of the proposed algorithm.« less

Using machine learning to accelerate sampling-based inversion

NASA Astrophysics Data System (ADS)

Valentine, A. P.; Sambridge, M.

2017-12-01

In most cases, a complete solution to a geophysical inverse problem (including robust understanding of the uncertainties associated with the result) requires a sampling-based approach. However, the computational burden is high, and proves intractable for many problems of interest. There is therefore considerable value in developing techniques that can accelerate sampling procedures.The main computational cost lies in evaluation of the forward operator (e.g. calculation of synthetic seismograms) for each candidate model. Modern machine learning techniques-such as Gaussian Processes-offer a route for constructing a computationally-cheap approximation to this calculation, which can replace the accurate solution during sampling. Importantly, the accuracy of the approximation can be refined as inversion proceeds, to ensure high-quality results.In this presentation, we describe and demonstrate this approach-which can be seen as an extension of popular current methods, such as the Neighbourhood Algorithm, and bridges the gap between prior- and posterior-sampling frameworks.

The New Method of Tsunami Source Reconstruction With r-Solution Inversion Method

NASA Astrophysics Data System (ADS)

Voronina, T. A.; Romanenko, A. A.

2016-12-01

Application of the r-solution method to reconstructing the initial tsunami waveform is discussed. This methodology is based on the inversion of remote measurements of water-level data. The wave propagation is considered within the scope of a linear shallow-water theory. The ill-posed inverse problem in question is regularized by means of a least square inversion using the truncated Singular Value Decomposition method. As a result of the numerical process, an r-solution is obtained. The method proposed allows one to control the instability of a numerical solution and to obtain an acceptable result in spite of ill posedness of the problem. Implementation of this methodology to reconstructing of the initial waveform to 2013 Solomon Islands tsunami validates the theoretical conclusion for synthetic data and a model tsunami source: the inversion result strongly depends on data noisiness, the azimuthal and temporal coverage of recording stations with respect to the source area. Furthermore, it is possible to make a preliminary selection of the most informative set of the available recording stations used in the inversion process.

Modularized seismic full waveform inversion based on waveform sensitivity kernels - The software package ASKI

NASA Astrophysics Data System (ADS)

Schumacher, Florian; Friederich, Wolfgang; Lamara, Samir; Gutt, Phillip; Paffrath, Marcel

2015-04-01

We present a seismic full waveform inversion concept for applications ranging from seismological to enineering contexts, based on sensitivity kernels for full waveforms. The kernels are derived from Born scattering theory as the Fréchet derivatives of linearized frequency-domain full waveform data functionals, quantifying the influence of elastic earth model parameters and density on the data values. For a specific source-receiver combination, the kernel is computed from the displacement and strain field spectrum originating from the source evaluated throughout the inversion domain, as well as the Green function spectrum and its strains originating from the receiver. By storing the wavefield spectra of specific sources/receivers, they can be re-used for kernel computation for different specific source-receiver combinations, optimizing the total number of required forward simulations. In the iterative inversion procedure, the solution of the forward problem, the computation of sensitivity kernels and the derivation of a model update is held completely separate. In particular, the model description for the forward problem and the description of the inverted model update are kept independent. Hence, the resolution of the inverted model as well as the complexity of solving the forward problem can be iteratively increased (with increasing frequency content of the inverted data subset). This may regularize the overall inverse problem and optimizes the computational effort of both, solving the forward problem and computing the model update. The required interconnection of arbitrary unstructured volume and point grids is realized by generalized high-order integration rules and 3D-unstructured interpolation methods. The model update is inferred solving a minimization problem in a least-squares sense, resulting in Gauss-Newton convergence of the overall inversion process. The inversion method was implemented in the modularized software package ASKI (Analysis of Sensitivity and Kernel Inversion), which provides a generalized interface to arbitrary external forward modelling codes. So far, the 3D spectral-element code SPECFEM3D (Tromp, Komatitsch and Liu, 2008) and the 1D semi-analytical code GEMINI (Friederich and Dalkolmo, 1995) in both, Cartesian and spherical framework are supported. The creation of interfaces to further forward codes is planned in the near future. ASKI is freely available under the terms of the GPL at www.rub.de/aski . Since the independent modules of ASKI must communicate via file output/input, large storage capacities need to be accessible conveniently. Storing the complete sensitivity matrix to file, however, permits the scientist full manual control over each step in a customized procedure of sensitivity/resolution analysis and full waveform inversion. In the presentation, we will show some aspects of the theory behind the full waveform inversion method and its practical realization by the software package ASKI, as well as synthetic and real-data applications from different scales and geometries.

Comparative evolution of the inverse problems (Introduction to an interdisciplinary study of the inverse problems)

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

The progressive realization of the consequences of nonuniqueness imply an evolution of both the methods and the centers of interest in inverse problems. This evolution is schematically described together with the various mathematical methods used. A comparative description is given of inverse methods in scientific research, with examples taken from mathematics, quantum and classical physics, seismology, transport theory, radiative transfer, electromagnetic scattering, electrocardiology, etc. It is hoped that this paper will pave the way for an interdisciplinary study of inverse problems.

Structural Damage Detection Using Changes in Natural Frequencies: Theory and Applications

NASA Astrophysics Data System (ADS)

He, K.; Zhu, W. D.

2011-07-01

A vibration-based method that uses changes in natural frequencies of a structure to detect damage has advantages over conventional nondestructive tests in detecting various types of damage, including loosening of bolted joints, using minimum measurement data. Two major challenges associated with applications of the vibration-based damage detection method to engineering structures are addressed: accurate modeling of structures and the development of a robust inverse algorithm to detect damage, which are defined as the forward and inverse problems, respectively. To resolve the forward problem, new physics-based finite element modeling techniques are developed for fillets in thin-walled beams and for bolted joints, so that complex structures can be accurately modeled with a reasonable model size. To resolve the inverse problem, a logistical function transformation is introduced to convert the constrained optimization problem to an unconstrained one, and a robust iterative algorithm using a trust-region method, called the Levenberg-Marquardt method, is developed to accurately detect the locations and extent of damage. The new methodology can ensure global convergence of the iterative algorithm in solving under-determined system equations and deal with damage detection problems with relatively large modeling error and measurement noise. The vibration-based damage detection method is applied to various structures including lightning masts, a space frame structure and one of its components, and a pipeline. The exact locations and extent of damage can be detected in the numerical simulation where there is no modeling error and measurement noise. The locations and extent of damage can be successfully detected in experimental damage detection.

A model reduction approach to numerical inversion for a parabolic partial differential equation

NASA Astrophysics Data System (ADS)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

Hybrid Weighted Minimum Norm Method A new method based LORETA to solve EEG inverse problem.

PubMed

Song, C; Zhuang, T; Wu, Q

2005-01-01

This Paper brings forward a new method to solve EEG inverse problem. Based on following physiological characteristic of neural electrical activity source: first, the neighboring neurons are prone to active synchronously; second, the distribution of source space is sparse; third, the active intensity of the sources are high centralized, we take these prior knowledge as prerequisite condition to develop the inverse solution of EEG, and not assume other characteristic of inverse solution to realize the most commonly 3D EEG reconstruction map. The proposed algorithm takes advantage of LORETA's low resolution method which emphasizes particularly on 'localization' and FOCUSS's high resolution method which emphasizes particularly on 'separability'. The method is still under the frame of the weighted minimum norm method. The keystone is to construct a weighted matrix which takes reference from the existing smoothness operator, competition mechanism and study algorithm. The basic processing is to obtain an initial solution's estimation firstly, then construct a new estimation using the initial solution's information, repeat this process until the solutions under last two estimate processing is keeping unchanged.

Superresolution radar imaging based on fast inverse-free sparse Bayesian learning for multiple measurement vectors

NASA Astrophysics Data System (ADS)

He, Xingyu; Tong, Ningning; Hu, Xiaowei

2018-01-01

Compressive sensing has been successfully applied to inverse synthetic aperture radar (ISAR) imaging of moving targets. By exploiting the block sparse structure of the target image, sparse solution for multiple measurement vectors (MMV) can be applied in ISAR imaging and a substantial performance improvement can be achieved. As an effective sparse recovery method, sparse Bayesian learning (SBL) for MMV involves a matrix inverse at each iteration. Its associated computational complexity grows significantly with the problem size. To address this problem, we develop a fast inverse-free (IF) SBL method for MMV. A relaxed evidence lower bound (ELBO), which is computationally more amiable than the traditional ELBO used by SBL, is obtained by invoking fundamental property for smooth functions. A variational expectation-maximization scheme is then employed to maximize the relaxed ELBO, and a computationally efficient IF-MSBL algorithm is proposed. Numerical results based on simulated and real data show that the proposed method can reconstruct row sparse signal accurately and obtain clear superresolution ISAR images. Moreover, the running time and computational complexity are reduced to a great extent compared with traditional SBL methods.

Large-scale 3D inversion of marine controlled source electromagnetic data using the integral equation method

NASA Astrophysics Data System (ADS)

Zhdanov, M. S.; Cuma, M.; Black, N.; Wilson, G. A.

2009-12-01

The marine controlled source electromagnetic (MCSEM) method has become widely used in offshore oil and gas exploration. Interpretation of MCSEM data is still a very challenging problem, especially if one would like to take into account the realistic 3D structure of the subsurface. The inversion of MCSEM data is complicated by the fact that the EM response of a hydrocarbon-bearing reservoir is very weak in comparison with the background EM fields generated by an electric dipole transmitter in complex geoelectrical structures formed by a conductive sea-water layer and the terranes beneath it. In this paper, we present a review of the recent developments in the area of large-scale 3D EM forward modeling and inversion. Our approach is based on using a new integral form of Maxwell’s equations allowing for an inhomogeneous background conductivity, which results in a numerically effective integral representation for 3D EM field. This representation provides an efficient tool for the solution of 3D EM inverse problems. To obtain a robust inverse model of the conductivity distribution, we apply regularization based on a focusing stabilizing functional which allows for the recovery of models with both smooth and sharp geoelectrical boundaries. The method is implemented in a fully parallel computer code, which makes it possible to run large-scale 3D inversions on grids with millions of inversion cells. This new technique can be effectively used for active EM detection and monitoring of the subsurface targets.

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

Parallelized Bayesian inversion for three-dimensional dental X-ray imaging.

PubMed

Kolehmainen, Ville; Vanne, Antti; Siltanen, Samuli; Järvenpää, Seppo; Kaipio, Jari P; Lassas, Matti; Kalke, Martti

2006-02-01

Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment. In this paper, we consider a novel type of 3-D imaging modality for dental radiology. We consider situations in which projection images of the teeth are taken from a few sparsely distributed projection directions using the dentist's regular (digital) X-ray equipment and the 3-D X-ray attenuation function is reconstructed. A complication in these experiments is that the reconstruction of the 3-D structure based on a few projection images becomes an ill-posed inverse problem. Bayesian inversion is a well suited framework for reconstruction from such incomplete data. In Bayesian inversion, the ill-posed reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete information of the projection data. In this paper we propose a Bayesian method for 3-D reconstruction in dental radiology. The method is partially based on Kolehmainen et al. 2003. The prior model for dental structures consist of a weighted l1 and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posteriori (MAP) estimate. To make the 3-D reconstruction computationally feasible, a parallelized version of an optimization algorithm is implemented for a Beowulf cluster computer. The method is tested with projection data from dental specimens and patient data. Tomosynthetic reconstructions are given as reference for the proposed method.

Sparsity-based acoustic inversion in cross-sectional multiscale optoacoustic imaging

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

Han, Yiyong; Tzoumas, Stratis; Nunes, Antonio

2015-09-15

Purpose: With recent advancement in hardware of optoacoustic imaging systems, highly detailed cross-sectional images may be acquired at a single laser shot, thus eliminating motion artifacts. Nonetheless, other sources of artifacts remain due to signal distortion or out-of-plane signals. The purpose of image reconstruction algorithms is to obtain the most accurate images from noisy, distorted projection data. Methods: In this paper, the authors use the model-based approach for acoustic inversion, combined with a sparsity-based inversion procedure. Specifically, a cost function is used that includes the L1 norm of the image in sparse representation and a total variation (TV) term. Themore » optimization problem is solved by a numerically efficient implementation of a nonlinear gradient descent algorithm. TV–L1 model-based inversion is tested in the cross section geometry for numerically generated data as well as for in vivo experimental data from an adult mouse. Results: In all cases, model-based TV–L1 inversion showed a better performance over the conventional Tikhonov regularization, TV inversion, and L1 inversion. In the numerical examples, the images reconstructed with TV–L1 inversion were quantitatively more similar to the originating images. In the experimental examples, TV–L1 inversion yielded sharper images and weaker streak artifact. Conclusions: The results herein show that TV–L1 inversion is capable of improving the quality of highly detailed, multiscale optoacoustic images obtained in vivo using cross-sectional imaging systems. As a result of its high fidelity, model-based TV–L1 inversion may be considered as the new standard for image reconstruction in cross-sectional imaging.« less

Use of Genetic Algorithms to solve Inverse Problems in Relativistic Hydrodynamics

NASA Astrophysics Data System (ADS)

Guzmán, F. S.; González, J. A.

2018-04-01

We present the use of Genetic Algorithms (GAs) as a strategy to solve inverse problems associated with models of relativistic hydrodynamics. The signal we consider to emulate an observation is the density of a relativistic gas, measured at a point where a shock is traveling. This shock is generated numerically out of a Riemann problem with mildly relativistic conditions. The inverse problem we propose is the prediction of the initial conditions of density, velocity and pressure of the Riemann problem that gave origin to that signal. For this we use the density, velocity and pressure of the gas at both sides of the discontinuity, as the six genes of an organism, initially with random values within a tolerance. We then prepare an initial population of N of these organisms and evolve them using methods based on GAs. In the end, the organism with the best fitness of each generation is compared to the signal and the process ends when the set of initial conditions of the organisms of a later generation fit the Signal within a tolerance.

Recovery of time-dependent volatility in option pricing model

NASA Astrophysics Data System (ADS)

Deng, Zui-Cha; Hon, Y. C.; Isakov, V.

2016-11-01

In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective. The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. CityU 101112) and grants from the NNSF of China (Nos. 11261029, 11461039), and NSF grants DMS 10-08902 and 15-14886 and by Emylou Keith and Betty Dutcher Distinguished Professorship at the Wichita State University (USA).

Model based approach to UXO imaging using the time domain electromagnetic method

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

Lavely, E.M.

1999-04-01

Time domain electromagnetic (TDEM) sensors have emerged as a field-worthy technology for UXO detection in a variety of geological and environmental settings. This success has been achieved with commercial equipment that was not optimized for UXO detection and discrimination. The TDEM response displays a rich spatial and temporal behavior which is not currently utilized. Therefore, in this paper the author describes a research program for enhancing the effectiveness of the TDEM method for UXO detection and imaging. Fundamental research is required in at least three major areas: (a) model based imaging capability i.e. the forward and inverse problem, (b) detectormore » modeling and instrument design, and (c) target recognition and discrimination algorithms. These research problems are coupled and demand a unified treatment. For example: (1) the inverse solution depends on solution of the forward problem and knowledge of the instrument response; (2) instrument design with improved diagnostic power requires forward and inverse modeling capability; and (3) improved target recognition algorithms (such as neural nets) must be trained with data collected from the new instrument and with synthetic data computed using the forward model. Further, the design of the appropriate input and output layers of the net will be informed by the results of the forward and inverse modeling. A more fully developed model of the TDEM response would enable the joint inversion of data collected from multiple sensors (e.g., TDEM sensors and magnetometers). Finally, the author suggests that a complementary approach to joint inversions is the statistical recombination of data using principal component analysis. The decomposition into principal components is useful since the first principal component contains those features that are most strongly correlated from image to image.« less

Forward and Inverse Modeling of Self-potential. A Tomography of Groundwater Flow and Comparison Between Deterministic and Stochastic Inversion Methods

NASA Astrophysics Data System (ADS)

Quintero-Chavarria, E.; Ochoa Gutierrez, L. H.

2016-12-01

Applications of the Self-potential Method in the fields of Hydrogeology and Environmental Sciences have had significant developments during the last two decades with a strong use on groundwater flows identification. Although only few authors deal with the forward problem's solution -especially in geophysics literature- different inversion procedures are currently being developed but in most cases they are compared with unconventional groundwater velocity fields and restricted to structured meshes. This research solves the forward problem based on the finite element method using the St. Venant's Principle to transform a point dipole, which is the field generated by a single vector, into a distribution of electrical monopoles. Then, two simple aquifer models were generated with specific boundary conditions and head potentials, velocity fields and electric potentials in the medium were computed. With the model's surface electric potential, the inverse problem is solved to retrieve the source of electric potential (vector field associated to groundwater flow) using deterministic and stochastic approaches. The first approach was carried out by implementing a Tikhonov regularization with a stabilized operator adapted to the finite element mesh while for the second a hierarchical Bayesian model based on Markov chain Monte Carlo (McMC) and Markov Random Fields (MRF) was constructed. For all implemented methods, the result between the direct and inverse models was contrasted in two ways: 1) shape and distribution of the vector field, and 2) magnitude's histogram. Finally, it was concluded that inversion procedures are improved when the velocity field's behavior is considered, thus, the deterministic method is more suitable for unconfined aquifers than confined ones. McMC has restricted applications and requires a lot of information (particularly in potentials fields) while MRF has a remarkable response especially when dealing with confined aquifers.

Radiative-conductive inverse problem for lumped parameter systems

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Nenarokomov, A. V.; Gonzalez, V. M.

2008-11-01

The purpose of this paper is to introduce a iterative regularization method in the research of radiative and thermal properties of materials with applications in the design of Thermal Control Systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the (TCS) for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the Inverse Heat Transfer Problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the inverse heat conduction problem is presented too. The practical testing were performed for specimen of the real MLI.

Study of multilayer thermal insulation by inverse problems method

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Nenarokomov, A. V.; Gonzalez, V. M.

2009-11-01

The purpose of this paper is to introduce a new method in the research of radiative and thermal properties of materials with further applications in the design of thermal control systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the TCS for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the inverse heat transfer problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the inverse heat conduction problem is presented as well. The practical approves were made for specimen of the real MLI.

ℓ1-Regularized full-waveform inversion with prior model information based on orthant-wise limited memory quasi-Newton method

NASA Astrophysics Data System (ADS)

Dai, Meng-Xue; Chen, Jing-Bo; Cao, Jian

2017-07-01

Full-waveform inversion (FWI) is an ill-posed optimization problem which is sensitive to noise and initial model. To alleviate the ill-posedness of the problem, regularization techniques are usually adopted. The ℓ1-norm penalty is a robust regularization method that preserves contrasts and edges. The Orthant-Wise Limited-Memory Quasi-Newton (OWL-QN) method extends the widely-used limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method to the ℓ1-regularized optimization problems and inherits the efficiency of L-BFGS. To take advantage of the ℓ1-regularized method and the prior model information obtained from sonic logs and geological information, we implement OWL-QN algorithm in ℓ1-regularized FWI with prior model information in this paper. Numerical experiments show that this method not only improve the inversion results but also has a strong anti-noise ability.

Calculation of susceptibility through multiple orientation sampling (COSMOS): a method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in MRI.

PubMed

Liu, Tian; Spincemaille, Pascal; de Rochefort, Ludovic; Kressler, Bryan; Wang, Yi

2009-01-01

Magnetic susceptibility differs among tissues based on their contents of iron, calcium, contrast agent, and other molecular compositions. Susceptibility modifies the magnetic field detected in the MR signal phase. The determination of an arbitrary susceptibility distribution from the induced field shifts is a challenging, ill-posed inverse problem. A method called "calculation of susceptibility through multiple orientation sampling" (COSMOS) is proposed to stabilize this inverse problem. The field created by the susceptibility distribution is sampled at multiple orientations with respect to the polarization field, B(0), and the susceptibility map is reconstructed by weighted linear least squares to account for field noise and the signal void region. Numerical simulations and phantom and in vitro imaging validations demonstrated that COSMOS is a stable and precise approach to quantify a susceptibility distribution using MRI.

Wave tilt sounding of multilayered structures. [for probing of stratified planetary surface electrical properties and thickness

NASA Technical Reports Server (NTRS)

Warne, L.; Jaggard, D. L.; Elachi, C.

1979-01-01

The relationship between the wave tilt and the electrical parameters of a multilayered structure is investigated. Particular emphasis is placed on the inverse problem associated with the sounding planetary surfaces. An inversion technique, based on multifrequency wave tilt, is proposed and demonstrated with several computer models. It is determined that there is close agreement between the electrical parameters used in the models and those in the inversion values.

Real-Time Wing-Vortex and Pressure Distribution Estimation on Wings Via Displacements and Strains in Unsteady and Transitional Flight Conditions

DTIC Science & Technology

2016-09-07

approach in co simulation with fluid-dynamics solvers is used. An original variational formulation is developed for the inverse problem of...by the inverse solution meshing. The same approach is used to map the structural and fluid interface kinematics and loads during the fluid structure...co-simulation. The inverse analysis is verified by reconstructing the deformed solution obtained with a corresponding direct formulation, based on

Full-Physics Inverse Learning Machine for Satellite Remote Sensing Retrievals

NASA Astrophysics Data System (ADS)

Loyola, D. G.

2017-12-01

The satellite remote sensing retrievals are usually ill-posed inverse problems that are typically solved by finding a state vector that minimizes the residual between simulated data and real measurements. The classical inversion methods are very time-consuming as they require iterative calls to complex radiative-transfer forward models to simulate radiances and Jacobians, and subsequent inversion of relatively large matrices. In this work we present a novel and extremely fast algorithm for solving inverse problems called full-physics inverse learning machine (FP-ILM). The FP-ILM algorithm consists of a training phase in which machine learning techniques are used to derive an inversion operator based on synthetic data generated using a radiative transfer model (which expresses the "full-physics" component) and the smart sampling technique, and an operational phase in which the inversion operator is applied to real measurements. FP-ILM has been successfully applied to the retrieval of the SO2 plume height during volcanic eruptions and to the retrieval of ozone profile shapes from UV/VIS satellite sensors. Furthermore, FP-ILM will be used for the near-real-time processing of the upcoming generation of European Sentinel sensors with their unprecedented spectral and spatial resolution and associated large increases in the amount of data.

BOOK REVIEW: Inverse Problems. Activities for Undergraduates

NASA Astrophysics Data System (ADS)

Yamamoto, Masahiro

2003-06-01

This book is a valuable introduction to inverse problems. In particular, from the educational point of view, the author addresses the questions of what constitutes an inverse problem and how and why we should study them. Such an approach has been eagerly awaited for a long time. Professor Groetsch, of the University of Cincinnati, is a world-renowned specialist in inverse problems, in particular the theory of regularization. Moreover, he has made a remarkable contribution to educational activities in the field of inverse problems, which was the subject of his previous book (Groetsch C W 1993 Inverse Problems in the Mathematical Sciences (Braunschweig: Vieweg)). For this reason, he is one of the most qualified to write an introductory book on inverse problems. Without question, inverse problems are important, necessary and appear in various aspects. So it is crucial to introduce students to exercises in inverse problems. However, there are not many introductory books which are directly accessible by students in the first two undergraduate years. As a consequence, students often encounter diverse concrete inverse problems before becoming aware of their general principles. The main purpose of this book is to present activities to allow first-year undergraduates to learn inverse theory. To my knowledge, this book is a rare attempt to do this and, in my opinion, a great success. The author emphasizes that it is very important to teach inverse theory in the early years. He writes; `If students consider only the direct problem, they are not looking at the problem from all sides .... The habit of always looking at problems from the direct point of view is intellectually limiting ...' (page 21). The book is very carefully organized so that teachers will be able to use it as a textbook. After an introduction in chapter 1, sucessive chapters deal with inverse problems in precalculus, calculus, differential equations and linear algebra. In order to let one gain some insight into the nature of inverse problems and the appropriate mode of thought, chapter 1 offers historical vignettes, most of which have played an essential role in the development of natural science. These vignettes cover the first successful application of `non-destructive testing' by Archimedes (page 4) via Newton's laws of motion up to literary tomography, and readers will be able to enjoy a wide overview of inverse problems. Therefore, as the author asks, the reader should not skip this chapter. This may not be hard to do, since the headings of the sections are quite intriguing (`Archimedes' Bath', `Another World', `Got the Time?', `Head Games', etc). The author embarks on the technical approach to inverse problems in chapter 2. He has elegantly designed each section with a guide specifying course level, objective, mathematical and scientifical background and appropriate technology (e.g. types of calculators required). The guides are designed such that teachers may be able to construct effective and attractive courses by themselves. The book is not intended to offer one rigidly determined course, but should be used flexibly and independently according to the situation. Moreover, every section closes with activities which can be chosen according to the students' interests and levels of ability. Some of these exercises do not have ready solutions, but require long-term study, so readers are not required to solve all of them. After chapter 5, which contains discrete inverse problems such as the algebraic reconstruction technique and the Backus - Gilbert method, there are answers and commentaries to the activities. Finally, scripts in MATLAB are attached, although they can also be downloaded from the author's web page (http://math.uc.edu/~groetsch/). This book is aimed at students but it will be very valuable to researchers wishing to retain a wide overview of inverse problems in the midst of busy research activities. A Japanese version was published in 2002.

Singular value decomposition for the truncated Hilbert transform

NASA Astrophysics Data System (ADS)

Katsevich, A.

2010-11-01

Starting from a breakthrough result by Gelfand and Graev, inversion of the Hilbert transform became a very important tool for image reconstruction in tomography. In particular, their result is useful when the tomographic data are truncated and one deals with an interior problem. As was established recently, the interior problem admits a stable and unique solution when some a priori information about the object being scanned is available. The most common approach to solving the interior problem is based on converting it to the Hilbert transform and performing analytic continuation. Depending on what type of tomographic data are available, one gets different Hilbert inversion problems. In this paper, we consider two such problems and establish singular value decomposition for the operators involved. We also propose algorithms for performing analytic continuation.

2D Seismic Imaging of Elastic Parameters by Frequency Domain Full Waveform Inversion

NASA Astrophysics Data System (ADS)

Brossier, R.; Virieux, J.; Operto, S.

2008-12-01

Thanks to recent advances in parallel computing, full waveform inversion is today a tractable seismic imaging method to reconstruct physical parameters of the earth interior at different scales ranging from the near- surface to the deep crust. We present a massively parallel 2D frequency-domain full-waveform algorithm for imaging visco-elastic media from multi-component seismic data. The forward problem (i.e. the resolution of the frequency-domain 2D PSV elastodynamics equations) is based on low-order Discontinuous Galerkin (DG) method (P0 and/or P1 interpolations). Thanks to triangular unstructured meshes, the DG method allows accurate modeling of both body waves and surface waves in case of complex topography for a discretization of 10 to 15 cells per shear wavelength. The frequency-domain DG system is solved efficiently for multiple sources with the parallel direct solver MUMPS. The local inversion procedure (i.e. minimization of residuals between observed and computed data) is based on the adjoint-state method which allows to efficiently compute the gradient of the objective function. Applying the inversion hierarchically from the low frequencies to the higher ones defines a multiresolution imaging strategy which helps convergence towards the global minimum. In place of expensive Newton algorithm, the combined use of the diagonal terms of the approximate Hessian matrix and optimization algorithms based on quasi-Newton methods (Conjugate Gradient, LBFGS, ...) allows to improve the convergence of the iterative inversion. The distribution of forward problem solutions over processors driven by a mesh partitioning performed by METIS allows to apply most of the inversion in parallel. We shall present the main features of the parallel modeling/inversion algorithm, assess its scalability and illustrate its performances with realistic synthetic case studies.

Forward and inverse kinematics of double universal joint robot wrists

NASA Technical Reports Server (NTRS)

Williams, Robert L., II

1991-01-01

A robot wrist consisting of two universal joints can eliminate the wrist singularity problem found on many individual robots. Forward and inverse position and velocity kinematics are presented for such a wrist having three degrees of freedom. Denavit-Hartenberg parameters are derived to find the transforms required for the kinematic equations. The Omni-Wrist, a commercial double universal joint robot wrist, is studied in detail. There are four levels of kinematic parameters identified for this wrist; three forward and three inverse maps are presented for both position and velocity. These equations relate the hand coordinate frame to the wrist base frame. They are sufficient for control of the wrist standing alone. When the wrist is attached to a manipulator arm; the offset between the two universal joints complicates the solution of the overall kinematics problem. All wrist coordinate frame origins are not coincident, which prevents decoupling of position and orientation for manipulator inverse kinematics.

Inversion for the driving forces of plate tectonics

NASA Technical Reports Server (NTRS)

Richardson, R. M.

1983-01-01

Inverse modeling techniques have been applied to the problem of determining the roles of various forces that may drive and resist plate tectonic motions. Separate linear inverse problems have been solved to find the best fitting pole of rotation for finite element grid point velocities and to find the best combination of force models to fit the observed relative plate velocities for the earth's twelve major plates using the generalized inverse operator. Variance-covariance data on plate motion have also been included. Results emphasize the relative importance of ridge push forces in the driving mechanism. Convergent margin forces are smaller by at least a factor of two, and perhaps by as much as a factor of twenty. Slab pull, apparently, is poorly transmitted to the surface plate as a driving force. Drag forces at the base of the plate are smaller than ridge push forces, although the sign of the force remains in question.

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.

Study on Material Parameters Identification of Brain Tissue Considering Uncertainty of Friction Coefficient

NASA Astrophysics Data System (ADS)

Guan, Fengjiao; Zhang, Guanjun; Liu, Jie; Wang, Shujing; Luo, Xu; Zhu, Feng

2017-10-01

Accurate material parameters are critical to construct the high biofidelity finite element (FE) models. However, it is hard to obtain the brain tissue parameters accurately because of the effects of irregular geometry and uncertain boundary conditions. Considering the complexity of material test and the uncertainty of friction coefficient, a computational inverse method for viscoelastic material parameters identification of brain tissue is presented based on the interval analysis method. Firstly, the intervals are used to quantify the friction coefficient in the boundary condition. And then the inverse problem of material parameters identification under uncertain friction coefficient is transformed into two types of deterministic inverse problem. Finally the intelligent optimization algorithm is used to solve the two types of deterministic inverse problems quickly and accurately, and the range of material parameters can be easily acquired with no need of a variety of samples. The efficiency and convergence of this method are demonstrated by the material parameters identification of thalamus. The proposed method provides a potential effective tool for building high biofidelity human finite element model in the study of traffic accident injury.

A New Inversion-Based Algorithm for Retrieval of Over-Water Rain Rate from SSM/I Multichannel Imagery

NASA Technical Reports Server (NTRS)

Petty, Grant W.; Stettner, David R.

1994-01-01

This paper discusses certain aspects of a new inversion based algorithm for the retrieval of rain rate over the open ocean from the special sensor microwave/imager (SSM/I) multichannel imagery. This algorithm takes a more detailed physical approach to the retrieval problem than previously discussed algorithms that perform explicit forward radiative transfer calculations based on detailed model hydrometer profiles and attempt to match the observations to the predicted brightness temperature.

Kinematics of an in-parallel actuated manipulator based on the Stewart platform mechanism

NASA Technical Reports Server (NTRS)

Williams, Robert L., II

1992-01-01

This paper presents kinematic equations and solutions for an in-parallel actuated robotic mechanism based on Stewart's platform. These equations are required for inverse position and resolved rate (inverse velocity) platform control. NASA LaRC has a Vehicle Emulator System (VES) platform designed by MIT which is based on Stewart's platform. The inverse position solution is straight-forward and computationally inexpensive. Given the desired position and orientation of the moving platform with respect to the base, the lengths of the prismatic leg actuators are calculated. The forward position solution is more complicated and theoretically has 16 solutions. The position and orientation of the moving platform with respect to the base is calculated given the leg actuator lengths. Two methods are pursued in this paper to solve this problem. The resolved rate (inverse velocity) solution is derived. Given the desired Cartesian velocity of the end-effector, the required leg actuator rates are calculated. The Newton-Raphson Jacobian matrix resulting from the second forward position kinematics solution is a modified inverse Jacobian matrix. Examples and simulations are given for the VES.

Resolution enhancement of robust Bayesian pre-stack inversion in the frequency domain

NASA Astrophysics Data System (ADS)

Yin, Xingyao; Li, Kun; Zong, Zhaoyun

2016-10-01

AVO/AVA (amplitude variation with an offset or angle) inversion is one of the most practical and useful approaches to estimating model parameters. So far, publications on AVO inversion in the Fourier domain have been quite limited in view of its poor stability and sensitivity to noise compared with time-domain inversion. For the resolution and stability of AVO inversion in the Fourier domain, a novel robust Bayesian pre-stack AVO inversion based on the mixed domain formulation of stationary convolution is proposed which could solve the instability and achieve superior resolution. The Fourier operator will be integrated into the objective equation and it avoids the Fourier inverse transform in our inversion process. Furthermore, the background constraints of model parameters are taken into consideration to improve the stability and reliability of inversion which could compensate for the low-frequency components of seismic signals. Besides, the different frequency components of seismic signals can realize decoupling automatically. This will help us to solve the inverse problem by means of multi-component successive iterations and the convergence precision of the inverse problem could be improved. So, superior resolution compared with the conventional time-domain pre-stack inversion could be achieved easily. Synthetic tests illustrate that the proposed method could achieve high-resolution results with a high degree of agreement with the theoretical model and verify the quality of anti-noise. Finally, applications on a field data case demonstrate that the proposed method could obtain stable inversion results of elastic parameters from pre-stack seismic data in conformity with the real logging data.

Computation of forces from deformed visco-elastic biological tissues

NASA Astrophysics Data System (ADS)

Muñoz, José J.; Amat, David; Conte, Vito

2018-04-01

We present a least-squares based inverse analysis of visco-elastic biological tissues. The proposed method computes the set of contractile forces (dipoles) at the cell boundaries that induce the observed and quantified deformations. We show that the computation of these forces requires the regularisation of the problem functional for some load configurations that we study here. The functional measures the error of the dynamic problem being discretised in time with a second-order implicit time-stepping and in space with standard finite elements. We analyse the uniqueness of the inverse problem and estimate the regularisation parameter by means of an L-curved criterion. We apply the methodology to a simple toy problem and to an in vivo set of morphogenetic deformations of the Drosophila embryo.

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

Absolute calibration of the mass scale in the inverse problem of the physical theory of fireballs

NASA Astrophysics Data System (ADS)

Kalenichenko, V. V.

1992-08-01

A method of the absolute calibration of the mass scale is proposed for solving the inverse problem of the physical theory of fireballs. The method is based on data on the masses of fallen meteorites whose fireballs have been photographed in flight. The method can be applied to fireballs whose bodies have not experienced significant fragmentation during their flight in the atmosphere and have kept their shape relatively well. Data on the Lost City and Innisfree meteorites are used to calculate the calibration coefficients.

A necessary condition for applying MUSIC algorithm in limited-view inverse scattering problem

NASA Astrophysics Data System (ADS)

Park, Taehoon; Park, Won-Kwang

2015-09-01

Throughout various results of numerical simulations, it is well-known that MUltiple SIgnal Classification (MUSIC) algorithm can be applied in the limited-view inverse scattering problems. However, the application is somehow heuristic. In this contribution, we identify a necessary condition of MUSIC for imaging of collection of small, perfectly conducting cracks. This is based on the fact that MUSIC imaging functional can be represented as an infinite series of Bessel function of integer order of the first kind. Numerical experiments from noisy synthetic data supports our investigation.

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.

Applications of Bayesian spectrum representation in acoustics

NASA Astrophysics Data System (ADS)

Botts, Jonathan M.

This dissertation utilizes a Bayesian inference framework to enhance the solution of inverse problems where the forward model maps to acoustic spectra. A Bayesian solution to filter design inverts a acoustic spectra to pole-zero locations of a discrete-time filter model. Spatial sound field analysis with a spherical microphone array is a data analysis problem that requires inversion of spatio-temporal spectra to directions of arrival. As with many inverse problems, a probabilistic analysis results in richer solutions than can be achieved with ad-hoc methods. In the filter design problem, the Bayesian inversion results in globally optimal coefficient estimates as well as an estimate the most concise filter capable of representing the given spectrum, within a single framework. This approach is demonstrated on synthetic spectra, head-related transfer function spectra, and measured acoustic reflection spectra. The Bayesian model-based analysis of spatial room impulse responses is presented as an analogous problem with equally rich solution. The model selection mechanism provides an estimate of the number of arrivals, which is necessary to properly infer the directions of simultaneous arrivals. Although, spectrum inversion problems are fairly ubiquitous, the scope of this dissertation has been limited to these two and derivative problems. The Bayesian approach to filter design is demonstrated on an artificial spectrum to illustrate the model comparison mechanism and then on measured head-related transfer functions to show the potential range of application. Coupled with sampling methods, the Bayesian approach is shown to outperform least-squares filter design methods commonly used in commercial software, confirming the need for a global search of the parameter space. The resulting designs are shown to be comparable to those that result from global optimization methods, but the Bayesian approach has the added advantage of a filter length estimate within the same unified framework. The application to reflection data is useful for representing frequency-dependent impedance boundaries in finite difference acoustic simulations. Furthermore, since the filter transfer function is a parametric model, it can be modified to incorporate arbitrary frequency weighting and account for the band-limited nature of measured reflection spectra. Finally, the model is modified to compensate for dispersive error in the finite difference simulation, from the filter design process. Stemming from the filter boundary problem, the implementation of pressure sources in finite difference simulation is addressed in order to assure that schemes properly converge. A class of parameterized source functions is proposed and shown to offer straightforward control of residual error in the simulation. Guided by the notion that the solution to be approximated affects the approximation error, sources are designed which reduce residual dispersive error to the size of round-off errors. The early part of a room impulse response can be characterized by a series of isolated plane waves. Measured with an array of microphones, plane waves map to a directional response of the array or spatial intensity map. Probabilistic inversion of this response results in estimates of the number and directions of image source arrivals. The model-based inversion is shown to avoid ambiguities associated with peak-finding or inspection of the spatial intensity map. For this problem, determining the number of arrivals in a given frame is critical for properly inferring the state of the sound field. This analysis is effectively compression of the spatial room response, which is useful for analysis or encoding of the spatial sound field. Parametric, model-based formulations of these problems enhance the solution in all cases, and a Bayesian interpretation provides a principled approach to model comparison and parameter estimation. v

Waveform inversion with source encoding for breast sound speed reconstruction in ultrasound computed tomography.

PubMed

Wang, Kun; Matthews, Thomas; Anis, Fatima; Li, Cuiping; Duric, Neb; Anastasio, Mark A

2015-03-01

Ultrasound computed tomography (USCT) holds great promise for improving the detection and management of breast cancer. Because they are based on the acoustic wave equation, waveform inversion-based reconstruction methods can produce images that possess improved spatial resolution properties over those produced by ray-based methods. However, waveform inversion methods are computationally demanding and have not been applied widely in USCT breast imaging. In this work, source encoding concepts are employed to develop an accelerated USCT reconstruction method that circumvents the large computational burden of conventional waveform inversion methods. This method, referred to as the waveform inversion with source encoding (WISE) method, encodes the measurement data using a random encoding vector and determines an estimate of the sound speed distribution by solving a stochastic optimization problem by use of a stochastic gradient descent algorithm. Both computer simulation and experimental phantom studies are conducted to demonstrate the use of the WISE method. The results suggest that the WISE method maintains the high spatial resolution of waveform inversion methods while significantly reducing the computational burden.

Appraisal of geodynamic inversion results: a data mining approach

NASA Astrophysics Data System (ADS)

Baumann, T. S.

2016-11-01

Bayesian sampling based inversions require many thousands or even millions of forward models, depending on how nonlinear or non-unique the inverse problem is, and how many unknowns are involved. The result of such a probabilistic inversion is not a single `best-fit' model, but rather a probability distribution that is represented by the entire model ensemble. Often, a geophysical inverse problem is non-unique, and the corresponding posterior distribution is multimodal, meaning that the distribution consists of clusters with similar models that represent the observations equally well. In these cases, we would like to visualize the characteristic model properties within each of these clusters of models. However, even for a moderate number of inversion parameters, a manual appraisal for a large number of models is not feasible. This poses the question whether it is possible to extract end-member models that represent each of the best-fit regions including their uncertainties. Here, I show how a machine learning tool can be used to characterize end-member models, including their uncertainties, from a complete model ensemble that represents a posterior probability distribution. The model ensemble used here results from a nonlinear geodynamic inverse problem, where rheological properties of the lithosphere are constrained from multiple geophysical observations. It is demonstrated that by taking vertical cross-sections through the effective viscosity structure of each of the models, the entire model ensemble can be classified into four end-member model categories that have a similar effective viscosity structure. These classification results are helpful to explore the non-uniqueness of the inverse problem and can be used to compute representative data fits for each of the end-member models. Conversely, these insights also reveal how new observational constraints could reduce the non-uniqueness. The method is not limited to geodynamic applications and a generalized MATLAB code is provided to perform the appraisal analysis.

Using an Equity/Performance Matrix to Address Salary Compression/Inversion and Performance Pay Issues

ERIC Educational Resources Information Center

Richardson, Peter; Thomas, Steven

2013-01-01

Pay compression and inversion are significant problems for many organizations and are often severe in schools of business in particular. At the same time, there is more insistence on showing accountability and paying employees based on performance. The authors explain and show a detailed example of how to use a Compensation Equity/ Performance…

The impact of approximations and arbitrary choices on geophysical images

NASA Astrophysics Data System (ADS)

Valentine, Andrew P.; Trampert, Jeannot

2016-01-01

Whenever a geophysical image is to be constructed, a variety of choices must be made. Some, such as those governing data selection and processing, or model parametrization, are somewhat arbitrary: there may be little reason to prefer one choice over another. Others, such as defining the theoretical framework within which the data are to be explained, may be more straightforward: typically, an `exact' theory exists, but various approximations may need to be adopted in order to make the imaging problem computationally tractable. Differences between any two images of the same system can be explained in terms of differences between these choices. Understanding the impact of each particular decision is essential if images are to be interpreted properly-but little progress has been made towards a quantitative treatment of this effect. In this paper, we consider a general linearized inverse problem, applicable to a wide range of imaging situations. We write down an expression for the difference between two images produced using similar inversion strategies, but where different choices have been made. This provides a framework within which inversion algorithms may be analysed, and allows us to consider how image effects may arise. In this paper, we take a general view, and do not specialize our discussion to any specific imaging problem or setup (beyond the restrictions implied by the use of linearized inversion techniques). In particular, we look at the concept of `hybrid inversion', in which highly accurate synthetic data (typically the result of an expensive numerical simulation) is combined with an inverse operator constructed based on theoretical approximations. It is generally supposed that this offers the benefits of using the more complete theory, without the full computational costs. We argue that the inverse operator is as important as the forward calculation in determining the accuracy of results. We illustrate this using a simple example, based on imaging the density structure of a vibrating string.

Multigrid-based reconstruction algorithm for quantitative photoacoustic tomography

PubMed Central

Li, Shengfu; Montcel, Bruno; Yuan, Zhen; Liu, Wanyu; Vray, Didier

2015-01-01

This paper proposes a multigrid inversion framework for quantitative photoacoustic tomography reconstruction. The forward model of optical fluence distribution and the inverse problem are solved at multiple resolutions. A fixed-point iteration scheme is formulated for each resolution and used as a cost function. The simulated and experimental results for quantitative photoacoustic tomography reconstruction show that the proposed multigrid inversion can dramatically reduce the required number of iterations for the optimization process without loss of reliability in the results. PMID:26203371

Inverse problems biomechanical imaging (Conference Presentation)

NASA Astrophysics Data System (ADS)

Oberai, Assad A.

2016-03-01

It is now well recognized that a host of imaging modalities (a list that includes Ultrasound, MRI, Optical Coherence Tomography, and optical microscopy) can be used to "watch" tissue as it deforms in response to an internal or external excitation. The result is a detailed map of the deformation field in the interior of the tissue. This deformation field can be used in conjunction with a material mechanical response to determine the spatial distribution of material properties of the tissue by solving an inverse problem. Images of material properties thus obtained can be used to quantify the health of the tissue. Recently, they have been used to detect, diagnose and monitor cancerous lesions, detect vulnerable plaque in arteries, diagnose liver cirrhosis, and possibly detect the onset of Alzheimer's disease. In this talk I will describe the mathematical and computational aspects of solving this class of inverse problems, and their applications in biology and medicine. In particular, I will discuss the well-posedness of these problems and quantify the amount of displacement data necessary to obtain a unique property distribution. I will describe an efficient algorithm for solving the resulting inverse problem. I will also describe some recent developments based on Bayesian inference in estimating the variance in the estimates of material properties. I will conclude with the applications of these techniques in diagnosing breast cancer and in characterizing the mechanical properties of cells with sub-cellular resolution.

Geostatistical regularization of inverse models for the retrieval of vegetation biophysical variables

NASA Astrophysics Data System (ADS)

Atzberger, C.; Richter, K.

2009-09-01

The robust and accurate retrieval of vegetation biophysical variables using radiative transfer models (RTM) is seriously hampered by the ill-posedness of the inverse problem. With this research we further develop our previously published (object-based) inversion approach [Atzberger (2004)]. The object-based RTM inversion takes advantage of the geostatistical fact that the biophysical characteristics of nearby pixel are generally more similar than those at a larger distance. A two-step inversion based on PROSPECT+SAIL generated look-up-tables is presented that can be easily implemented and adapted to other radiative transfer models. The approach takes into account the spectral signatures of neighboring pixel and optimizes a common value of the average leaf angle (ALA) for all pixel of a given image object, such as an agricultural field. Using a large set of leaf area index (LAI) measurements (n = 58) acquired over six different crops of the Barrax test site, Spain), we demonstrate that the proposed geostatistical regularization yields in most cases more accurate and spatially consistent results compared to the traditional (pixel-based) inversion. Pros and cons of the approach are discussed and possible future extensions presented.

Inverse procedure for simultaneous evaluation of viscosity and density of Newtonian liquids from dispersion curves of Love waves

NASA Astrophysics Data System (ADS)

Kiełczyński, P.; Szalewski, M.; Balcerzak, A.

2014-07-01

Simultaneous determination of the viscosity and density of liquids is of great importance in the monitoring of technological processes in the chemical, petroleum, and pharmaceutical industry, as well as in geophysics. In this paper, the authors present the application of Love waves for simultaneous inverse determination of the viscosity and density of liquids. The inversion procedure is based on measurements of the dispersion curves of phase velocity and attenuation of ultrasonic Love waves. The direct problem of the Love wave propagation in a layered waveguide covered by a viscous liquid was formulated and solved. Love waves propagate in an elastic layered waveguide covered on its surface with a viscous (Newtonian) liquid. The inverse problem is formulated as an optimization problem with appropriately constructed objective function that depends on the material properties of an elastic waveguide of the Love wave, material parameters of a liquid (i.e., viscosity and density), and the experimental data. The results of numerical calculations show that Love waves can be efficiently applied to determine simultaneously the physical properties of liquids (i.e., viscosity and density). Sensors based on this method can be very attractive for industrial applications to monitor on-line the parameters (density and viscosity) of process liquid during the course of technological processes, e.g., in polymer industry.

Escript: Open Source Environment For Solving Large-Scale Geophysical Joint Inversion Problems in Python

NASA Astrophysics Data System (ADS)

Gross, Lutz; Altinay, Cihan; Fenwick, Joel; Smith, Troy

2014-05-01

The program package escript has been designed for solving mathematical modeling problems using python, see Gross et al. (2013). Its development and maintenance has been funded by the Australian Commonwealth to provide open source software infrastructure for the Australian Earth Science community (recent funding by the Australian Geophysical Observing System EIF (AGOS) and the AuScope Collaborative Research Infrastructure Scheme (CRIS)). The key concepts of escript are based on the terminology of spatial functions and partial differential equations (PDEs) - an approach providing abstraction from the underlying spatial discretization method (i.e. the finite element method (FEM)). This feature presents a programming environment to the user which is easy to use even for complex models. Due to the fact that implementations are independent from data structures simulations are easily portable across desktop computers and scalable compute clusters without modifications to the program code. escript has been successfully applied in a variety of applications including modeling mantel convection, melting processes, volcanic flow, earthquakes, faulting, multi-phase flow, block caving and mineralization (see Poulet et al. 2013). The recent escript release (see Gross et al. (2013)) provides an open framework for solving joint inversion problems for geophysical data sets (potential field, seismic and electro-magnetic). The strategy bases on the idea to formulate the inversion problem as an optimization problem with PDE constraints where the cost function is defined by the data defect and the regularization term for the rock properties, see Gross & Kemp (2013). This approach of first-optimize-then-discretize avoids the assemblage of the - in general- dense sensitivity matrix as used in conventional approaches where discrete programming techniques are applied to the discretized problem (first-discretize-then-optimize). In this paper we will discuss the mathematical framework for inversion and appropriate solution schemes in escript. We will also give a brief introduction into escript's open framework for defining and solving geophysical inversion problems. Finally we will show some benchmark results to demonstrate the computational scalability of the inversion method across a large number of cores and compute nodes in a parallel computing environment. References: - L. Gross et al. (2013): Escript Solving Partial Differential Equations in Python Version 3.4, The University of Queensland, https://launchpad.net/escript-finley - L. Gross and C. Kemp (2013) Large Scale Joint Inversion of Geophysical Data using the Finite Element Method in escript. ASEG Extended Abstracts 2013, http://dx.doi.org/10.1071/ASEG2013ab306 - T. Poulet, L. Gross, D. Georgiev, J. Cleverley (2012): escript-RT: Reactive transport simulation in Python using escript, Computers & Geosciences, Volume 45, 168-176. http://dx.doi.org/10.1016/j.cageo.2011.11.005.

Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study

NASA Astrophysics Data System (ADS)

Grayver, Alexander V.

2015-07-01

This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated that the adaptive mesh refinement can be particularly efficient in resolving complex shapes. The implemented inversion scheme was able to resolve a hemisphere object with sufficient resolution starting from a coarse discretization and refining mesh adaptively in a fully automatic process. The code is able to harness the computational power of modern distributed platforms and is shown to work with models consisting of millions of degrees of freedom. Significant computational savings were achieved by using locally refined decoupled meshes.

Electromagnetic Inverse Methods and Applications for Inhomogeneous Media Probing and Synthesis.

NASA Astrophysics Data System (ADS)

Xia, Jake Jiqing

The electromagnetic inverse scattering problems concerned in this thesis are to find unknown inhomogeneous permittivity and conductivity profiles in a medium from the scattering data. Both analytical and numerical methods are studied in the thesis. The inverse methods can be applied to geophysical medium probing, non-destructive testing, medical imaging, optical waveguide synthesis and material characterization. An introduction is given in Chapter 1. The first part of the thesis presents inhomogeneous media probing. The Riccati equation approach is discussed in Chapter 2 for a one-dimensional planar profile inversion problem. Two types of the Riccati equations are derived and distinguished. New renormalized formulae based inverting one specific type of the Riccati equation are derived. Relations between the inverse methods of Green's function, the Riccati equation and the Gel'fand-Levitan-Marchenko (GLM) theory are studied. In Chapter 3, the renormalized source-type integral equation (STIE) approach is formulated for inversion of cylindrically inhomogeneous permittivity and conductivity profiles. The advantages of the renormalized STIE approach are demonstrated in numerical examples. The cylindrical profile inversion problem has an application for borehole inversion. In Chapter 4 the renormalized STIE approach is extended to a planar case where the two background media are different. Numerical results have shown fast convergence. This formulation is applied to inversion of the underground soil moisture profiles in remote sensing. The second part of the thesis presents the synthesis problem of inhomogeneous dielectric waveguides using the electromagnetic inverse methods. As a particular example, the rational function representation of reflection coefficients in the GLM theory is used. The GLM method is reviewed in Chapter 5. Relations between modal structures and transverse reflection coefficients of an inhomogeneous medium are established in Chapter 6. A stratified medium model is used to derive the guidance condition and the reflection coefficient. Results obtained in Chapter 6 provide the physical foundation for applying the inverse methods for the waveguide design problem. In Chapter 7, a global guidance condition for continuously varying medium is derived using the Riccati equation. It is further shown that the discrete modes in an inhomogeneous medium have the same wave vectors as the poles of the transverse reflection coefficient. An example of synthesizing an inhomogeneous dielectric waveguide using a rational reflection coefficient is presented. A summary of the thesis is given in Chapter 8. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

A Forward Glimpse into Inverse Problems through a Geology Example

ERIC Educational Resources Information Center

Winkel, Brian J.

2012-01-01

This paper describes a forward approach to an inverse problem related to detecting the nature of geological substrata which makes use of optimization techniques in a multivariable calculus setting. The true nature of the related inverse problem is highlighted. (Contains 2 figures.)

The Copenhagen problem with a quasi-homogeneous potential

NASA Astrophysics Data System (ADS)

Fakis, Demetrios; Kalvouridis, Tilemahos

2017-05-01

The Copenhagen problem is a well-known case of the famous restricted three-body problem. In this work instead of considering Newtonian potentials and forces we assume that the two primaries create a quasi-homogeneous potential, which means that we insert to the inverse square law of gravitation an inverse cube corrective term in order to approximate various phenomena as the radiation pressure of the primaries or the non-sphericity of them. Based on this new consideration we investigate the equilibrium locations of the small body and their parametric dependence, as well as the zero-velocity curves and surfaces for the planar motion, and the evolution of the regions where this motion is permitted when the Jacobian constant varies.

Optimization method for an evolutional type inverse heat conduction problem

NASA Astrophysics Data System (ADS)

Deng, Zui-Cha; Yu, Jian-Ning; Yang, Liu

2008-01-01

This paper deals with the determination of a pair (q, u) in the heat conduction equation u_t-u_{xx}+q(x,t)u=0, with initial and boundary conditions u(x,0)=u_0(x),\\qquad u_x|_{x=0}=u_x|_{x=1}=0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced.

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Calibrating the Spatiotemporal Root Density Distribution for Macroscopic Water Uptake Models Using Tikhonov Regularization

NASA Astrophysics Data System (ADS)

Li, N.; Yue, X. Y.

2018-03-01

Macroscopic root water uptake models proportional to a root density distribution function (RDDF) are most commonly used to model water uptake by plants. As the water uptake is difficult and labor intensive to measure, these models are often calibrated by inverse modeling. Most previous inversion studies assume RDDF to be constant with depth and time or dependent on only depth for simplification. However, under field conditions, this function varies with type of soil and root growth and thus changes with both depth and time. This study proposes an inverse method to calibrate both spatially and temporally varying RDDF in unsaturated water flow modeling. To overcome the difficulty imposed by the ill-posedness, the calibration is formulated as an optimization problem in the framework of the Tikhonov regularization theory, adding additional constraint to the objective function. Then the formulated nonlinear optimization problem is numerically solved with an efficient algorithm on the basis of the finite element method. The advantage of our method is that the inverse problem is translated into a Tikhonov regularization functional minimization problem and then solved based on the variational construction, which circumvents the computational complexity in calculating the sensitivity matrix involved in many derivative-based parameter estimation approaches (e.g., Levenberg-Marquardt optimization). Moreover, the proposed method features optimization of RDDF without any prior form, which is applicable to a more general root water uptake model. Numerical examples are performed to illustrate the applicability and effectiveness of the proposed method. Finally, discussions on the stability and extension of this method are presented.

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.

Ensemble-based data assimilation and optimal sensor placement for scalar source reconstruction

NASA Astrophysics Data System (ADS)

Mons, Vincent; Wang, Qi; Zaki, Tamer

2017-11-01

Reconstructing the characteristics of a scalar source from limited remote measurements in a turbulent flow is a problem of great interest for environmental monitoring, and is challenging due to several aspects. Firstly, the numerical estimation of the scalar dispersion in a turbulent flow requires significant computational resources. Secondly, in actual practice, only a limited number of observations are available, which generally makes the corresponding inverse problem ill-posed. Ensemble-based variational data assimilation techniques are adopted to solve the problem of scalar source localization in a turbulent channel flow at Reτ = 180 . This approach combines the components of variational data assimilation and ensemble Kalman filtering, and inherits the robustness from the former and the ease of implementation from the latter. An ensemble-based methodology for optimal sensor placement is also proposed in order to improve the condition of the inverse problem, which enhances the performances of the data assimilation scheme. This work has been partially funded by the Office of Naval Research (Grant N00014-16-1-2542) and by the National Science Foundation (Grant 1461870).

Dynamic Inversion based Control of a Docking Mechanism

NASA Technical Reports Server (NTRS)

Kulkarni, Nilesh V.; Ippolito, Corey; Krishnakumar, Kalmanje

2006-01-01

The problem of position and attitude control of the Stewart platform based docking mechanism is considered motivated by its future application in space missions requiring the autonomous docking capability. The control design is initiated based on the framework of the intelligent flight control architecture being developed at NASA Ames Research Center. In this paper, the baseline position and attitude control system is designed using dynamic inversion with proportional-integral augmentation. The inverse dynamics uses a Newton-Euler formulation that includes the platform dynamics, the dynamics of the individual legs along with viscous friction in the joints. Simulation results are presented using forward dynamics simulated by a commercial physics engine that builds the system as individual elements with appropriate joints and uses constrained numerical integration,

Three-dimensional imaging of buried objects in very lossy earth by inversion of VETEM data

USGS Publications Warehouse

Cui, T.J.; Aydiner, A.A.; Chew, W.C.; Wright, D.L.; Smith, D.V.

2003-01-01

The very early time electromagnetic system (VETEM) is an efficient tool for the detection of buried objects in very lossy earth, which allows a deeper penetration depth compared to the ground-penetrating radar. In this paper, the inversion of VETEM data is investigated using three-dimensional (3-D) inverse scattering techniques, where multiple frequencies are applied in the frequency range from 0-5 MHz. For small and moderately sized problems, the Born approximation and/or the Born iterative method have been used with the aid of the singular value decomposition and/or the conjugate gradient method in solving the linearized integral equations. For large-scale problems, a localized 3-D inversion method based on the Born approximation has been proposed for the inversion of VETEM data over a large measurement domain. Ways to process and to calibrate the experimental VETEM data are discussed to capture the real physics of buried objects. Reconstruction examples using synthesized VETEM data and real-world VETEM data are given to test the validity and efficiency of the proposed approach.

Bayesian approach to inverse statistical mechanics.

PubMed

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Bayesian approach to inverse statistical mechanics

NASA Astrophysics Data System (ADS)

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Identification procedure for epistemic uncertainties using inverse fuzzy arithmetic

NASA Astrophysics Data System (ADS)

Haag, T.; Herrmann, J.; Hanss, M.

2010-10-01

For the mathematical representation of systems with epistemic uncertainties, arising, for example, from simplifications in the modeling procedure, models with fuzzy-valued parameters prove to be a suitable and promising approach. In practice, however, the determination of these parameters turns out to be a non-trivial problem. The identification procedure to appropriately update these parameters on the basis of a reference output (measurement or output of an advanced model) requires the solution of an inverse problem. Against this background, an inverse method for the computation of the fuzzy-valued parameters of a model with epistemic uncertainties is presented. This method stands out due to the fact that it only uses feedforward simulations of the model, based on the transformation method of fuzzy arithmetic, along with the reference output. An inversion of the system equations is not necessary. The advancement of the method presented in this paper consists of the identification of multiple input parameters based on a single reference output or measurement. An optimization is used to solve the resulting underdetermined problems by minimizing the uncertainty of the identified parameters. Regions where the identification procedure is reliable are determined by the computation of a feasibility criterion which is also based on the output data of the transformation method only. For a frequency response function of a mechanical system, this criterion allows a restriction of the identification process to some special range of frequency where its solution can be guaranteed. Finally, the practicability of the method is demonstrated by covering the measured output of a fluid-filled piping system by the corresponding uncertain FE model in a conservative way.

Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

NASA Astrophysics Data System (ADS)

Duan, Lian; Farmer, Chris L.; Moroz, Irene M.

2010-09-01

Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection.

Joint inversion of geophysical data using petrophysical clustering and facies deformation wth the level set technique

NASA Astrophysics Data System (ADS)

Revil, A.

2015-12-01

Geological expertise and petrophysical relationships can be brought together to provide prior information while inverting multiple geophysical datasets. The merging of such information can result in more realistic solution in the distribution of the model parameters, reducing ipse facto the non-uniqueness of the inverse problem. We consider two level of heterogeneities: facies, described by facies boundaries and heteroegenities inside each facies determined by a correlogram. In this presentation, we pose the geophysical inverse problem in terms of Gaussian random fields with mean functions controlled by petrophysical relationships and covariance functions controlled by a prior geological cross-section, including the definition of spatial boundaries for the geological facies. The petrophysical relationship problem is formulated as a regression problem upon each facies. The inversion of the geophysical data is performed in a Bayesian framework. We demonstrate the usefulness of this strategy using a first synthetic case for which we perform a joint inversion of gravity and galvanometric resistivity data with the stations located at the ground surface. The joint inversion is used to recover the density and resistivity distributions of the subsurface. In a second step, we consider the possibility that the facies boundaries are deformable and their shapes are inverted as well. We use the level set approach to perform such deformation preserving prior topological properties of the facies throughout the inversion. With the help of prior facies petrophysical relationships and topological characteristic of each facies, we make posterior inference about multiple geophysical tomograms based on their corresponding geophysical data misfits. The method is applied to a second synthetic case showing that we can recover the heterogeneities inside the facies, the mean values for the petrophysical properties, and, to some extent, the facies boundaries using the 2D joint inversion of gravity and galvanometric resistivity data. For this 2D synthetic example, we note that the position of the facies are well-recovered except far from the ground surfce where the sensitivity is too low. The figure shows the evolution of the shape of the facies during the inversion itertion by iteration.

Inverse scattering theory: Inverse scattering series method for one dimensional non-compact support potential

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

Yao, Jie, E-mail: yjie2@uh.edu; Lesage, Anne-Cécile; Hussain, Fazle

2014-12-15

The reversion of the Born-Neumann series of the Lippmann-Schwinger equation is one of the standard ways to solve the inverse acoustic scattering problem. One limitation of the current inversion methods based on the reversion of the Born-Neumann series is that the velocity potential should have compact support. However, this assumption cannot be satisfied in certain cases, especially in seismic inversion. Based on the idea of distorted wave scattering, we explore an inverse scattering method for velocity potentials without compact support. The strategy is to decompose the actual medium as a known single interface reference medium, which has the same asymptoticmore » form as the actual medium and a perturbative scattering potential with compact support. After introducing the method to calculate the Green’s function for the known reference potential, the inverse scattering series and Volterra inverse scattering series are derived for the perturbative potential. Analytical and numerical examples demonstrate the feasibility and effectiveness of this method. Besides, to ensure stability of the numerical computation, the Lanczos averaging method is employed as a filter to reduce the Gibbs oscillations for the truncated discrete inverse Fourier transform of each order. Our method provides a rigorous mathematical framework for inverse acoustic scattering with a non-compact support velocity potential.« less

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor E.

2013-01-01

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

An inverse problem in thermal imaging

NASA Technical Reports Server (NTRS)

Bryan, Kurt; Caudill, Lester F., Jr.

1994-01-01

This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring the induced temperature on the boundary of the sample. The problem is studied both in the case in which one has data at every point on the boundary of the region and the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.

Inverse problems in quantum chemistry

NASA Astrophysics Data System (ADS)

Karwowski, Jacek

Inverse problems constitute a branch of applied mathematics with well-developed methodology and formalism. A broad family of tasks met in theoretical physics, in civil and mechanical engineering, as well as in various branches of medical and biological sciences has been formulated as specific implementations of the general theory of inverse problems. In this article, it is pointed out that a number of approaches met in quantum chemistry can (and should) be classified as inverse problems. Consequently, the methodology used in these approaches may be enriched by applying ideas and theorems developed within the general field of inverse problems. Several examples, including the RKR method for the construction of potential energy curves, determining parameter values in semiempirical methods, and finding external potentials for which the pertinent Schrödinger equation is exactly solvable, are discussed in detail.

Forward and inverse models of electromagnetic scattering from layered media with rough interfaces

NASA Astrophysics Data System (ADS)

Tabatabaeenejad, Seyed Alireza

This work addresses the problem of electromagnetic scattering from layered dielectric structures with rough boundaries and the associated inverse problem of retrieving the subsurface parameters of the structure using the scattered field. To this end, a forward scattering model based on the Small Perturbation Method (SPM) is developed to calculate the first-order spectral-domain bistatic scattering coefficients of a two-layer rough surface structure. SPM requires the boundaries to be slightly rough compared to the wavelength, but to understand the range of applicability of this method in scattering from two-layer rough surfaces, its region of validity is investigated by comparing its output with that of a first principle solver that does not impose roughness restrictions. The Method of Moments (MoM) is used for this purpose. Finally, for retrieval of the model parameters of the layered structure using scattered field, an inversion scheme based on the Simulated Annealing method is investigated and a strategy is proposed to address convergence to local minimum.

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

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, Longxiao; Gu, Hanming

2018-03-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.

Young children's use of derived fact strategies for addition and subtraction

PubMed Central

Dowker, Ann

2014-01-01

Forty-four children between 6;0 and 7;11 took part in a study of derived fact strategy use. They were assigned to addition and subtraction levels on the basis of calculation pretests. They were then given Dowker's (1998) test of derived fact strategies in addition, involving strategies based on the Identity, Commutativity, Addend +1, Addend −1, and addition/subtraction Inverse principles; and test of derived fact strategies in subtraction, involving strategies based on the Identity, Minuend +1, Minuend −1, Subtrahend +1, Subtrahend −1, Complement and addition/subtraction Inverse principles. The exact arithmetic problems given varied according to the child's previously assessed calculation level and were selected to be just a little too difficult for the child to solve unaided. Children were given the answer to a problem and then asked to solve another problem that could be solved quickly by using this answer, together with the principle being assessed. The children also took the WISC Arithmetic subtest. Strategies differed greatly in difficulty, with Identity being the easiest, and the Inverse and Complement principles being most difficult. The Subtrahend +1 and Subtrahend −1 problems often elicited incorrect strategies based on an overextension of the principles of addition to subtraction. It was concluded that children may have difficulty with understanding and applying the relationships between addition and subtraction. Derived fact strategy use was significantly related to both calculation level and to WISC Arithmetic scaled score. PMID:24431996

Analysis of space telescope data collection system

NASA Technical Reports Server (NTRS)

Ingels, F. M.; Schoggen, W. O.

1982-01-01

An analysis of the expected performance for the Multiple Access (MA) system is provided. The analysis covers the expected bit error rate performance, the effects of synchronization loss, the problem of self-interference, and the problem of phase ambiguity. The problem of false acceptance of a command word due to data inversion is discussed. A mathematical determination of the probability of accepting an erroneous command word due to a data inversion is presented. The problem is examined for three cases: (1) a data inversion only, (2) a data inversion and a random error within the same command word, and a block (up to 256 48-bit words) containing both a data inversion and a random error.

Data fitting and image fine-tuning approach to solve the inverse problem in fluorescence molecular imaging

NASA Astrophysics Data System (ADS)

Gorpas, Dimitris; Politopoulos, Kostas; Yova, Dido; Andersson-Engels, Stefan

2008-02-01

One of the most challenging problems in medical imaging is to "see" a tumour embedded into tissue, which is a turbid medium, by using fluorescent probes for tumour labeling. This problem, despite the efforts made during the last years, has not been fully encountered yet, due to the non-linear nature of the inverse problem and the convergence failures of many optimization techniques. This paper describes a robust solution of the inverse problem, based on data fitting and image fine-tuning techniques. As a forward solver the coupled radiative transfer equation and diffusion approximation model is proposed and compromised via a finite element method, enhanced with adaptive multi-grids for faster and more accurate convergence. A database is constructed by application of the forward model on virtual tumours with known geometry, and thus fluorophore distribution, embedded into simulated tissues. The fitting procedure produces the best matching between the real and virtual data, and thus provides the initial estimation of the fluorophore distribution. Using this information, the coupled radiative transfer equation and diffusion approximation model has the required initial values for a computational reasonable and successful convergence during the image fine-tuning application.

Clinical knowledge-based inverse treatment planning

NASA Astrophysics Data System (ADS)

Yang, Yong; Xing, Lei

2004-11-01

Clinical IMRT treatment plans are currently made using dose-based optimization algorithms, which do not consider the nonlinear dose-volume effects for tumours and normal structures. The choice of structure specific importance factors represents an additional degree of freedom of the system and makes rigorous optimization intractable. The purpose of this work is to circumvent the two problems by developing a biologically more sensible yet clinically practical inverse planning framework. To implement this, the dose-volume status of a structure was characterized by using the effective volume in the voxel domain. A new objective function was constructed with the incorporation of the volumetric information of the system so that the figure of merit of a given IMRT plan depends not only on the dose deviation from the desired distribution but also the dose-volume status of the involved organs. The conventional importance factor of an organ was written into a product of two components: (i) a generic importance that parametrizes the relative importance of the organs in the ideal situation when the goals for all the organs are met; (ii) a dose-dependent factor that quantifies our level of clinical/dosimetric satisfaction for a given plan. The generic importance can be determined a priori, and in most circumstances, does not need adjustment, whereas the second one, which is responsible for the intractable behaviour of the trade-off seen in conventional inverse planning, was determined automatically. An inverse planning module based on the proposed formalism was implemented and applied to a prostate case and a head-neck case. A comparison with the conventional inverse planning technique indicated that, for the same target dose coverage, the critical structure sparing was substantially improved for both cases. The incorporation of clinical knowledge allows us to obtain better IMRT plans and makes it possible to auto-select the importance factors, greatly facilitating the inverse planning process. The new formalism proposed also reveals the relationship between different inverse planning schemes and gives important insight into the problem of therapeutic plan optimization. In particular, we show that the EUD-based optimization is a special case of the general inverse planning formalism described in this paper.

A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2015-04-29

Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) andmore » fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO 2 (ffCO 2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

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

Ray, J.; Lee, J.; Yadav, V.

Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) andmore » fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO 2 (ffCO 2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

Subspace-based optimization method for inverse scattering problems with an inhomogeneous background medium

NASA Astrophysics Data System (ADS)

Chen, Xudong

2010-07-01

This paper proposes a version of the subspace-based optimization method to solve the inverse scattering problem with an inhomogeneous background medium where the known inhomogeneities are bounded in a finite domain. Although the background Green's function at each discrete point in the computational domain is not directly available in an inhomogeneous background scenario, the paper uses the finite element method to simultaneously obtain the Green's function at all discrete points. The essence of the subspace-based optimization method is that part of the contrast source is determined from the spectrum analysis without using any optimization, whereas the orthogonally complementary part is determined by solving a lower dimension optimization problem. This feature significantly speeds up the convergence of the algorithm and at the same time makes it robust against noise. Numerical simulations illustrate the efficacy of the proposed algorithm. The algorithm presented in this paper finds wide applications in nondestructive evaluation, such as through-wall imaging.

Kinematic source inversions of teleseismic data based on the QUESO library for uncertainty quantification and prediction

NASA Astrophysics Data System (ADS)

Zielke, O.; McDougall, D.; Mai, P. M.; Babuska, I.

2014-12-01

One fundamental aspect of seismic hazard mitigation is gaining a better understanding of the rupture process. Because direct observation of the relevant parameters and properties is not possible, other means such as kinematic source inversions are used instead. By constraining the spatial and temporal evolution of fault slip during an earthquake, those inversion approaches may enable valuable insights in the physics of the rupture process. However, due to the underdetermined nature of this inversion problem (i.e., inverting a kinematic source model for an extended fault based on seismic data), the provided solutions are generally non-unique. Here we present a statistical (Bayesian) inversion approach based on an open-source library for uncertainty quantification (UQ) called QUESO that was developed at ICES (UT Austin). The approach has advantages with respect to deterministic inversion approaches as it provides not only a single (non-unique) solution but also provides uncertainty bounds with it. Those uncertainty bounds help to qualitatively and quantitatively judge how well constrained an inversion solution is and how much rupture complexity the data reliably resolve. The presented inversion scheme uses only tele-seismically recorded body waves but future developments may lead us towards joint inversion schemes. After giving an insight in the inversion scheme ifself (based on delayed rejection adaptive metropolis, DRAM) we explore the method's resolution potential. For that, we synthetically generate tele-seismic data, add for example different levels of noise and/or change fault plane parameterization and then apply our inversion scheme in the attempt to extract the (known) kinematic rupture model. We conclude with exemplary inverting real tele-seismic data of a recent large earthquake and compare those results with deterministically derived kinematic source models provided by other research groups.

PREFACE: The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches

NASA Astrophysics Data System (ADS)

Cheng, Jin; Hon, Yiu-Chung; Seo, Jin Keun; Yamamoto, Masahiro

2005-01-01

The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches was held at Fudan University, Shanghai from 16-21 June 2004. The first conference in this series was held at the City University of Hong Kong in January 2002 and it was agreed to hold the conference once every two years in a Pan-Pacific Asian country. The next conference is scheduled to be held at Hokkaido University, Sapporo, Japan in July 2006. The purpose of this series of biennial conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries. In recent decades, interest in inverse problems has been flourishing all over the globe because of both the theoretical interest and practical requirements. In particular, in Asian countries, one is witnessing remarkable new trends of research in inverse problems as well as the participation of many young talents. Considering these trends, the second conference was organized with the chairperson Professor Li Tat-tsien (Fudan University), in order to provide forums for developing research cooperation and to promote activities in the field of inverse problems. Because solutions to inverse problems are needed in various applied fields, we entertained a total of 92 participants at the second conference and arranged various talks which ranged from mathematical analyses to solutions of concrete inverse problems in the real world. This volume contains 18 selected papers, all of which have undergone peer review. The 18 papers are classified as follows: Surveys: four papers give reviews of specific inverse problems. Theoretical aspects: six papers investigate the uniqueness, stability, and reconstruction schemes. Numerical methods: four papers devise new numerical methods and their applications to inverse problems. Solutions to applied inverse problems: four papers discuss concrete inverse problems such as scattering problems and inverse problems in atmospheric sciences and oceanography. Last but not least is our gratitude. As editors we would like to express our sincere thanks to all the plenary and invited speakers, the members of the International Scientific Committee and the Advisory Board for the success of the conference, which has given rise to this present volume of selected papers. We would also like to thank Mr Wang Yanbo, Miss Wan Xiqiong and the graduate students at Fudan University for their effective work to make this conference a success. The conference was financially supported by the NFS of China, the Mathematical Center of Ministry of Education of China, E-Institutes of Shanghai Municipal Education Commission (No E03004) and Fudan University, Grant 15340027 from the Japan Society for the Promotion of Science, and Grant 15654015 from the Ministry of Education, Cultures, Sports and Technology.

Joint inversion of hydraulic head and self-potential data associated with harmonic pumping tests

NASA Astrophysics Data System (ADS)

Soueid Ahmed, A.; Jardani, A.; Revil, A.; Dupont, J. P.

2016-09-01

Harmonic pumping tests consist in stimulating an aquifer by the means of hydraulic stimulations at some discrete frequencies. The inverse problem consisting in retrieving the hydraulic properties is inherently ill posed and is usually underdetermined when considering the number of well head data available in field conditions. To better constrain this inverse problem, we add self-potential data recorded at the ground surface to the head data. The self-potential method is a passive geophysical method. Its signals are generated by the groundwater flow through an electrokinetic coupling. We showed using a 3-D saturated unconfined synthetic aquifer that the self-potential method significantly improves the results of the harmonic hydraulic tomography. The hydroelectric forward problem is obtained by solving first the Richards equation, describing the groundwater flow, and then using the result in an electrical Poisson equation describing the self-potential problem. The joint inversion problem is solved using a reduction model based on the principal component geostatistical approach. In this method, the large prior covariance matrix is truncated and replaced by its low-rank approximation, allowing thus for notable computational time and storage savings. Three test cases are studied, to assess the validity of our approach. In the first test, we show that when the number of harmonic stimulations is low, combining the harmonic hydraulic and self-potential data does not improve the inversion results. In the second test where enough harmonic stimulations are performed, a significant improvement of the hydraulic parameters is observed. In the last synthetic test, we show that the electrical conductivity field required to invert the self-potential data can be determined with enough accuracy using an electrical resistivity tomography survey using the same electrodes configuration as used for the self-potential investigation.

Inverse problems in 1D hemodynamics on systemic networks: a sequential approach.

PubMed

Lombardi, D

2014-02-01

In this work, a sequential approach based on the unscented Kalman filter is applied to solve inverse problems in 1D hemodynamics, on a systemic network. For instance, the arterial stiffness is estimated by exploiting cross-sectional area and mean speed observations in several locations of the arteries. The results are compared with those ones obtained by estimating the pulse wave velocity and the Moens-Korteweg formula. In the last section, a perspective concerning the identification of the terminal models parameters and peripheral circulation (modeled by a Windkessel circuit) is presented. Copyright © 2013 John Wiley & Sons, Ltd.

SaaS Platform for Time Series Data Handling

NASA Astrophysics Data System (ADS)

Oplachko, Ekaterina; Rykunov, Stanislav; Ustinin, Mikhail

2018-02-01

The paper is devoted to the description of MathBrain, a cloud-based resource, which works as a "Software as a Service" model. It is designed to maximize the efficiency of the current technology and to provide a tool for time series data handling. The resource provides access to the following analysis methods: direct and inverse Fourier transforms, Principal component analysis and Independent component analysis decompositions, quantitative analysis, magnetoencephalography inverse problem solution in a single dipole model based on multichannel spectral data.

A novel resource sharing algorithm based on distributed construction for radiant enclosure problems

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

Finzell, Peter; Bryden, Kenneth M.

This study demonstrates a novel approach to solving inverse radiant enclosure problems based on distributed construction. Specifically, the problem of determining the temperature distribution needed on the heater surfaces to achieve a desired design surface temperature profile is recast as a distributed construction problem in which a shared resource, temperature, is distributed by computational agents moving blocks. The sharing of blocks between agents enables them to achieve their desired local state, which in turn achieves the desired global state. Each agent uses the current state of their local environment and a simple set of rules to determine when to exchangemore » blocks, each block representing a discrete unit of temperature change. This algorithm is demonstrated using the established two-dimensional inverse radiation enclosure problem. The temperature profile on the heater surfaces is adjusted to achieve a desired temperature profile on the design surfaces. The resource sharing algorithm was able to determine the needed temperatures on the heater surfaces to obtain the desired temperature distribution on the design surfaces in the nine cases examined.« less

A novel resource sharing algorithm based on distributed construction for radiant enclosure problems

DOE PAGES

Finzell, Peter; Bryden, Kenneth M.

2017-03-06

This study demonstrates a novel approach to solving inverse radiant enclosure problems based on distributed construction. Specifically, the problem of determining the temperature distribution needed on the heater surfaces to achieve a desired design surface temperature profile is recast as a distributed construction problem in which a shared resource, temperature, is distributed by computational agents moving blocks. The sharing of blocks between agents enables them to achieve their desired local state, which in turn achieves the desired global state. Each agent uses the current state of their local environment and a simple set of rules to determine when to exchangemore » blocks, each block representing a discrete unit of temperature change. This algorithm is demonstrated using the established two-dimensional inverse radiation enclosure problem. The temperature profile on the heater surfaces is adjusted to achieve a desired temperature profile on the design surfaces. The resource sharing algorithm was able to determine the needed temperatures on the heater surfaces to obtain the desired temperature distribution on the design surfaces in the nine cases examined.« less

Neural network explanation using inversion.

PubMed

Saad, Emad W; Wunsch, Donald C

2007-01-01

An important drawback of many artificial neural networks (ANN) is their lack of explanation capability [Andrews, R., Diederich, J., & Tickle, A. B. (1996). A survey and critique of techniques for extracting rules from trained artificial neural networks. Knowledge-Based Systems, 8, 373-389]. This paper starts with a survey of algorithms which attempt to explain the ANN output. We then present HYPINV, a new explanation algorithm which relies on network inversion; i.e. calculating the ANN input which produces a desired output. HYPINV is a pedagogical algorithm, that extracts rules, in the form of hyperplanes. It is able to generate rules with arbitrarily desired fidelity, maintaining a fidelity-complexity tradeoff. To our knowledge, HYPINV is the only pedagogical rule extraction method, which extracts hyperplane rules from continuous or binary attribute neural networks. Different network inversion techniques, involving gradient descent as well as an evolutionary algorithm, are presented. An information theoretic treatment of rule extraction is presented. HYPINV is applied to example synthetic problems, to a real aerospace problem, and compared with similar algorithms using benchmark problems.

The Prediction Properties of Inverse and Reverse Regression for the Simple Linear Calibration Problem

NASA Technical Reports Server (NTRS)

Parker, Peter A.; Geoffrey, Vining G.; Wilson, Sara R.; Szarka, John L., III; Johnson, Nels G.

2010-01-01

The calibration of measurement systems is a fundamental but under-studied problem within industrial statistics. The origins of this problem go back to basic chemical analysis based on NIST standards. In today's world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST. This paper considers the classic "forward regression followed by inverse regression" approach. In this approach the initial experiment treats the "standards" as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to "reverse regression," which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it avoids the need for the inverse regression. However, it also violates some of the basic regression assumptions.

Numerical reconstruction of tsunami source using combined seismic, satellite and DART data

NASA Astrophysics Data System (ADS)

Krivorotko, Olga; Kabanikhin, Sergey; Marinin, Igor

2014-05-01

Recent tsunamis, for instance, in Japan (2011), in Sumatra (2004), and at the Indian coast (2004) showed that a system of producing exact and timely information about tsunamis is of a vital importance. Numerical simulation is an effective instrument for providing such information. Bottom relief characteristics and the initial perturbation data (a tsunami source) are required for the direct simulation of tsunamis. The seismic data about the source are usually obtained in a few tens of minutes after an event has occurred (the seismic waves velocity being about five hundred kilometres per minute, while the velocity of tsunami waves is less than twelve kilometres per minute). A difference in the arrival times of seismic and tsunami waves can be used when operationally refining the tsunami source parameters and modelling expected tsunami wave height on the shore. The most suitable physical models related to the tsunamis simulation are based on the shallow water equations. The problem of identification parameters of a tsunami source using additional measurements of a passing wave is called inverse tsunami problem. We investigate three different inverse problems of determining a tsunami source using three different additional data: Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements, satellite wave-form images and seismic data. These problems are severely ill-posed. We apply regularization techniques to control the degree of ill-posedness such as Fourier expansion, truncated singular value decomposition, numerical regularization. The algorithm of selecting the truncated number of singular values of an inverse problem operator which is agreed with the error level in measured data is described and analyzed. In numerical experiment we used gradient methods (Landweber iteration and conjugate gradient method) for solving inverse tsunami problems. Gradient methods are based on minimizing the corresponding misfit function. To calculate the gradient of the misfit function, the adjoint problem is solved. The conservative finite-difference schemes for solving the direct and adjoint problems in the approximation of shallow water are constructed. Results of numerical experiments of the tsunami source reconstruction are presented and discussed. We show that using a combination of three different types of data allows one to increase the stability and efficiency of tsunami source reconstruction. Non-profit organization WAPMERR (World Agency of Planetary Monitoring and Earthquake Risk Reduction) in collaboration with Informap software development department developed the Integrated Tsunami Research and Information System (ITRIS) to simulate tsunami waves and earthquakes, river course changes, coastal zone floods, and risk estimates for coastal constructions at wave run-ups and earthquakes. The special scientific plug-in components are embedded in a specially developed GIS-type graphic shell for easy data retrieval, visualization and processing. This work was supported by the Russian Foundation for Basic Research (project No. 12-01-00773 'Theory and Numerical Methods for Solving Combined Inverse Problems of Mathematical Physics') and interdisciplinary project of SB RAS 14 'Inverse Problems and Applications: Theory, Algorithms, Software'.

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

Recovering Long-wavelength Velocity Models using Spectrogram Inversion with Single- and Multi-frequency Components

NASA Astrophysics Data System (ADS)

Ha, J.; Chung, W.; Shin, S.

2015-12-01

Many waveform inversion algorithms have been proposed in order to construct subsurface velocity structures from seismic data sets. These algorithms have suffered from computational burden, local minima problems, and the lack of low-frequency components. Computational efficiency can be improved by the application of back-propagation techniques and advances in computing hardware. In addition, waveform inversion algorithms, for obtaining long-wavelength velocity models, could avoid both the local minima problem and the effect of the lack of low-frequency components in seismic data. In this study, we proposed spectrogram inversion as a technique for recovering long-wavelength velocity models. In spectrogram inversion, decomposed frequency components from spectrograms of traces, in the observed and calculated data, are utilized to generate traces with reproduced low-frequency components. Moreover, since each decomposed component can reveal the different characteristics of a subsurface structure, several frequency components were utilized to analyze the velocity features in the subsurface. We performed the spectrogram inversion using a modified SEG/SEGE salt A-A' line. Numerical results demonstrate that spectrogram inversion could also recover the long-wavelength velocity features. However, inversion results varied according to the frequency components utilized. Based on the results of inversion using a decomposed single-frequency component, we noticed that robust inversion results are obtained when a dominant frequency component of the spectrogram was utilized. In addition, detailed information on recovered long-wavelength velocity models was obtained using a multi-frequency component combined with single-frequency components. Numerical examples indicate that various detailed analyses of long-wavelength velocity models can be carried out utilizing several frequency components.

Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

NASA Technical Reports Server (NTRS)

Chu, W. P.

1985-01-01

The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

Cross-borehole flowmeter tests for transient heads in heterogeneous aquifers.

PubMed

Le Borgne, Tanguy; Paillet, Frederick; Bour, Olivier; Caudal, Jean-Pierre

2006-01-01

Cross-borehole flowmeter tests have been proposed as an efficient method to investigate preferential flowpaths in heterogeneous aquifers, which is a major task in the characterization of fractured aquifers. Cross-borehole flowmeter tests are based on the idea that changing the pumping conditions in a given aquifer will modify the hydraulic head distribution in large-scale flowpaths, producing measurable changes in the vertical flow profiles in observation boreholes. However, inversion of flow measurements to derive flowpath geometry and connectivity and to characterize their hydraulic properties is still a subject of research. In this study, we propose a framework for cross-borehole flowmeter test interpretation that is based on a two-scale conceptual model: discrete fractures at the borehole scale and zones of interconnected fractures at the aquifer scale. We propose that the two problems may be solved independently. The first inverse problem consists of estimating the hydraulic head variations that drive the transient borehole flow observed in the cross-borehole flowmeter experiments. The second inverse problem is related to estimating the geometry and hydraulic properties of large-scale flowpaths in the region between pumping and observation wells that are compatible with the head variations deduced from the first problem. To solve the borehole-scale problem, we treat the transient flow data as a series of quasi-steady flow conditions and solve for the hydraulic head changes in individual fractures required to produce these data. The consistency of the method is verified using field experiments performed in a fractured-rock aquifer.

Inverse optimal design of input-to-state stabilisation for affine nonlinear systems with input delays

NASA Astrophysics Data System (ADS)

Cai, Xiushan; Meng, Lingxin; Zhang, Wei; Liu, Leipo

2018-03-01

We establish robustness of the predictor feedback control law to perturbations appearing at the system input for affine nonlinear systems with time-varying input delay and additive disturbances. Furthermore, it is shown that it is inverse optimal with respect to a differential game problem. All of the stability and inverse optimality proofs are based on the infinite-dimensional backstepping transformation and an appropriate Lyapunov functional. A single-link manipulator subject to input delays and disturbances is given to illustrate the validity of the proposed method.

Breast ultrasound computed tomography using waveform inversion with source encoding

NASA Astrophysics Data System (ADS)

Wang, Kun; Matthews, Thomas; Anis, Fatima; Li, Cuiping; Duric, Neb; Anastasio, Mark A.

2015-03-01

Ultrasound computed tomography (USCT) holds great promise for improving the detection and management of breast cancer. Because they are based on the acoustic wave equation, waveform inversion-based reconstruction methods can produce images that possess improved spatial resolution properties over those produced by ray-based methods. However, waveform inversion methods are computationally demanding and have not been applied widely in USCT breast imaging. In this work, source encoding concepts are employed to develop an accelerated USCT reconstruction method that circumvents the large computational burden of conventional waveform inversion methods. This method, referred to as the waveform inversion with source encoding (WISE) method, encodes the measurement data using a random encoding vector and determines an estimate of the speed-of-sound distribution by solving a stochastic optimization problem by use of a stochastic gradient descent algorithm. Computer-simulation studies are conducted to demonstrate the use of the WISE method. Using a single graphics processing unit card, each iteration can be completed within 25 seconds for a 128 × 128 mm2 reconstruction region. The results suggest that the WISE method maintains the high spatial resolution of waveform inversion methods while significantly reducing the computational burden.

Computational inverse methods of heat source in fatigue damage problems

NASA Astrophysics Data System (ADS)

Chen, Aizhou; Li, Yuan; Yan, Bo

2018-04-01

Fatigue dissipation energy is the research focus in field of fatigue damage at present. It is a new idea to solve the problem of calculating fatigue dissipation energy by introducing inverse method of heat source into parameter identification of fatigue dissipation energy model. This paper introduces the research advances on computational inverse method of heat source and regularization technique to solve inverse problem, as well as the existing heat source solution method in fatigue process, prospects inverse method of heat source applying in fatigue damage field, lays the foundation for further improving the effectiveness of fatigue dissipation energy rapid prediction.

Modeling the 16 September 2015 Chile tsunami source with the inversion of deep-ocean tsunami records by means of the r - solution method

NASA Astrophysics Data System (ADS)

Voronina, Tatyana; Romanenko, Alexey; Loskutov, Artem

2017-04-01

The key point in the state-of-the-art in the tsunami forecasting is constructing a reliable tsunami source. In this study, we present an application of the original numerical inversion technique to modeling the tsunami sources of the 16 September 2015 Chile tsunami. The problem of recovering a tsunami source from remote measurements of the incoming wave in the deep-water tsunameters is considered as an inverse problem of mathematical physics in the class of ill-posed problems. This approach is based on the least squares and the truncated singular value decomposition techniques. The tsunami wave propagation is considered within the scope of the linear shallow-water theory. As in inverse seismic problem, the numerical solutions obtained by mathematical methods become unstable due to the presence of noise in real data. A method of r-solutions makes it possible to avoid instability in the solution to the ill-posed problem under study. This method seems to be attractive from the computational point of view since the main efforts are required only once for calculating the matrix whose columns consist of computed waveforms for each harmonic as a source (an unknown tsunami source is represented as a part of a spatial harmonics series in the source area). Furthermore, analyzing the singular spectra of the matrix obtained in the course of numerical calculations one can estimate the future inversion by a certain observational system that will allow offering a more effective disposition for the tsunameters with the help of precomputations. In other words, the results obtained allow finding a way to improve the inversion by selecting the most informative set of available recording stations. The case study of the 6 February 2013 Solomon Islands tsunami highlights a critical role of arranging deep-water tsunameters for obtaining the inversion results. Implementation of the proposed methodology to the 16 September 2015 Chile tsunami has successfully produced tsunami source model. The function recovered by the method proposed can find practical applications both as an initial condition for various optimization approaches and for computer calculation of the tsunami wave propagation.

A flexible, extendable, modular and computationally efficient approach to scattering-integral-based seismic full waveform inversion

NASA Astrophysics Data System (ADS)

Schumacher, F.; Friederich, W.; Lamara, S.

2016-02-01

We present a new conceptual approach to scattering-integral-based seismic full waveform inversion (FWI) that allows a flexible, extendable, modular and both computationally and storage-efficient numerical implementation. To achieve maximum modularity and extendability, interactions between the three fundamental steps carried out sequentially in each iteration of the inversion procedure, namely, solving the forward problem, computing waveform sensitivity kernels and deriving a model update, are kept at an absolute minimum and are implemented by dedicated interfaces. To realize storage efficiency and maximum flexibility, the spatial discretization of the inverted earth model is allowed to be completely independent of the spatial discretization employed by the forward solver. For computational efficiency reasons, the inversion is done in the frequency domain. The benefits of our approach are as follows: (1) Each of the three stages of an iteration is realized by a stand-alone software program. In this way, we avoid the monolithic, unflexible and hard-to-modify codes that have often been written for solving inverse problems. (2) The solution of the forward problem, required for kernel computation, can be obtained by any wave propagation modelling code giving users maximum flexibility in choosing the forward modelling method. Both time-domain and frequency-domain approaches can be used. (3) Forward solvers typically demand spatial discretizations that are significantly denser than actually desired for the inverted model. Exploiting this fact by pre-integrating the kernels allows a dramatic reduction of disk space and makes kernel storage feasible. No assumptions are made on the spatial discretization scheme employed by the forward solver. (4) In addition, working in the frequency domain effectively reduces the amount of data, the number of kernels to be computed and the number of equations to be solved. (5) Updating the model by solving a large equation system can be done using different mathematical approaches. Since kernels are stored on disk, it can be repeated many times for different regularization parameters without need to solve the forward problem, making the approach accessible to Occam's method. Changes of choice of misfit functional, weighting of data and selection of data subsets are still possible at this stage. We have coded our approach to FWI into a program package called ASKI (Analysis of Sensitivity and Kernel Inversion) which can be applied to inverse problems at various spatial scales in both Cartesian and spherical geometries. It is written in modern FORTRAN language using object-oriented concepts that reflect the modular structure of the inversion procedure. We validate our FWI method by a small-scale synthetic study and present first results of its application to high-quality seismological data acquired in the southern Aegean.

3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

NASA Astrophysics Data System (ADS)

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling

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

Li, Weixuan, E-mail: weixuan.li@usc.edu; Lin, Guang, E-mail: guang.lin@pnnl.gov; Zhang, Dongxiao, E-mail: dxz@pku.edu.cn

2014-02-01

The probabilistic collocation-based Kalman filter (PCKF) is a recently developed approach for solving inverse problems. It resembles the ensemble Kalman filter (EnKF) in every aspect—except that it represents and propagates model uncertainty by polynomial chaos expansion (PCE) instead of an ensemble of model realizations. Previous studies have shown PCKF is a more efficient alternative to EnKF for many data assimilation problems. However, the accuracy and efficiency of PCKF depends on an appropriate truncation of the PCE series. Having more polynomial chaos basis functions in the expansion helps to capture uncertainty more accurately but increases computational cost. Selection of basis functionsmore » is particularly important for high-dimensional stochastic problems because the number of polynomial chaos basis functions required to represent model uncertainty grows dramatically as the number of input parameters (random dimensions) increases. In classic PCKF algorithms, the PCE basis functions are pre-set based on users' experience. Also, for sequential data assimilation problems, the basis functions kept in PCE expression remain unchanged in different Kalman filter loops, which could limit the accuracy and computational efficiency of classic PCKF algorithms. To address this issue, we present a new algorithm that adaptively selects PCE basis functions for different problems and automatically adjusts the number of basis functions in different Kalman filter loops. The algorithm is based on adaptive functional ANOVA (analysis of variance) decomposition, which approximates a high-dimensional function with the summation of a set of low-dimensional functions. Thus, instead of expanding the original model into PCE, we implement the PCE expansion on these low-dimensional functions, which is much less costly. We also propose a new adaptive criterion for ANOVA that is more suited for solving inverse problems. The new algorithm was tested with different examples and demonstrated great effectiveness in comparison with non-adaptive PCKF and EnKF algorithms.« less

A practical method to assess model sensitivity and parameter uncertainty in C cycle models

NASA Astrophysics Data System (ADS)

Delahaies, Sylvain; Roulstone, Ian; Nichols, Nancy

2015-04-01

The carbon cycle combines multiple spatial and temporal scales, from minutes to hours for the chemical processes occurring in plant cells to several hundred of years for the exchange between the atmosphere and the deep ocean and finally to millennia for the formation of fossil fuels. Together with our knowledge of the transformation processes involved in the carbon cycle, many Earth Observation systems are now available to help improving models and predictions using inverse modelling techniques. A generic inverse problem consists in finding a n-dimensional state vector x such that h(x) = y, for a given N-dimensional observation vector y, including random noise, and a given model h. The problem is well posed if the three following conditions hold: 1) there exists a solution, 2) the solution is unique and 3) the solution depends continuously on the input data. If at least one of these conditions is violated the problem is said ill-posed. The inverse problem is often ill-posed, a regularization method is required to replace the original problem with a well posed problem and then a solution strategy amounts to 1) constructing a solution x, 2) assessing the validity of the solution, 3) characterizing its uncertainty. The data assimilation linked ecosystem carbon (DALEC) model is a simple box model simulating the carbon budget allocation for terrestrial ecosystems. Intercomparison experiments have demonstrated the relative merit of various inverse modelling strategies (MCMC, ENKF) to estimate model parameters and initial carbon stocks for DALEC using eddy covariance measurements of net ecosystem exchange of CO2 and leaf area index observations. Most results agreed on the fact that parameters and initial stocks directly related to fast processes were best estimated with narrow confidence intervals, whereas those related to slow processes were poorly estimated with very large uncertainties. While other studies have tried to overcome this difficulty by adding complementary data streams or by considering longer observation windows no systematic analysis has been carried out so far to explain the large differences among results. We consider adjoint based methods to investigate inverse problems using DALEC and various data streams. Using resolution matrices we study the nature of the inverse problems (solution existence, uniqueness and stability) and show how standard regularization techniques affect resolution and stability properties. Instead of using standard prior information as a penalty term in the cost function to regularize the problems we constraint the parameter space using ecological balance conditions and inequality constraints. The efficiency and rapidity of this approach allows us to compute ensembles of solutions to the inverse problems from which we can establish the robustness of the variational method and obtain non Gaussian posterior distributions for the model parameters and initial carbon stocks.

Spectral reflectance inversion with high accuracy on green target

NASA Astrophysics Data System (ADS)

Jiang, Le; Yuan, Jinping; Li, Yong; Bai, Tingzhu; Liu, Shuoqiong; Jin, Jianzhou; Shen, Jiyun

2016-09-01

Using Landsat-7 ETM remote sensing data, the inversion of spectral reflectance of green wheat in visible and near infrared waveband in Yingke, China is studied. In order to solve the problem of lower inversion accuracy, custom atmospheric conditions method based on moderate resolution transmission model (MODTRAN) is put forward. Real atmospheric parameters are considered when adopting this method. The atmospheric radiative transfer theory to calculate atmospheric parameters is introduced first and then the inversion process of spectral reflectance is illustrated in detail. At last the inversion result is compared with simulated atmospheric conditions method which was a widely used method by previous researchers. The comparison shows that the inversion accuracy of this paper's method is higher in all inversion bands; the inversed spectral reflectance curve by this paper's method is more similar to the measured reflectance curve of wheat and better reflects the spectral reflectance characteristics of green plant which is very different from green artificial target. Thus, whether a green target is a plant or artificial target can be judged by reflectance inversion based on remote sensing image. This paper's research is helpful for the judgment of green artificial target hidden in the greenery, which has a great significance on the precise strike of green camouflaged weapons in military field.

3D CSEM inversion based on goal-oriented adaptive finite element method

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with complex geological scenarios by applying it to the inversion of synthetic marine controlled source EM data generated for a complex 3D offshore model with significant seafloor topography.

Numerical Aspects of Cone Beam Contour Reconstruction

NASA Astrophysics Data System (ADS)

Louis, Alfred K.

2017-12-01

We describe a method for directly calculating the contours of a function from cone beam data. The algorithm is based on a new inversion formula for the gradient of a function presented in Louis (Inverse Probl 32(11):115005, 2016. http://stacks.iop.org/0266-5611/32/i=11/a=115005). The Radon transform of the gradient is found by using a Grangeat type of formula, reducing the inversion problem to the inversion of the Radon transform. In that way the influence of the scanning curve, vital for all exact inversion formulas for complete data, is avoided Numerical results are presented for the circular scanning geometry which neither fulfills the Tuy-Kirillov condition nor the much weaker condition given by the author in Louis (Inverse Probl 32(11):115005, 2016. http://stacks.iop.org/0266-5611/32/i=11/a=115005).

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.

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

Dall-Anese, Emiliano; Simonetto, Andrea

This paper focuses on the design of online algorithms based on prediction-correction steps to track the optimal solution of a time-varying constrained problem. Existing prediction-correction methods have been shown to work well for unconstrained convex problems and for settings where obtaining the inverse of the Hessian of the cost function can be computationally affordable. The prediction-correction algorithm proposed in this paper addresses the limitations of existing methods by tackling constrained problems and by designing a first-order prediction step that relies on the Hessian of the cost function (and do not require the computation of its inverse). Analytical results are establishedmore » to quantify the tracking error. Numerical simulations corroborate the analytical results and showcase performance and benefits of the algorithms.« less

FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems

NASA Astrophysics Data System (ADS)

Vourc'h, Eric; Rodet, Thomas

2015-11-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific research presented during the 5th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2015 (http://complement.farman.ens-cachan.fr/NCMIP_2015.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 29, 2015. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013 and May 2014. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2015 was a one-day workshop held in May 2015 which attracted around 70 attendees. Each of the submitted papers has been reviewed by two reviewers. There have been 15 accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks: GDR ISIS, GDR MIA, GDR MOA and GDR Ondes. The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA and SATIE.

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.

An introduction of Markov chain Monte Carlo method to geochemical inverse problems: Reading melting parameters from REE abundances in abyssal peridotites

NASA Astrophysics Data System (ADS)

Liu, Boda; Liang, Yan

2017-04-01

Markov chain Monte Carlo (MCMC) simulation is a powerful statistical method in solving inverse problems that arise from a wide range of applications. In Earth sciences applications of MCMC simulations are primarily in the field of geophysics. The purpose of this study is to introduce MCMC methods to geochemical inverse problems related to trace element fractionation during mantle melting. MCMC methods have several advantages over least squares methods in deciphering melting processes from trace element abundances in basalts and mantle rocks. Here we use an MCMC method to invert for extent of melting, fraction of melt present during melting, and extent of chemical disequilibrium between the melt and residual solid from REE abundances in clinopyroxene in abyssal peridotites from Mid-Atlantic Ridge, Central Indian Ridge, Southwest Indian Ridge, Lena Trough, and American-Antarctic Ridge. We consider two melting models: one with exact analytical solution and the other without. We solve the latter numerically in a chain of melting models according to the Metropolis-Hastings algorithm. The probability distribution of inverted melting parameters depends on assumptions of the physical model, knowledge of mantle source composition, and constraints from the REE data. Results from MCMC inversion are consistent with and provide more reliable uncertainty estimates than results based on nonlinear least squares inversion. We show that chemical disequilibrium is likely to play an important role in fractionating LREE in residual peridotites during partial melting beneath mid-ocean ridge spreading centers. MCMC simulation is well suited for more complicated but physically more realistic melting problems that do not have analytical solutions.

Children's Understanding of the Inverse Relation between Multiplication and Division

ERIC Educational Resources Information Center

Robinson, Katherine M.; Dube, Adam K.

2009-01-01

Children's understanding of the inversion concept in multiplication and division problems (i.e., that on problems of the form "d multiplied by e/e" no calculations are required) was investigated. Children in Grades 6, 7, and 8 completed an inversion problem-solving task, an assessment of procedures task, and a factual knowledge task of simple…

Identifing Atmospheric Pollutant Sources Using Artificial Neural Networks

NASA Astrophysics Data System (ADS)

Paes, F. F.; Campos, H. F.; Luz, E. P.; Carvalho, A. R.

2008-05-01

The estimation of the area source pollutant strength is a relevant issue for atmospheric environment. This characterizes an inverse problem in the atmospheric pollution dispersion. In the inverse analysis, an area source domain is considered, where the strength of such area source term is assumed unknown. The inverse problem is solved by using a supervised artificial neural network: multi-layer perceptron. The conection weights of the neural network are computed from delta rule - learning process. The neural network inversion is compared with results from standard inverse analysis (regularized inverse solution). In the regularization method, the inverse problem is formulated as a non-linear optimization approach, whose the objective function is given by the square difference between the measured pollutant concentration and the mathematical models, associated with a regularization operator. In our numerical experiments, the forward problem is addressed by a source-receptor scheme, where a regressive Lagrangian model is applied to compute the transition matrix. The second order maximum entropy regularization is used, and the regularization parameter is calculated by the L-curve technique. The objective function is minimized employing a deterministic scheme (a quasi-Newton algorithm) [1] and a stochastic technique (PSO: particle swarm optimization) [2]. The inverse problem methodology is tested with synthetic observational data, from six measurement points in the physical domain. The best inverse solutions were obtained with neural networks. References: [1] D. R. Roberti, D. Anfossi, H. F. Campos Velho, G. A. Degrazia (2005): Estimating Emission Rate and Pollutant Source Location, Ciencia e Natura, p. 131-134. [2] E.F.P. da Luz, H.F. de Campos Velho, J.C. Becceneri, D.R. Roberti (2007): Estimating Atmospheric Area Source Strength Through Particle Swarm Optimization. Inverse Problems, Desing and Optimization Symposium IPDO-2007, April 16-18, Miami (FL), USA, vol 1, p. 354-359.

Inverse regression-based uncertainty quantification algorithms for high-dimensional models: Theory and practice

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

Li, Weixuan; Lin, Guang; Li, Bing

2016-09-01

A well-known challenge in uncertainty quantification (UQ) is the "curse of dimensionality". However, many high-dimensional UQ problems are essentially low-dimensional, because the randomness of the quantity of interest (QoI) is caused only by uncertain parameters varying within a low-dimensional subspace, known as the sufficient dimension reduction (SDR) subspace. Motivated by this observation, we propose and demonstrate in this paper an inverse regression-based UQ approach (IRUQ) for high-dimensional problems. Specifically, we use an inverse regression procedure to estimate the SDR subspace and then convert the original problem to a low-dimensional one, which can be efficiently solved by building a response surface model such as a polynomial chaos expansion. The novelty and advantages of the proposed approach is seen in its computational efficiency and practicality. Comparing with Monte Carlo, the traditionally preferred approach for high-dimensional UQ, IRUQ with a comparable cost generally gives much more accurate solutions even for high-dimensional problems, and even when the dimension reduction is not exactly sufficient. Theoretically, IRUQ is proved to converge twice as fast as the approach it uses seeking the SDR subspace. For example, while a sliced inverse regression method converges to the SDR subspace at the rate ofmore » $$O(n^{-1/2})$$, the corresponding IRUQ converges at $$O(n^{-1})$$. IRUQ also provides several desired conveniences in practice. It is non-intrusive, requiring only a simulator to generate realizations of the QoI, and there is no need to compute the high-dimensional gradient of the QoI. Finally, error bars can be derived for the estimation results reported by IRUQ.« less

A Subspace Pursuit–based Iterative Greedy Hierarchical Solution to the Neuromagnetic Inverse Problem

PubMed Central

Babadi, Behtash; Obregon-Henao, Gabriel; Lamus, Camilo; Hämäläinen, Matti S.; Brown, Emery N.; Purdon, Patrick L.

2013-01-01

Magnetoencephalography (MEG) is an important non-invasive method for studying activity within the human brain. Source localization methods can be used to estimate spatiotemporal activity from MEG measurements with high temporal resolution, but the spatial resolution of these estimates is poor due to the ill-posed nature of the MEG inverse problem. Recent developments in source localization methodology have emphasized temporal as well as spatial constraints to improve source localization accuracy, but these methods can be computationally intense. Solutions emphasizing spatial sparsity hold tremendous promise, since the underlying neurophysiological processes generating MEG signals are often sparse in nature, whether in the form of focal sources, or distributed sources representing large-scale functional networks. Recent developments in the theory of compressed sensing (CS) provide a rigorous framework to estimate signals with sparse structure. In particular, a class of CS algorithms referred to as greedy pursuit algorithms can provide both high recovery accuracy and low computational complexity. Greedy pursuit algorithms are difficult to apply directly to the MEG inverse problem because of the high-dimensional structure of the MEG source space and the high spatial correlation in MEG measurements. In this paper, we develop a novel greedy pursuit algorithm for sparse MEG source localization that overcomes these fundamental problems. This algorithm, which we refer to as the Subspace Pursuit-based Iterative Greedy Hierarchical (SPIGH) inverse solution, exhibits very low computational complexity while achieving very high localization accuracy. We evaluate the performance of the proposed algorithm using comprehensive simulations, as well as the analysis of human MEG data during spontaneous brain activity and somatosensory stimuli. These studies reveal substantial performance gains provided by the SPIGH algorithm in terms of computational complexity, localization accuracy, and robustness. PMID:24055554

A novel post-processing scheme for two-dimensional electrical impedance tomography based on artificial neural networks

PubMed Central

2017-01-01

Objective Electrical Impedance Tomography (EIT) is a powerful non-invasive technique for imaging applications. The goal is to estimate the electrical properties of living tissues by measuring the potential at the boundary of the domain. Being safe with respect to patient health, non-invasive, and having no known hazards, EIT is an attractive and promising technology. However, it suffers from a particular technical difficulty, which consists of solving a nonlinear inverse problem in real time. Several nonlinear approaches have been proposed as a replacement for the linear solver, but in practice very few are capable of stable, high-quality, and real-time EIT imaging because of their very low robustness to errors and inaccurate modeling, or because they require considerable computational effort. Methods In this paper, a post-processing technique based on an artificial neural network (ANN) is proposed to obtain a nonlinear solution to the inverse problem, starting from a linear solution. While common reconstruction methods based on ANNs estimate the solution directly from the measured data, the method proposed here enhances the solution obtained from a linear solver. Conclusion Applying a linear reconstruction algorithm before applying an ANN reduces the effects of noise and modeling errors. Hence, this approach significantly reduces the error associated with solving 2D inverse problems using machine-learning-based algorithms. Significance This work presents radical enhancements in the stability of nonlinear methods for biomedical EIT applications. PMID:29206856

Convergence analysis of surrogate-based methods for Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Yan, Liang; Zhang, Yuan-Xiang

2017-12-01

The major challenges in the Bayesian inverse problems arise from the need for repeated evaluations of the forward model, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. Many attempts at accelerating Bayesian inference have relied on surrogates for the forward model, typically constructed through repeated forward simulations that are performed in an offline phase. Although such approaches can be quite effective at reducing computation cost, there has been little analysis of the approximation on posterior inference. In this work, we prove error bounds on the Kullback-Leibler (KL) distance between the true posterior distribution and the approximation based on surrogate models. Our rigorous error analysis show that if the forward model approximation converges at certain rate in the prior-weighted L 2 norm, then the posterior distribution generated by the approximation converges to the true posterior at least two times faster in the KL sense. The error bound on the Hellinger distance is also provided. To provide concrete examples focusing on the use of the surrogate model based methods, we present an efficient technique for constructing stochastic surrogate models to accelerate the Bayesian inference approach. The Christoffel least squares algorithms, based on generalized polynomial chaos, are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. The numerical strategy and the predicted convergence rates are then demonstrated on the nonlinear inverse problems, involving the inference of parameters appearing in partial differential equations.

Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling

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

Bledsoe, Keith C.

2015-04-01

The DiffeRential Evolution Adaptive Metropolis (DREAM) method is a powerful optimization/uncertainty quantification tool used to solve inverse transport problems in Los Alamos National Laboratory’s INVERSE code system. The DREAM method has been shown to be adept at accurate uncertainty quantification, but it can be very computationally demanding. Previously, the DREAM method in INVERSE performed a user-defined number of particle transport calculations. This placed a burden on the user to guess the number of calculations that would be required to accurately solve any given problem. This report discusses a new approach that has been implemented into INVERSE, the Gelman-Rubin convergence metric.more » This metric automatically detects when an appropriate number of transport calculations have been completed and the uncertainty in the inverse problem has been accurately calculated. In a test problem with a spherical geometry, this method was found to decrease the number of transport calculations (and thus time required) to solve a problem by an average of over 90%. In a cylindrical test geometry, a 75% decrease was obtained.« less

Distributed micro-releases of bioterror pathogens : threat characterizations and epidemiology from uncertain patient observables.

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

Wolf, Michael M.; Marzouk, Youssef M.; Adams, Brian M.

2008-10-01

Terrorist attacks using an aerosolized pathogen preparation have gained credibility as a national security concern since the anthrax attacks of 2001. The ability to characterize the parameters of such attacks, i.e., to estimate the number of people infected, the time of infection, the average dose received, and the rate of disease spread in contemporary American society (for contagious diseases), is important when planning a medical response. For non-contagious diseases, we address the characterization problem by formulating a Bayesian inverse problem predicated on a short time-series of diagnosed patients exhibiting symptoms. To keep the approach relevant for response planning, we limitmore » ourselves to 3.5 days of data. In computational tests performed for anthrax, we usually find these observation windows sufficient, especially if the outbreak model employed in the inverse problem is accurate. For contagious diseases, we formulated a Bayesian inversion technique to infer both pathogenic transmissibility and the social network from outbreak observations, ensuring that the two determinants of spreading are identified separately. We tested this technique on data collected from a 1967 smallpox epidemic in Abakaliki, Nigeria. We inferred, probabilistically, different transmissibilities in the structured Abakaliki population, the social network, and the chain of transmission. Finally, we developed an individual-based epidemic model to realistically simulate the spread of a rare (or eradicated) disease in a modern society. This model incorporates the mixing patterns observed in an (American) urban setting and accepts, as model input, pathogenic transmissibilities estimated from historical outbreaks that may have occurred in socio-economic environments with little resemblance to contemporary society. Techniques were also developed to simulate disease spread on static and sampled network reductions of the dynamic social networks originally in the individual-based model, yielding faster, though approximate, network-based epidemic models. These reduced-order models are useful in scenario analysis for medical response planning, as well as in computationally intensive inverse problems.« less

2-D inversion of VES data in Saqqara archaeological area, Egypt

NASA Astrophysics Data System (ADS)

El-Qady, Gad; Sakamoto, Chika; Ushijima, Keisuke

1999-10-01

The interpretation of actual geophysical field data still has a problem for obtaining a unique solution. In order to investigate the groundwater potentials in Saqqara archaeological area, vertical electrical soundings with Schlumberger array have been carried out. In the interpretation of VES data, 1D resistivity inversion has been performed based on a horizontally layered earth model by El-Qady (1995). However, some results of 1D inversion are not fully satisfied for actual 3D structures such as archaeological tombs. Therefore, we have carried out 2D inversion based on ABIC least squares method for Schlumberger VES data obtained in Saqqara area. Although the results of 2D cross sections were correlated with the previous interpretation, the 2D inversion still shows a rough spatial resistivity distribution, which is the abrupt change in resistivity between two neighboring blocks of the computed region. It is concluded that 3D interpretation is recommended for visualizing ground water distribution with depth in the Saqqara area.

A Synthetic Study on the Resolution of 2D Elastic Full Waveform Inversion

NASA Astrophysics Data System (ADS)

Cui, C.; Wang, Y.

2017-12-01

Gradient based full waveform inversion is an effective method in seismic study, it makes full use of the information given by seismic records and is capable of providing a more accurate model of the interior of the earth at a relatively low computational cost. However, the strong non-linearity of the problem brings about many difficulties in the assessment of its resolution. Synthetic inversions are therefore helpful before an inversion based on real data is made. Checker-board test is a commonly used method, but it is not always reliable due to the significant difference between a checker-board and the true model. Our study aims to provide a basic understanding of the resolution of 2D elastic inversion by examining three main factors that affect the inversion result respectively: 1. The structural characteristic of the model; 2. The level of similarity between the initial model and the true model; 3. The spacial distribution of sources and receivers. We performed about 150 synthetic inversions to demonstrate how each factor contributes to quality of the result, and compared the inversion results with those achieved by checker-board tests. The study can be a useful reference to assess the resolution of an inversion in addition to regular checker-board tests, or to determine whether the seismic data of a specific region is sufficient for a successful inversion.

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

NASA Astrophysics Data System (ADS)

Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

2018-04-01

We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

Assessing non-uniqueness: An algebraic approach

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

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

A multiwave range test for obstacle reconstructions with unknown physical properties

NASA Astrophysics Data System (ADS)

Potthast, Roland; Schulz, Jochen

2007-08-01

We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A `range test' for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533-547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhauser, Basel, 1986, pp. 93-102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Gottingen, 1999]. In particular, we propose a new version of the Kirsch-Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided.

Study of the Rotational Structure of the v 2 Inversion Band of the 15NH2D Molecule

NASA Astrophysics Data System (ADS)

Fomchenko, A. L.; Belova, A. S.; Kwabia Tchana, F.

2018-04-01

The Fourier spectrum of the 15NH2D molecule in the range from 650 to 1150 cm-1, where the ν2 vibrationinversion band is located, is first studied. Analysis of the given band allows the energy rovibrational structure of the examined state to be determined. The inverse spectroscopic problem is solved based on the data obtained.

Inverse Diffusion Curves Using Shape Optimization.

PubMed

Zhao, Shuang; Durand, Fredo; Zheng, Changxi

2018-07-01

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.

Interpretation of deep directional resistivity measurements acquired in high-angle and horizontal wells using 3-D inversion

NASA Astrophysics Data System (ADS)

Puzyrev, Vladimir; Torres-Verdín, Carlos; Calo, Victor

2018-05-01

The interpretation of resistivity measurements acquired in high-angle and horizontal wells is a critical technical problem in formation evaluation. We develop an efficient parallel 3-D inversion method to estimate the spatial distribution of electrical resistivity in the neighbourhood of a well from deep directional electromagnetic induction measurements. The methodology places no restriction on the spatial distribution of the electrical resistivity around arbitrary well trajectories. The fast forward modelling of triaxial induction measurements performed with multiple transmitter-receiver configurations employs a parallel direct solver. The inversion uses a pre-conditioned gradient-based method whose accuracy is improved using the Wolfe conditions to estimate optimal step lengths at each iteration. The large transmitter-receiver offsets, used in the latest generation of commercial directional resistivity tools, improve the depth of investigation to over 30 m from the wellbore. Several challenging synthetic examples confirm the feasibility of the full 3-D inversion-based interpretations for these distances, hence enabling the integration of resistivity measurements with seismic amplitude data to improve the forecast of the petrophysical and fluid properties. Employing parallel direct solvers for the triaxial induction problems allows for large reductions in computational effort, thereby opening the possibility to invert multiposition 3-D data in practical CPU times.

Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm

NASA Astrophysics Data System (ADS)

Sun, Cheng-Yu; Wang, Yan-Yan; Wu, Dun-Shi; Qin, Xiao-Jun

2017-12-01

At present, near-surface shear wave velocities are mainly calculated through Rayleigh wave dispersion-curve inversions in engineering surface investigations, but the required calculations pose a highly nonlinear global optimization problem. In order to alleviate the risk of falling into a local optimal solution, this paper introduces a new global optimization method, the shuffle frog-leaping algorithm (SFLA), into the Rayleigh wave dispersion-curve inversion process. SFLA is a swarm-intelligence-based algorithm that simulates a group of frogs searching for food. It uses a few parameters, achieves rapid convergence, and is capability of effective global searching. In order to test the reliability and calculation performance of SFLA, noise-free and noisy synthetic datasets were inverted. We conducted a comparative analysis with other established algorithms using the noise-free dataset, and then tested the ability of SFLA to cope with data noise. Finally, we inverted a real-world example to examine the applicability of SFLA. Results from both synthetic and field data demonstrated the effectiveness of SFLA in the interpretation of Rayleigh wave dispersion curves. We found that SFLA is superior to the established methods in terms of both reliability and computational efficiency, so it offers great potential to improve our ability to solve geophysical inversion problems.

Mineral inversion for element capture spectroscopy logging based on optimization theory

NASA Astrophysics Data System (ADS)

Zhao, Jianpeng; Chen, Hui; Yin, Lu; Li, Ning

2017-12-01

Understanding the mineralogical composition of a formation is an essential key step in the petrophysical evaluation of petroleum reservoirs. Geochemical logging tools can provide quantitative measurements of a wide range of elements. In this paper, element capture spectroscopy (ECS) was taken as an example and an optimization method was adopted to solve the mineral inversion problem for ECS. This method used the converting relationship between elements and minerals as response equations and took into account the statistical uncertainty of the element measurements and established an optimization function for ECS. Objective function value and reconstructed elemental logs were used to check the robustness and reliability of the inversion method. Finally, the inversion mineral results had a good agreement with x-ray diffraction laboratory data. The accurate conversion of elemental dry weights to mineral dry weights formed the foundation for the subsequent applications based on ECS.

Computational methods for inverse problems in geophysics: inversion of travel time observations

USGS Publications Warehouse

Pereyra, V.; Keller, H.B.; Lee, W.H.K.

1980-01-01

General ways of solving various inverse problems are studied for given travel time observations between sources and receivers. These problems are separated into three components: (a) the representation of the unknown quantities appearing in the model; (b) the nonlinear least-squares problem; (c) the direct, two-point ray-tracing problem used to compute travel time once the model parameters are given. Novel software is described for (b) and (c), and some ideas given on (a). Numerical results obtained with artificial data and an implementation of the algorithm are also presented. ?? 1980.

A fixed energy fixed angle inverse scattering in interior transmission problem

NASA Astrophysics Data System (ADS)

Chen, Lung-Hui

2017-06-01

We study the inverse acoustic scattering problem in mathematical physics. The problem is to recover the index of refraction in an inhomogeneous medium by measuring the scattered wave fields in the far field. We transform the problem to the interior transmission problem in the study of the Helmholtz equation. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics in the far field, we can determine uniquely the perturbation source for the radially symmetric perturbations.

Intelligent inversion method for pre-stack seismic big data based on MapReduce

NASA Astrophysics Data System (ADS)

Yan, Xuesong; Zhu, Zhixin; Wu, Qinghua

2018-01-01

Seismic exploration is a method of oil exploration that uses seismic information; that is, according to the inversion of seismic information, the useful information of the reservoir parameters can be obtained to carry out exploration effectively. Pre-stack data are characterised by a large amount of data, abundant information, and so on, and according to its inversion, the abundant information of the reservoir parameters can be obtained. Owing to the large amount of pre-stack seismic data, existing single-machine environments have not been able to meet the computational needs of the huge amount of data; thus, the development of a method with a high efficiency and the speed to solve the inversion problem of pre-stack seismic data is urgently needed. The optimisation of the elastic parameters by using a genetic algorithm easily falls into a local optimum, which results in a non-obvious inversion effect, especially for the optimisation effect of the density. Therefore, an intelligent optimisation algorithm is proposed in this paper and used for the elastic parameter inversion of pre-stack seismic data. This algorithm improves the population initialisation strategy by using the Gardner formula and the genetic operation of the algorithm, and the improved algorithm obtains better inversion results when carrying out a model test with logging data. All of the elastic parameters obtained by inversion and the logging curve of theoretical model are fitted well, which effectively improves the inversion precision of the density. This algorithm was implemented with a MapReduce model to solve the seismic big data inversion problem. The experimental results show that the parallel model can effectively reduce the running time of the algorithm.

An evolutive real-time source inversion based on a linear inverse formulation

NASA Astrophysics Data System (ADS)

Sanchez Reyes, H. S.; Tago, J.; Cruz-Atienza, V. M.; Metivier, L.; Contreras Zazueta, M. A.; Virieux, J.

2016-12-01

Finite source inversion is a steppingstone to unveil earthquake rupture. It is used on ground motion predictions and its results shed light on seismic cycle for better tectonic understanding. It is not yet used for quasi-real-time analysis. Nowadays, significant progress has been made on approaches regarding earthquake imaging, thanks to new data acquisition and methodological advances. However, most of these techniques are posterior procedures once seismograms are available. Incorporating source parameters estimation into early warning systems would require to update the source build-up while recording data. In order to go toward this dynamic estimation, we developed a kinematic source inversion formulated in the time-domain, for which seismograms are linearly related to the slip distribution on the fault through convolutions with Green's functions previously estimated and stored (Perton et al., 2016). These convolutions are performed in the time-domain as we progressively increase the time window of records at each station specifically. Selected unknowns are the spatio-temporal slip-rate distribution to keep the linearity of the forward problem with respect to unknowns, as promoted by Fan and Shearer (2014). Through the spatial extension of the expected rupture zone, we progressively build-up the slip-rate when adding new data by assuming rupture causality. This formulation is based on the adjoint-state method for efficiency (Plessix, 2006). The inverse problem is non-unique and, in most cases, underdetermined. While standard regularization terms are used for stabilizing the inversion, we avoid strategies based on parameter reduction leading to an unwanted non-linear relationship between parameters and seismograms for our progressive build-up. Rise time, rupture velocity and other quantities can be extracted later on as attributs from the slip-rate inversion we perform. Satisfactory results are obtained on a synthetic example (FIgure 1) proposed by the Source Inversion Validation project (Mai et al. 2011). A real case application is currently being explored. Our specific formulation, combined with simple prior information, as well as numerical results obtained so far, yields interesting perspectives for a real-time implementation.

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, L.; Gu, H.

2017-12-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion has a better applicability. It doesn't need some assumptions and can estimate more parameters simultaneously. Meanwhile, by using the generalized linear method, the inversion is easily realized and its calculation amount is small. We use the Marmousi model to generate synthetic seismic records to test and analyze the influence of random noise. Without noise, all estimation results are relatively accurate. With the increase of noise, P-wave velocity change and oil saturation change are stable and less affected by noise. S-wave velocity change is most affected by noise. Finally we use the actual field data of time-lapse seismic prospecting to process and the results can prove the availability and feasibility of our method in actual situation.

Geostatistical regularization operators for geophysical inverse problems on irregular meshes

NASA Astrophysics Data System (ADS)

Jordi, C.; Doetsch, J.; Günther, T.; Schmelzbach, C.; Robertsson, J. OA

2018-05-01

Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.

FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)

NASA Astrophysics Data System (ADS)

2014-10-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 4th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2014 (http://www.farman.ens-cachan.fr/NCMIP_2014.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 23, 2014. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 and May 2013, (http://www.farman.ens-cachan.fr/NCMIP_2012.html), (http://www.farman.ens-cachan.fr/NCMIP_2013.html). The New Computational Methods for Inverse Problems (NCMIP) Workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2014 was a one-day workshop held in May 2014 which attracted around sixty attendees. Each of the submitted papers has been reviewed by two reviewers. There have been nine accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks (GDR ISIS, GDR MIA, GDR MOA, GDR Ondes). The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA, SATIE. Eric Vourc'h and Thomas Rodet

Developing a particle tracking surrogate model to improve inversion of ground water - Surface water models

NASA Astrophysics Data System (ADS)

Cousquer, Yohann; Pryet, Alexandre; Atteia, Olivier; Ferré, Ty P. A.; Delbart, Célestine; Valois, Rémi; Dupuy, Alain

2018-03-01

The inverse problem of groundwater models is often ill-posed and model parameters are likely to be poorly constrained. Identifiability is improved if diverse data types are used for parameter estimation. However, some models, including detailed solute transport models, are further limited by prohibitive computation times. This often precludes the use of concentration data for parameter estimation, even if those data are available. In the case of surface water-groundwater (SW-GW) models, concentration data can provide SW-GW mixing ratios, which efficiently constrain the estimate of exchange flow, but are rarely used. We propose to reduce computational limits by simulating SW-GW exchange at a sink (well or drain) based on particle tracking under steady state flow conditions. Particle tracking is used to simulate advective transport. A comparison between the particle tracking surrogate model and an advective-dispersive model shows that dispersion can often be neglected when the mixing ratio is computed for a sink, allowing for use of the particle tracking surrogate model. The surrogate model was implemented to solve the inverse problem for a real SW-GW transport problem with heads and concentrations combined in a weighted hybrid objective function. The resulting inversion showed markedly reduced uncertainty in the transmissivity field compared to calibration on head data alone.

Bayesian Inversion of 2D Models from Airborne Transient EM Data

NASA Astrophysics Data System (ADS)

Blatter, D. B.; Key, K.; Ray, A.

2016-12-01

The inherent non-uniqueness in most geophysical inverse problems leads to an infinite number of Earth models that fit observed data to within an adequate tolerance. To resolve this ambiguity, traditional inversion methods based on optimization techniques such as the Gauss-Newton and conjugate gradient methods rely on an additional regularization constraint on the properties that an acceptable model can possess, such as having minimal roughness. While allowing such an inversion scheme to converge on a solution, regularization makes it difficult to estimate the uncertainty associated with the model parameters. This is because regularization biases the inversion process toward certain models that satisfy the regularization constraint and away from others that don't, even when both may suitably fit the data. By contrast, a Bayesian inversion framework aims to produce not a single `most acceptable' model but an estimate of the posterior likelihood of the model parameters, given the observed data. In this work, we develop a 2D Bayesian framework for the inversion of transient electromagnetic (TEM) data. Our method relies on a reversible-jump Markov Chain Monte Carlo (RJ-MCMC) Bayesian inverse method with parallel tempering. Previous gradient-based inversion work in this area used a spatially constrained scheme wherein individual (1D) soundings were inverted together and non-uniqueness was tackled by using lateral and vertical smoothness constraints. By contrast, our work uses a 2D model space of Voronoi cells whose parameterization (including number of cells) is fully data-driven. To make the problem work practically, we approximate the forward solution for each TEM sounding using a local 1D approximation where the model is obtained from the 2D model by retrieving a vertical profile through the Voronoi cells. The implicit parsimony of the Bayesian inversion process leads to the simplest models that adequately explain the data, obviating the need for explicit smoothness constraints. In addition, credible intervals in model space are directly obtained, resolving some of the uncertainty introduced by regularization. An example application shows how the method can be used to quantify the uncertainty in airborne EM soundings for imaging subglacial brine channels and groundwater systems.

3D near-to-surface conductivity reconstruction by inversion of VETEM data using the distorted Born iterative method

USGS Publications Warehouse

Wang, G.L.; Chew, W.C.; Cui, T.J.; Aydiner, A.A.; Wright, D.L.; Smith, D.V.

2004-01-01

Three-dimensional (3D) subsurface imaging by using inversion of data obtained from the very early time electromagnetic system (VETEM) was discussed. The study was carried out by using the distorted Born iterative method to match the internal nonlinear property of the 3D inversion problem. The forward solver was based on the total-current formulation bi-conjugate gradient-fast Fourier transform (BCCG-FFT). It was found that the selection of regularization parameter follow a heuristic rule as used in the Levenberg-Marquardt algorithm so that the iteration is stable.

An iterative solver for the 3D Helmholtz equation

NASA Astrophysics Data System (ADS)

Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

2017-09-01

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

Multimodal, high-dimensional, model-based, Bayesian inverse problems with applications in biomechanics

NASA Astrophysics Data System (ADS)

Franck, I. M.; Koutsourelakis, P. S.

2017-01-01

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of unknown (latent) variables is high. This is the setting in many problems in computational physics where forward models with nonlinear PDEs are used and the parameters to be calibrated involve spatio-temporarily varying coefficients, which upon discretization give rise to a high-dimensional vector of unknowns. One of the consequences of the well-documented ill-posedness of inverse problems is the possibility of multiple solutions. While such information is contained in the posterior density in Bayesian formulations, the discovery of a single mode, let alone multiple, poses a formidable computational task. The goal of the present paper is two-fold. On one hand, we propose approximate, adaptive inference strategies using mixture densities to capture multi-modal posteriors. On the other, we extend our work in [1] with regard to effective dimensionality reduction techniques that reveal low-dimensional subspaces where the posterior variance is mostly concentrated. We validate the proposed model by employing Importance Sampling which confirms that the bias introduced is small and can be efficiently corrected if the analyst wishes to do so. We demonstrate the performance of the proposed strategy in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical diagnosis. The discovery of multiple modes (solutions) in such problems is critical in achieving the diagnostic objectives.

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.

On the Development of Multi-Step Inverse FEM with Shell Model

NASA Astrophysics Data System (ADS)

Huang, Y.; Du, R.

2005-08-01

The inverse or one-step finite element approach is increasingly used in the sheet metal stamping industry to predict strain distribution and the initial blank shape in the preliminary design stage. Based on the existing theory, there are two types of method: one is based on the principle of virtual work and the other is based on the principle of extreme work. Much research has been conducted to improve the accuracy of simulation results. For example, based on the virtual work principle, Batoz et al. developed a new method using triangular DKT shell elements. In this new method, the bending and unbending effects are considered. Based on the principle of extreme work, Majlessi and et al. proposed the multi-step inverse approach with membrane elements and applied it to an axis-symmetric part. Lee and et al. presented an axis-symmetric shell element model to solve the similar problem. In this paper, a new multi-step inverse method is introduced with no limitation on the workpiece shape. It is a shell element model based on the virtual work principle. The new method is validated by means of comparing to the commercial software system (PAMSTAMP®). The comparison results indicate that the accuracy is good.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

NASA Astrophysics Data System (ADS)

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2-D and a random hydraulic conductivity field in 3-D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ˜101 to ˜102 in a multicore computational environment. Therefore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate to large-scale problems.

Sparsity constrained split feasibility for dose-volume constraints in inverse planning of intensity-modulated photon or proton therapy

NASA Astrophysics Data System (ADS)

Penfold, Scott; Zalas, Rafał; Casiraghi, Margherita; Brooke, Mark; Censor, Yair; Schulte, Reinhard

2017-05-01

A split feasibility formulation for the inverse problem of intensity-modulated radiation therapy treatment planning with dose-volume constraints included in the planning algorithm is presented. It involves a new type of sparsity constraint that enables the inclusion of a percentage-violation constraint in the model problem and its handling by continuous (as opposed to integer) methods. We propose an iterative algorithmic framework for solving such a problem by applying the feasibility-seeking CQ-algorithm of Byrne combined with the automatic relaxation method that uses cyclic projections. Detailed implementation instructions are furnished. Functionality of the algorithm was demonstrated through the creation of an intensity-modulated proton therapy plan for a simple 2D C-shaped geometry and also for a realistic base-of-skull chordoma treatment site. Monte Carlo simulations of proton pencil beams of varying energy were conducted to obtain dose distributions for the 2D test case. A research release of the Pinnacle 3 proton treatment planning system was used to extract pencil beam doses for a clinical base-of-skull chordoma case. In both cases the beamlet doses were calculated to satisfy dose-volume constraints according to our new algorithm. Examination of the dose-volume histograms following inverse planning with our algorithm demonstrated that it performed as intended. The application of our proposed algorithm to dose-volume constraint inverse planning was successfully demonstrated. Comparison with optimized dose distributions from the research release of the Pinnacle 3 treatment planning system showed the algorithm could achieve equivalent or superior results.

Beam hardening correction for interior tomography based on exponential formed model and radon inversion transform

NASA Astrophysics Data System (ADS)

Chen, Siyu; Zhang, Hanming; Li, Lei; Xi, Xiaoqi; Han, Yu; Yan, Bin

2016-10-01

X-ray computed tomography (CT) has been extensively applied in industrial non-destructive testing (NDT). However, in practical applications, the X-ray beam polychromaticity often results in beam hardening problems for image reconstruction. The beam hardening artifacts, which manifested as cupping, streaks and flares, not only debase the image quality, but also disturb the subsequent analyses. Unfortunately, conventional CT scanning requires that the scanned object is completely covered by the field of view (FOV), the state-of-art beam hardening correction methods only consider the ideal scanning configuration, and often suffer problems for interior tomography due to the projection truncation. Aiming at this problem, this paper proposed a beam hardening correction method based on radon inversion transform for interior tomography. Experimental results show that, compared to the conventional correction algorithms, the proposed approach has achieved excellent performance in both beam hardening artifacts reduction and truncation artifacts suppression. Therefore, the presented method has vitally theoretic and practicable meaning in artifacts correction of industrial CT.

Estimating uncertainties in complex joint inverse problems

NASA Astrophysics Data System (ADS)

Afonso, Juan Carlos

2016-04-01

Sources of uncertainty affecting geophysical inversions can be classified either as reflective (i.e. the practitioner is aware of her/his ignorance) or non-reflective (i.e. the practitioner does not know that she/he does not know!). Although we should be always conscious of the latter, the former are the ones that, in principle, can be estimated either empirically (by making measurements or collecting data) or subjectively (based on the experience of the researchers). For complex parameter estimation problems in geophysics, subjective estimation of uncertainty is the most common type. In this context, probabilistic (aka Bayesian) methods are commonly claimed to offer a natural and realistic platform from which to estimate model uncertainties. This is because in the Bayesian approach, errors (whatever their nature) can be naturally included as part of the global statistical model, the solution of which represents the actual solution to the inverse problem. However, although we agree that probabilistic inversion methods are the most powerful tool for uncertainty estimation, the common claim that they produce "realistic" or "representative" uncertainties is not always justified. Typically, ALL UNCERTAINTY ESTIMATES ARE MODEL DEPENDENT, and therefore, besides a thorough characterization of experimental uncertainties, particular care must be paid to the uncertainty arising from model errors and input uncertainties. We recall here two quotes by G. Box and M. Gunzburger, respectively, of special significance for inversion practitioners and for this session: "…all models are wrong, but some are useful" and "computational results are believed by no one, except the person who wrote the code". In this presentation I will discuss and present examples of some problems associated with the estimation and quantification of uncertainties in complex multi-observable probabilistic inversions, and how to address them. Although the emphasis will be on sources of uncertainty related to the forward and statistical models, I will also address other uncertainties associated with data and uncertainty propagation.

Kolmogorov complexity, statistical regularization of inverse problems, and Birkhoff's formalization of beauty

NASA Astrophysics Data System (ADS)

Kreinovich, Vladik; Longpre, Luc; Koshelev, Misha

1998-09-01

Most practical applications of statistical methods are based on the implicit assumption that if an event has a very small probability, then it cannot occur. For example, the probability that a kettle placed on a cold stove would start boiling by itself is not 0, it is positive, but it is so small, that physicists conclude that such an event is simply impossible. This assumption is difficult to formalize in traditional probability theory, because this theory only describes measures on sets and does not allow us to divide functions into 'random' and non-random ones. This distinction was made possible by the idea of algorithmic randomness, introduce by Kolmogorov and his student Martin- Loef in the 1960s. We show that this idea can also be used for inverse problems. In particular, we prove that for every probability measure, the corresponding set of random functions is compact, and, therefore, the corresponding restricted inverse problem is well-defined. The resulting techniques turns out to be interestingly related with the qualitative esthetic measure introduced by G. Birkhoff as order/complexity.

Scaling of plane-wave functions in statistically optimized near-field acoustic holography.

PubMed

Hald, Jørgen

2014-11-01

Statistically Optimized Near-field Acoustic Holography (SONAH) is a Patch Holography method, meaning that it can be applied in cases where the measurement area covers only part of the source surface. The method performs projections directly in the spatial domain, avoiding the use of spatial discrete Fourier transforms and the associated errors. First, an inverse problem is solved using regularization. For each calculation point a multiplication must then be performed with two transfer vectors--one to get the sound pressure and the other to get the particle velocity. Considering SONAH based on sound pressure measurements, existing derivations consider only pressure reconstruction when setting up the inverse problem, so the evanescent wave amplification associated with the calculation of particle velocity is not taken into account in the regularized solution of the inverse problem. The present paper introduces a scaling of the applied plane wave functions that takes the amplification into account, and it is shown that the previously published virtual source-plane retraction has almost the same effect. The effectiveness of the different solutions is verified through a set of simulated measurements.

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.

Inverse methods for 3D quantitative optical coherence elasticity imaging (Conference Presentation)

NASA Astrophysics Data System (ADS)

Dong, Li; Wijesinghe, Philip; Hugenberg, Nicholas; Sampson, David D.; Munro, Peter R. T.; Kennedy, Brendan F.; Oberai, Assad A.

2017-02-01

In elastography, quantitative elastograms are desirable as they are system and operator independent. Such quantification also facilitates more accurate diagnosis, longitudinal studies and studies performed across multiple sites. In optical elastography (compression, surface-wave or shear-wave), quantitative elastograms are typically obtained by assuming some form of homogeneity. This simplifies data processing at the expense of smearing sharp transitions in elastic properties, and/or introducing artifacts in these regions. Recently, we proposed an inverse problem-based approach to compression OCE that does not assume homogeneity, and overcomes the drawbacks described above. In this approach, the difference between the measured and predicted displacement field is minimized by seeking the optimal distribution of elastic parameters. The predicted displacements and recovered elastic parameters together satisfy the constraint of the equations of equilibrium. This approach, which has been applied in two spatial dimensions assuming plane strain, has yielded accurate material property distributions. Here, we describe the extension of the inverse problem approach to three dimensions. In addition to the advantage of visualizing elastic properties in three dimensions, this extension eliminates the plane strain assumption and is therefore closer to the true physical state. It does, however, incur greater computational costs. We address this challenge through a modified adjoint problem, spatially adaptive grid resolution, and three-dimensional decomposition techniques. Through these techniques the inverse problem is solved on a typical desktop machine within a wall clock time of 20 hours. We present the details of the method and quantitative elasticity images of phantoms and tissue samples.

Salvus: A flexible open-source package for waveform modelling and inversion from laboratory to global scales

NASA Astrophysics Data System (ADS)

Afanasiev, M.; Boehm, C.; van Driel, M.; Krischer, L.; May, D.; Rietmann, M.; Fichtner, A.

2016-12-01

Recent years have been witness to the application of waveform inversion to new and exciting domains, ranging from non-destructive testing to global seismology. Often, each new application brings with it novel wave propagation physics, spatial and temporal discretizations, and models of variable complexity. Adapting existing software to these novel applications often requires a significant investment of time, and acts as a barrier to progress. To combat these problems we introduce Salvus, a software package designed to solve large-scale full-waveform inverse problems, with a focus on both flexibility and performance. Based on a high order finite (spectral) element discretization, we have built Salvus to work on unstructured quad/hex meshes in both 2 or 3 dimensions, with support for P1-P3 bases on triangles and tetrahedra. A diverse (and expanding) collection of wave propagation physics are supported (i.e. coupled solid-fluid). With a focus on the inverse problem, functionality is provided to ease integration with internal and external optimization libraries. Additionally, a python-based meshing package is included to simplify the generation and manipulation of regional to global scale Earth models (quad/hex), with interfaces available to external mesh generators for complex engineering-scale applications (quad/hex/tri/tet). Finally, to ensure that the code remains accurate and maintainable, we build upon software libraries such as PETSc and Eigen, and follow modern software design and testing protocols. Salvus bridges the gap between research and production codes with a design based on C++ mixins and Python wrappers that separates the physical equations from the numerical core. This allows domain scientists to add new equations using a high-level interface, without having to worry about optimized implementation details. Our goal in this presentation is to introduce the code, show several examples across the scales, and discuss some of the extensible design points.

Salvus: A flexible high-performance and open-source package for waveform modelling and inversion from laboratory to global scales

NASA Astrophysics Data System (ADS)

Afanasiev, Michael; Boehm, Christian; van Driel, Martin; Krischer, Lion; May, Dave; Rietmann, Max; Fichtner, Andreas

2017-04-01

Recent years have been witness to the application of waveform inversion to new and exciting domains, ranging from non-destructive testing to global seismology. Often, each new application brings with it novel wave propagation physics, spatial and temporal discretizations, and models of variable complexity. Adapting existing software to these novel applications often requires a significant investment of time, and acts as a barrier to progress. To combat these problems we introduce Salvus, a software package designed to solve large-scale full-waveform inverse problems, with a focus on both flexibility and performance. Currently based on an abstract implementation of high order finite (spectral) elements, we have built Salvus to work on unstructured quad/hex meshes in both 2 or 3 dimensions, with support for P1-P3 bases on triangles and tetrahedra. A diverse (and expanding) collection of wave propagation physics are supported (i.e. viscoelastic, coupled solid-fluid). With a focus on the inverse problem, functionality is provided to ease integration with internal and external optimization libraries. Additionally, a python-based meshing package is included to simplify the generation and manipulation of regional to global scale Earth models (quad/hex), with interfaces available to external mesh generators for complex engineering-scale applications (quad/hex/tri/tet). Finally, to ensure that the code remains accurate and maintainable, we build upon software libraries such as PETSc and Eigen, and follow modern software design and testing protocols. Salvus bridges the gap between research and production codes with a design based on C++ template mixins and Python wrappers that separates the physical equations from the numerical core. This allows domain scientists to add new equations using a high-level interface, without having to worry about optimized implementation details. Our goal in this presentation is to introduce the code, show several examples across the scales, and discuss some of the extensible design points.

Distributed Cooperative Optimal Control for Multiagent Systems on Directed Graphs: An Inverse Optimal Approach.

PubMed

Zhang, Huaguang; Feng, Tao; Yang, Guang-Hong; Liang, Hongjing

2015-07-01

In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.

Using a derivative-free optimization method for multiple solutions of inverse transport problems

DOE PAGES

Armstrong, Jerawan C.; Favorite, Jeffrey A.

2016-01-14

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a meshmore » adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.« less

Full-wave Moment Tensor and Tomographic Inversions Based on 3D Strain Green Tensor

DTIC Science & Technology

2010-01-31

propagation in three-dimensional (3D) earth, linearizes the inverse problem by iteratively updating the earth model , and provides an accurate way to...self-consistent FD-SGT databases constructed from finite-difference simulations of wave propagation in full-wave tomographic models can be used to...determine the moment tensors within minutes after a seismic event, making it possible for real time monitoring using 3D models . 15. SUBJECT TERMS

Adaptive multi-step Full Waveform Inversion based on Waveform Mode Decomposition

NASA Astrophysics Data System (ADS)

Hu, Yong; Han, Liguo; Xu, Zhuo; Zhang, Fengjiao; Zeng, Jingwen

2017-04-01

Full Waveform Inversion (FWI) can be used to build high resolution velocity models, but there are still many challenges in seismic field data processing. The most difficult problem is about how to recover long-wavelength components of subsurface velocity models when seismic data is lacking of low frequency information and without long-offsets. To solve this problem, we propose to use Waveform Mode Decomposition (WMD) method to reconstruct low frequency information for FWI to obtain a smooth model, so that the initial model dependence of FWI can be reduced. In this paper, we use adjoint-state method to calculate the gradient for Waveform Mode Decomposition Full Waveform Inversion (WMDFWI). Through the illustrative numerical examples, we proved that the low frequency which is reconstructed by WMD method is very reliable. WMDFWI in combination with the adaptive multi-step inversion strategy can obtain more faithful and accurate final inversion results. Numerical examples show that even if the initial velocity model is far from the true model and lacking of low frequency information, we still can obtain good inversion results with WMD method. From numerical examples of anti-noise test, we see that the adaptive multi-step inversion strategy for WMDFWI has strong ability to resist Gaussian noise. WMD method is promising to be able to implement for the land seismic FWI, because it can reconstruct the low frequency information, lower the dominant frequency in the adjoint source, and has a strong ability to resist noise.

A simulation based method to assess inversion algorithms for transverse relaxation data

NASA Astrophysics Data System (ADS)

Ghosh, Supriyo; Keener, Kevin M.; Pan, Yong

2008-04-01

NMR relaxometry is a very useful tool for understanding various chemical and physical phenomena in complex multiphase systems. A Carr-Purcell-Meiboom-Gill (CPMG) [P.T. Callaghan, Principles of Nuclear Magnetic Resonance Microscopy, Clarendon Press, Oxford, 1991] experiment is an easy and quick way to obtain transverse relaxation constant (T2) in low field. Most of the samples usually have a distribution of T2 values. Extraction of this distribution of T2s from the noisy decay data is essentially an ill-posed inverse problem. Various inversion approaches have been used to solve this problem, to date. A major issue in using an inversion algorithm is determining how accurate the computed distribution is. A systematic analysis of an inversion algorithm, UPEN [G.C. Borgia, R.J.S. Brown, P. Fantazzini, Uniform-penalty inversion of multiexponential decay data, Journal of Magnetic Resonance 132 (1998) 65-77; G.C. Borgia, R.J.S. Brown, P. Fantazzini, Uniform-penalty inversion of multiexponential decay data II. Data spacing, T2 data, systematic data errors, and diagnostics, Journal of Magnetic Resonance 147 (2000) 273-285] was performed by means of simulated CPMG data generation. Through our simulation technique and statistical analyses, the effects of various experimental parameters on the computed distribution were evaluated. We converged to the true distribution by matching up the inversion results from a series of true decay data and a noisy simulated data. In addition to simulation studies, the same approach was also applied on real experimental data to support the simulation results.

Training-Image Based Geostatistical Inversion Using a Spatial Generative Adversarial Neural Network

NASA Astrophysics Data System (ADS)

Laloy, Eric; Hérault, Romain; Jacques, Diederik; Linde, Niklas

2018-01-01

Probabilistic inversion within a multiple-point statistics framework is often computationally prohibitive for high-dimensional problems. To partly address this, we introduce and evaluate a new training-image based inversion approach for complex geologic media. Our approach relies on a deep neural network of the generative adversarial network (GAN) type. After training using a training image (TI), our proposed spatial GAN (SGAN) can quickly generate 2-D and 3-D unconditional realizations. A key characteristic of our SGAN is that it defines a (very) low-dimensional parameterization, thereby allowing for efficient probabilistic inversion using state-of-the-art Markov chain Monte Carlo (MCMC) methods. In addition, available direct conditioning data can be incorporated within the inversion. Several 2-D and 3-D categorical TIs are first used to analyze the performance of our SGAN for unconditional geostatistical simulation. Training our deep network can take several hours. After training, realizations containing a few millions of pixels/voxels can be produced in a matter of seconds. This makes it especially useful for simulating many thousands of realizations (e.g., for MCMC inversion) as the relative cost of the training per realization diminishes with the considered number of realizations. Synthetic inversion case studies involving 2-D steady state flow and 3-D transient hydraulic tomography with and without direct conditioning data are used to illustrate the effectiveness of our proposed SGAN-based inversion. For the 2-D case, the inversion rapidly explores the posterior model distribution. For the 3-D case, the inversion recovers model realizations that fit the data close to the target level and visually resemble the true model well.

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

Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.

An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems.more » Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.« less

Mathematics of Computed Tomography

NASA Astrophysics Data System (ADS)

Hawkins, William Grant

A review of the applications of the Radon transform is presented, with emphasis on emission computed tomography and transmission computed tomography. The theory of the 2D and 3D Radon transforms, and the effects of attenuation for emission computed tomography are presented. The algebraic iterative methods, their importance and limitations are reviewed. Analytic solutions of the 2D problem the convolution and frequency filtering methods based on linear shift invariant theory, and the solution of the circular harmonic decomposition by integral transform theory--are reviewed. The relation between the invisible kernels, the inverse circular harmonic transform, and the consistency conditions are demonstrated. The discussion and review are extended to the 3D problem-convolution, frequency filtering, spherical harmonic transform solutions, and consistency conditions. The Cormack algorithm based on reconstruction with Zernike polynomials is reviewed. An analogous algorithm and set of reconstruction polynomials is developed for the spherical harmonic transform. The relations between the consistency conditions, boundary conditions and orthogonal basis functions for the 2D projection harmonics are delineated and extended to the 3D case. The equivalence of the inverse circular harmonic transform, the inverse Radon transform, and the inverse Cormack transform is presented. The use of the number of nodes of a projection harmonic as a filter is discussed. Numerical methods for the efficient implementation of angular harmonic algorithms based on orthogonal functions and stable recursion are presented. The derivation of a lower bound for the signal-to-noise ratio of the Cormack algorithm is derived.

First Calderón Prize

NASA Astrophysics Data System (ADS)

Rundell, William; Somersalo, Erkki

2008-07-01

The Inverse Problems International Association (IPIA) awarded the first Calderón Prize to Matti Lassas for his outstanding contributions to the field of inverse problems, especially in geometric inverse problems. The Calderón Prize is given to a researcher under the age of 40 who has made distinguished contributions to the field of inverse problems broadly defined. The first Calderón Prize Committee consisted of Professors Adrian Nachman, Lassi Päivärinta, William Rundell (chair), and Michael Vogelius. William Rundell For the Calderón Prize Committee Prize ceremony The ceremony awarding the Calderón Prize. Matti Lassas is on the left. He and William Rundell are on the right. Photos by P Stefanov. Brief Biography of Matti Lassas Matti Lassas was born in 1969 in Helsinki, Finland, and studied at the University of Helsinki. He finished his Master's studies in 1992 in three years and earned his PhD in 1996. His PhD thesis, written under the supervision of Professor Erkki Somersalo was entitled `Non-selfadjoint inverse spectral problems and their applications to random bodies'. Already in his thesis, Matti demonstrated a remarkable command of different fields of mathematics, bringing together the spectral theory of operators, geometry of Riemannian surfaces, Maxwell's equations and stochastic analysis. He has continued to develop all of these branches in the framework of inverse problems, the most remarkable results perhaps being in the field of differential geometry and inverse problems. Matti has always been a very generous researcher, sharing his ideas with his numerous collaborators. He has authored over sixty scientific articles, among which a monograph on inverse boundary spectral problems with Alexander Kachalov and Yaroslav Kurylev and over forty articles in peer reviewed journals of the highest standards. To get an idea of the wide range of Matti's interests, it is enough to say that he also has three US patents on medical imaging applications. Matti is currently professor of mathematics at Helsinki University of Technology, where he has created his own line of research with young talented researchers around him. He is a central person in the Centre of Excellence in Inverse Problems Research of the Academy of Finland. Previously, Matti Lassas has won several awards in his home country, including the prestigious Vaisala price of the Finnish Academy of Science and Letters in 2004. He is a highly esteemed colleague, teacher and friend, and the Great Diving Beetle of the Finnish Inverse Problems Society (http://venda.uku.fi/research/FIPS/), an honorary title for a person who has no fear of the deep. Erkki Somersalo

High performance GPU processing for inversion using uniform grid searches

NASA Astrophysics Data System (ADS)

Venetis, Ioannis E.; Saltogianni, Vasso; Stiros, Stathis; Gallopoulos, Efstratios

2017-04-01

Many geophysical problems are described by systems of redundant, highly non-linear systems of ordinary equations with constant terms deriving from measurements and hence representing stochastic variables. Solution (inversion) of such problems is based on numerical, optimization methods, based on Monte Carlo sampling or on exhaustive searches in cases of two or even three "free" unknown variables. Recently the TOPological INVersion (TOPINV) algorithm, a grid search-based technique in the Rn space, has been proposed. TOPINV is not based on the minimization of a certain cost function and involves only forward computations, hence avoiding computational errors. The basic concept is to transform observation equations into inequalities on the basis of an optimization parameter k and of their standard errors, and through repeated "scans" of n-dimensional search grids for decreasing values of k to identify the optimal clusters of gridpoints which satisfy observation inequalities and by definition contain the "true" solution. Stochastic optimal solutions and their variance-covariance matrices are then computed as first and second statistical moments. Such exhaustive uniform searches produce an excessive computational load and are extremely time consuming for common computers based on a CPU. An alternative is to use a computing platform based on a GPU, which nowadays is affordable to the research community, which provides a much higher computing performance. Using the CUDA programming language to implement TOPINV allows the investigation of the attained speedup in execution time on such a high performance platform. Based on synthetic data we compared the execution time required for two typical geophysical problems, modeling magma sources and seismic faults, described with up to 18 unknown variables, on both CPU/FORTRAN and GPU/CUDA platforms. The same problems for several different sizes of search grids (up to 1012 gridpoints) and numbers of unknown variables were solved on both platforms, and execution time as a function of the grid dimension for each problem was recorded. Results indicate an average speedup in calculations by a factor of 100 on the GPU platform; for example problems with 1012 grid-points require less than two hours instead of several days on conventional desktop computers. Such a speedup encourages the application of TOPINV on high performance platforms, as a GPU, in cases where nearly real time decisions are necessary, for example finite fault modeling to identify possible tsunami sources.

3-D Magnetotelluric Forward Modeling And Inversion Incorporating Topography By Using Vector Finite-Element Method Combined With Divergence Corrections Based On The Magnetic Field (VFEH++)

NASA Astrophysics Data System (ADS)

Shi, X.; Utada, H.; Jiaying, W.

2009-12-01

The vector finite-element method combined with divergence corrections based on the magnetic field H, referred to as VFEH++ method, is developed to simulate the magnetotelluric (MT) responses of 3-D conductivity models. The advantages of the new VFEH++ method are the use of edge-elements to eliminate the vector parasites and the divergence corrections to explicitly guarantee the divergence-free conditions in the whole modeling domain. 3-D MT topographic responses are modeling using the new VFEH++ method, and are compared with those calculated by other numerical methods. The results show that MT responses can be modeled highly accurate using the VFEH+ +method. The VFEH++ algorithm is also employed for the 3-D MT data inversion incorporating topography. The 3-D MT inverse problem is formulated as a minimization problem of the regularized misfit function. In order to avoid the huge memory requirement and very long time for computing the Jacobian sensitivity matrix for Gauss-Newton method, we employ the conjugate gradient (CG) approach to solve the inversion equation. In each iteration of CG algorithm, the cost computation is the product of the Jacobian sensitivity matrix with a model vector x or its transpose with a data vector y, which can be transformed into two pseudo-forwarding modeling. This avoids the full explicitly Jacobian matrix calculation and storage which leads to considerable savings in the memory required by the inversion program in PC computer. The performance of CG algorithm will be illustrated by several typical 3-D models with horizontal earth surface and topographic surfaces. The results show that the VFEH++ and CG algorithms can be effectively employed to 3-D MT field data inversion.

Hydrologic characterization of desert soils with varying degrees of pedogenesis: 2. Inverse modeling for eff ective properties

USGS Publications Warehouse

Mirus, B.B.; Perkins, K.S.; Nimmo, J.R.; Singha, K.

2009-01-01

To understand their relation to pedogenic development, soil hydraulic properties in the Mojave Desert were investi- gated for three deposit types: (i) recently deposited sediments in an active wash, (ii) a soil of early Holocene age, and (iii) a highly developed soil of late Pleistocene age. Eff ective parameter values were estimated for a simplifi ed model based on Richards' equation using a fl ow simulator (VS2D), an inverse algorithm (UCODE-2005), and matric pressure and water content data from three ponded infi ltration experiments. The inverse problem framework was designed to account for the eff ects of subsurface lateral spreading of infi ltrated water. Although none of the inverse problems converged on a unique, best-fi t parameter set, a minimum standard error of regression was reached for each deposit type. Parameter sets from the numerous inversions that reached the minimum error were used to develop probability distribu tions for each parameter and deposit type. Electrical resistance imaging obtained for two of the three infi ltration experiments was used to independently test fl ow model performance. Simulations for the active wash and Holocene soil successfully depicted the lateral and vertical fl uxes. Simulations of the more pedogenically developed Pleistocene soil did not adequately replicate the observed fl ow processes, which would require a more complex conceptual model to include smaller scale heterogeneities. The inverse-modeling results, however, indicate that with increasing age, the steep slope of the soil water retention curve shitis toward more negative matric pressures. Assigning eff ective soil hydraulic properties based on soil age provides a promising framework for future development of regional-scale models of soil moisture dynamics in arid environments for land-management applications. ?? Soil Science Society of America.

Prediction-Correction Algorithms for Time-Varying Constrained Optimization

DOE PAGES

Simonetto, Andrea; Dall'Anese, Emiliano

2017-07-26

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do notmore » require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.« less

Identification of dynamic characteristics of flexible rotors as dynamic inverse problem

NASA Technical Reports Server (NTRS)

Roisman, W. P.; Vajingortin, L. D.

1991-01-01

The problem of dynamic and balancing of flexible rotors were considered, which were set and solved as the problem of the identification of flexible rotor systems, which is the same as the inverse problem of the oscillation theory dealing with the task of the identifying the outside influences and system parameters on the basis of the known laws of motion. This approach to the problem allows the disclosure the picture of disbalances throughout the rotor-under-test (which traditional methods of flexible rotor balancing, based on natural oscillations, could not provide), and identify dynamic characteristics of the system, which correspond to a selected mathematical model. Eventually, various methods of balancing were developed depending on the special features of the machines as to their design, technology, and operation specifications. Also, theoretical and practical methods are given for the flexible rotor balancing at far from critical rotation frequencies, which does not necessarily require the knowledge forms of oscillation, dissipation, and elasticity and inertia characteristics, and to use testing masses.

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

Simonetto, Andrea; Dall'Anese, Emiliano

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do notmore » require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.« less

ASKI: A modular toolbox for scattering-integral-based seismic full waveform inversion and sensitivity analysis utilizing external forward codes

NASA Astrophysics Data System (ADS)

Schumacher, Florian; Friederich, Wolfgang

Due to increasing computational resources, the development of new numerically demanding methods and software for imaging Earth's interior remains of high interest in Earth sciences. Here, we give a description from a user's and programmer's perspective of the highly modular, flexible and extendable software package ASKI-Analysis of Sensitivity and Kernel Inversion-recently developed for iterative scattering-integral-based seismic full waveform inversion. In ASKI, the three fundamental steps of solving the seismic forward problem, computing waveform sensitivity kernels and deriving a model update are solved by independent software programs that interact via file output/input only. Furthermore, the spatial discretizations of the model space used for solving the seismic forward problem and for deriving model updates, respectively, are kept completely independent. For this reason, ASKI does not contain a specific forward solver but instead provides a general interface to established community wave propagation codes. Moreover, the third fundamental step of deriving a model update can be repeated at relatively low costs applying different kinds of model regularization or re-selecting/weighting the inverted dataset without need to re-solve the forward problem or re-compute the kernels. Additionally, ASKI offers the user sensitivity and resolution analysis tools based on the full sensitivity matrix and allows to compose customized workflows in a consistent computational environment. ASKI is written in modern Fortran and Python, it is well documented and freely available under terms of the GNU General Public License (http://www.rub.de/aski).

Mantle Circulation Models with variational data assimilation: Inferring past mantle flow and structure from plate motion histories and seismic tomography

NASA Astrophysics Data System (ADS)

Bunge, H.; Hagelberg, C.; Travis, B.

2002-12-01

EarthScope will deliver data on structure and dynamics of continental North America and the underlying mantle on an unprecedented scale. Indeed, the scope of EarthScope makes its mission comparable to the large remote sensing efforts that are transforming the oceanographic and atmospheric sciences today. Arguably the main impact of new solid Earth observing systems is to transform our use of geodynamic models increasingly from conditions that are data poor to an environment that is data rich. Oceanographers and meteorologists already have made substantial progress in adapting to this environment, by developing new approaches of interpreting oceanographic and atmospheric data objectively through data assimilation methods in their models. However, a similarly rigorous theoretical framework for merging EarthScope derived solid Earth data with geodynamic models has yet to be devised. Here we explore the feasibility of data assimilation in mantle convection studies in an attempt to fit global geodynamic model calculations explicitly to tomographic and tectonic constraints. This is an inverse problem not quite unlike the inverse problem of finding optimal seismic velocity structures faced by seismologists. We derive the generalized inverse of mantle convection from a variational approach and present the adjoint equations of mantle flow. The substantial computational burden associated with solutions to the generalized inverse problem of mantle convection is made feasible using a highly efficient finite element approach based on the 3-D spherical fully parallelized mantle dynamics code TERRA, implemented on a cost-effective topical PC-cluster (geowulf) dedicated specifically to large-scale geophysical simulations. This dedicated geophysical modeling computer allows us to investigate global inverse convection problems having a spatial discretization of less than 50 km throughout the mantle. We present a synthetic high-resolution modeling experiment to demonstrate that mid-Cretaceous mantle structure can be inferred accurately from our inverse approach assuming present-day mantle structure is well-known, even if an initial first guess assumption about the mid-Cretaceous mantle involved only a simple 1-D radial temperature profile. We suggest that geodynamic inverse modeling should make it possible to infer a number of flow parameters from observational constraints of the mantle.

Porosity Estimation By Artificial Neural Networks Inversion . Application to Algerian South Field

NASA Astrophysics Data System (ADS)

Eladj, Said; Aliouane, Leila; Ouadfeul, Sid-Ali

2017-04-01

One of the main geophysicist's current challenge is the discovery and the study of stratigraphic traps, this last is a difficult task and requires a very fine analysis of the seismic data. The seismic data inversion allows obtaining lithological and stratigraphic information for the reservoir characterization . However, when solving the inverse problem we encounter difficult problems such as: Non-existence and non-uniqueness of the solution add to this the instability of the processing algorithm. Therefore, uncertainties in the data and the non-linearity of the relationship between the data and the parameters must be taken seriously. In this case, the artificial intelligence techniques such as Artificial Neural Networks(ANN) is used to resolve this ambiguity, this can be done by integrating different physical properties data which requires a supervised learning methods. In this work, we invert the acoustic impedance 3D seismic cube using the colored inversion method, then, the introduction of the acoustic impedance volume resulting from the first step as an input of based model inversion method allows to calculate the Porosity volume using the Multilayer Perceptron Artificial Neural Network. Application to an Algerian South hydrocarbon field clearly demonstrate the power of the proposed processing technique to predict the porosity for seismic data, obtained results can be used for reserves estimation, permeability prediction, recovery factor and reservoir monitoring. Keywords: Artificial Neural Networks, inversion, non-uniqueness , nonlinear, 3D porosity volume, reservoir characterization .

PREFACE: Inverse Problems in Applied Sciences—towards breakthrough

NASA Astrophysics Data System (ADS)

Cheng, Jin; Iso, Yuusuke; Nakamura, Gen; Yamamoto, Masahiro

2007-06-01

These are the proceedings of the international conference `Inverse Problems in Applied Sciences—towards breakthrough' which was held at Hokkaido University, Sapporo, Japan on 3-7 July 2006 (http://coe.math.sci.hokudai.ac.jp/sympo/inverse/). There were 88 presentations and more than 100 participants, and we are proud to say that the conference was very successful. Nowadays, many new activities on inverse problems are flourishing at many centers of research around the world, and the conference has successfully gathered a world-wide variety of researchers. We believe that this volume contains not only main papers, but also conveys the general status of current research into inverse problems. This conference was the third biennial international conference on inverse problems, the core of which is the Pan-Pacific Asian area. The purpose of this series of conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries, and to lead the organization of activities concerning inverse problems centered in East Asia. The first conference was held at City University of Hong Kong in January 2002 and the second was held at Fudan University in June 2004. Following the preceding two successes, the third conference was organized in order to extend the scope of activities and build useful bridges to the next conference in Seoul in 2008. Therefore this third biennial conference was intended not only to establish collaboration and links between researchers in Asia and leading researchers worldwide in inverse problems but also to nurture interdisciplinary collaboration in theoretical fields such as mathematics, applied fields and evolving aspects of inverse problems. For these purposes, we organized tutorial lectures, serial lectures and a panel discussion as well as conference research presentations. This volume contains three lecture notes from the tutorial and serial lectures, and 22 papers. Especially at this flourishing time, it is necessary to carefully analyse the current status of inverse problems for further development. Thus we have opened with the panel discussion entitled `Future of Inverse Problems' with panelists: Professors J Cheng, H W Engl, V Isakov, R Kress, J-K Seo, G Uhlmann and the commentator: Elaine Longden-Chapman from IOP Publishing. The aims of the panel discussion were to examine the current research status from various viewpoints, to discuss how we can overcome any difficulties and how we can promote young researchers and open new possibilities for inverse problems such as industrial linkages. As one output, the panel discussion has triggered the organization of the Inverse Problems International Association (IPIA) which has led to its first international congress in the summer of 2007. Another remarkable outcome of the conference is, of course, the present volume: this is the very high quality online proceedings volume of Journal of Physics: Conference Series. Readers can see in these proceedings very well written tutorial lecture notes, and very high quality original research and review papers all of which show what was achieved by the time the conference was held. The electronic publication of the proceedings is a new way of publicizing the achievement of the conference. It has the advantage of wide circulation and cost reduction. We believe this is a most efficient method for our needs and purposes. We would like to take this opportunity to acknowledge all the people who helped to organize the conference. Guest Editors Jin Cheng, Fudan University, Shanghai, China Yuusuke Iso, Kyoto University, Kyoto, Japan Gen Nakamura, Hokkaido University, Sapporo, Japan Masahiro Yamamoto, University of Tokyo, Tokyo, Japan

2D Inversion of Transient Electromagnetic Method (TEM)

NASA Astrophysics Data System (ADS)

Bortolozo, Cassiano Antonio; Luís Porsani, Jorge; Acácio Monteiro dos Santos, Fernando

2017-04-01

A new methodology was developed for 2D inversion of Transient Electromagnetic Method (TEM). The methodology consists in the elaboration of a set of routines in Matlab code for modeling and inversion of TEM data and the determination of the most efficient field array for the problem. In this research, the 2D TEM modeling uses the finite differences discretization. To solve the inversion problem, were applied an algorithm based on Marquardt technique, also known as Ridge Regression. The algorithm is stable and efficient and it is widely used in geoelectrical inversion problems. The main advantage of 1D survey is the rapid data acquisition in a large area, but in regions with two-dimensional structures or that need more details, is essential to use two-dimensional interpretation methodologies. For an efficient field acquisition we used in an innovative form the fixed-loop array, with a square transmitter loop (200m x 200m) and 25m spacing between the sounding points. The TEM surveys were conducted only inside the transmitter loop, in order to not deal with negative apparent resistivity values. Although it is possible to model the negative values, it makes the inversion convergence more difficult. Therefore the methodology described above has been developed in order to achieve maximum optimization of data acquisition. Since it is necessary only one transmitter loop disposition in the surface for each series of soundings inside the loop. The algorithms were tested with synthetic data and the results were essential to the interpretation of the results with real data and will be useful in future situations. With the inversion of the real data acquired over the Paraná Sedimentary Basin (PSB) was successful realized a 2D TEM inversion. The results indicate a robust geoelectrical characterization for the sedimentary and crystalline aquifers in the PSB. Therefore, using a new and relevant approach for 2D TEM inversion, this research effectively contributed to map the most promising regions for groundwater exploration. In addition, there was the development of new geophysical software that can be applied as an important tool for many geological/hydrogeological applications and educational purposes.

Toward 2D and 3D imaging of magnetic nanoparticles using EPR measurements.

PubMed

Coene, A; Crevecoeur, G; Leliaert, J; Dupré, L

2015-09-01

Magnetic nanoparticles (MNPs) are an important asset in many biomedical applications. An effective working of these applications requires an accurate knowledge of the spatial MNP distribution. A promising, noninvasive, and sensitive technique to visualize MNP distributions in vivo is electron paramagnetic resonance (EPR). Currently only 1D MNP distributions can be reconstructed. In this paper, the authors propose extending 1D EPR toward 2D and 3D using computer simulations to allow accurate imaging of MNP distributions. To find the MNP distribution belonging to EPR measurements, an inverse problem needs to be solved. The solution of this inverse problem highly depends on the stability of the inverse problem. The authors adapt 1D EPR imaging to realize the imaging of multidimensional MNP distributions. Furthermore, the authors introduce partial volume excitation in which only parts of the volume are imaged to increase stability of the inverse solution and to speed up the measurements. The authors simulate EPR measurements of different 2D and 3D MNP distributions and solve the inverse problem. The stability is evaluated by calculating the condition measure and by comparing the actual MNP distribution to the reconstructed MNP distribution. Based on these simulations, the authors define requirements for the EPR system to cope with the added dimensions. Moreover, the authors investigate how EPR measurements should be conducted to improve the stability of the associated inverse problem and to increase reconstruction quality. The approach used in 1D EPR can only be employed for the reconstruction of small volumes in 2D and 3D EPRs due to numerical instability of the inverse solution. The authors performed EPR measurements of increasing cylindrical volumes and evaluated the condition measure. This showed that a reduction of the inherent symmetry in the EPR methodology is necessary. By reducing the symmetry of the EPR setup, quantitative images of larger volumes can be obtained. The authors found that, by selectively exciting parts of the volume, the authors could increase the reconstruction quality even further while reducing the amount of measurements. Additionally, the inverse solution of this activation method degrades slower for increasing volumes. Finally, the methodology was applied to noisy EPR measurements: using the reduced EPR setup's symmetry and the partial activation method, an increase in reconstruction quality of ≈ 80% can be seen with a speedup of the measurements with 10%. Applying the aforementioned requirements to the EPR setup and stabilizing the EPR measurements showed a tremendous increase in noise robustness, thereby making EPR a valuable method for quantitative imaging of multidimensional MNP distributions.

Nonlinear functional approximation with networks using adaptive neurons

NASA Technical Reports Server (NTRS)

Tawel, Raoul

1992-01-01

A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.

Estimation of coefficients and boundary parameters in hyperbolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Murphy, K. A.

1984-01-01

Semi-discrete Galerkin approximation schemes are considered in connection with inverse problems for the estimation of spatially varying coefficients and boundary condition parameters in second order hyperbolic systems typical of those arising in 1-D surface seismic problems. Spline based algorithms are proposed for which theoretical convergence results along with a representative sample of numerical findings are given.

Using the ARTMO toolbox for automated retrieval of biophysical parameters through radiative transfer model inversion: Optimizing LUT-based inversion

NASA Astrophysics Data System (ADS)

Verrelst, J.; Rivera, J. P.; Leonenko, G.; Alonso, L.; Moreno, J.

2012-04-01

Radiative transfer (RT) modeling plays a key role for earth observation (EO) because it is needed to design EO instruments and to develop and test inversion algorithms. The inversion of a RT model is considered as a successful approach for the retrieval of biophysical parameters because of being physically-based and generally applicable. However, to the broader community this approach is considered as laborious because of its many processing steps and expert knowledge is required to realize precise model parameterization. We have recently developed a radiative transfer toolbox ARTMO (Automated Radiative Transfer Models Operator) with the purpose of providing in a graphical user interface (GUI) essential models and tools required for terrestrial EO applications such as model inversion. In short, the toolbox allows the user: i) to choose between various plant leaf and canopy RT models (e.g. models from the PROSPECT and SAIL family, FLIGHT), ii) to choose between spectral band settings of various air- and space-borne sensors or defining own sensor settings, iii) to simulate a massive amount of spectra based on a look up table (LUT) approach and storing it in a relational database, iv) to plot spectra of multiple models and compare them with measured spectra, and finally, v) to run model inversion against optical imagery given several cost options and accuracy estimates. In this work ARTMO was used to tackle some well-known problems related to model inversion. According to Hadamard conditions, mathematical models of physical phenomena are mathematically invertible if the solution of the inverse problem to be solved exists, is unique and depends continuously on data. This assumption is not always met because of the large number of unknowns and different strategies have been proposed to overcome this problem. Several of these strategies have been implemented in ARTMO and were here analyzed to optimize the inversion performance. Data came from the SPARC-2003 dataset, which was acquired on the agricultural test site Barrax, Spain. LUTs were created using the 4SAIL and FLIGHT models and were inverted against CHRIS data in order to retrieve maps of chlorophyll content (chl) and leaf area index (LAI). The following inversion steps have been optimized: 1. Cost function. The performances of about 50 different cost functions (i.e. minimum distance functions) were compared. Remarkably, in none of the studied cases the widely used root mean square error (RMSE) led to most accurate results. Depending on the retrieved parameter, more successful functions were: 'Sharma and Mittal', 'Shannońs entropy', 'Hellinger distance', 'Pearsońs chi-square'. 2. Gaussian noise. Earth observation data typically encompass a certain degree of noise due to errors related to radiometric and geometric processing. In all cases, adding 5% Gaussian noise to the simulated spectra led to more accurate retrievals as compared to without noise. 3. Average of multiple best solutions. Because multiple parameter combinations may lead to the same spectra, a way to overcome this problem is not searching for the top best match but for a percentage of best matches. Optimized retrievals were encountered when including an average of 7% (Chl) to 10% (LAI) top best matches. 4. Integration of estimates. The option is provided to integrate estimates of biochemical contents at the canopy level (e.g., total chlorophyll: Chl × LAI, or water: Cw × LAI), which can lead to increased robustness and accuracy. 5. Class-based inversion. This option is probably ARTMÓs most powerful feature as it allows model parameterization depending on the imagés land cover classes (e.g. different soil or vegetation types). Class-based inversion can lead to considerably improved accuracies compared to one generic class. Results suggest that 4SAIL and FLIGHT performed alike for Chl but not for LAI. While both models rely on the leaf model PROSPECT for Chl retrieval, their different nature (e.g. numerical vs. ray tracing) may cause that retrieval of structural parameters such as LAI differ. Finally, it should be noted that the whole analysis can be intuitively performed by the toolbox. ARTMO is freely available to the EO community for further development. Expressions of interest are welcome and should be directed to the corresponding author.

Solvability of the electrocardiology inverse problem for a moving dipole.

PubMed

Tolkachev, V; Bershadsky, B; Nemirko, A

1993-01-01

New formulations of the direct and inverse problems for the moving dipole are offered. It has been suggested to limit the study by a small area on the chest surface. This lowers the role of the medium inhomogeneity. When formulating the direct problem, irregular components are considered. The algorithm of simultaneous determination of the dipole and regular noise parameters has been described and analytically investigated. It is shown that temporal overdetermination of the equations offers a single solution of the inverse problem for the four leads.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

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

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

DOE PAGES

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

MAP Estimators for Piecewise Continuous Inversion

DTIC Science & Technology

2016-08-08

MAP estimators for piecewise continuous inversion M M Dunlop1 and A M Stuart Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK E...Published 8 August 2016 Abstract We study the inverse problem of estimating a field ua from data comprising a finite set of nonlinear functionals of ua...then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP

Mature red blood cells: from optical model to inverse light-scattering problem.

PubMed

Gilev, Konstantin V; Yurkin, Maxim A; Chernyshova, Ekaterina S; Strokotov, Dmitry I; Chernyshev, Andrei V; Maltsev, Valeri P

2016-04-01

We propose a method for characterization of mature red blood cells (RBCs) morphology, based on measurement of light-scattering patterns (LSPs) of individual RBCs with the scanning flow cytometer and on solution of the inverse light-scattering (ILS) problem for each LSP. We considered a RBC shape model, corresponding to the minimal bending energy of the membrane with isotropic elasticity, and constructed an analytical approximation, which allows rapid simulation of the shape, given the diameter and minimal and maximal thicknesses. The ILS problem was solved by the nearest-neighbor interpolation using a preliminary calculated database of 250,000 theoretical LSPs. For each RBC in blood sample we determined three abovementioned shape characteristics and refractive index, which also allows us to calculate volume, surface area, sphericity index, spontaneous curvature, hemoglobin concentration and content.

Mature red blood cells: from optical model to inverse light-scattering problem

PubMed Central

Gilev, Konstantin V.; Yurkin, Maxim A.; Chernyshova, Ekaterina S.; Strokotov, Dmitry I.; Chernyshev, Andrei V.; Maltsev, Valeri P.

2016-01-01

We propose a method for characterization of mature red blood cells (RBCs) morphology, based on measurement of light-scattering patterns (LSPs) of individual RBCs with the scanning flow cytometer and on solution of the inverse light-scattering (ILS) problem for each LSP. We considered a RBC shape model, corresponding to the minimal bending energy of the membrane with isotropic elasticity, and constructed an analytical approximation, which allows rapid simulation of the shape, given the diameter and minimal and maximal thicknesses. The ILS problem was solved by the nearest-neighbor interpolation using a preliminary calculated database of 250,000 theoretical LSPs. For each RBC in blood sample we determined three abovementioned shape characteristics and refractive index, which also allows us to calculate volume, surface area, sphericity index, spontaneous curvature, hemoglobin concentration and content. PMID:27446656

Time-lapse ERT interpretation methodology for leachate injection monitoring based on multiple inversions and a clustering strategy (MICS)

NASA Astrophysics Data System (ADS)

Audebert, M.; Clément, R.; Touze-Foltz, N.; Günther, T.; Moreau, S.; Duquennoi, C.

2014-12-01

Leachate recirculation is a key process in municipal waste landfills functioning as bioreactors. To quantify the water content and to assess the leachate injection system, in-situ methods are required to obtain spatially distributed information, usually electrical resistivity tomography (ERT). This geophysical method is based on the inversion process, which presents two major problems in terms of delimiting the infiltration area. First, it is difficult for ERT users to choose an appropriate inversion parameter set. Indeed, it might not be sufficient to interpret only the optimum model (i.e. the model with the chosen regularisation strength) because it is not necessarily the model which best represents the physical process studied. Second, it is difficult to delineate the infiltration front based on resistivity models because of the smoothness of the inversion results. This paper proposes a new methodology called MICS (multiple inversions and clustering strategy), which allows ERT users to improve the delimitation of the infiltration area in leachate injection monitoring. The MICS methodology is based on (i) a multiple inversion step by varying the inversion parameter values to take a wide range of resistivity models into account and (ii) a clustering strategy to improve the delineation of the infiltration front. In this paper, MICS was assessed on two types of data. First, a numerical assessment allows us to optimise and test MICS for different infiltration area sizes, contrasts and shapes. Second, MICS was applied to a field data set gathered during leachate recirculation on a bioreactor.

Solutions to inverse plume in a crosswind problem using a predictor - corrector method

NASA Astrophysics Data System (ADS)

Vanderveer, Joseph; Jaluria, Yogesh

2013-11-01

Investigation for minimalist solutions to the inverse convection problem of a plume in a crosswind has developed a predictor - corrector method. The inverse problem is to predict the strength and location of the plume with respect to a select few downstream sampling points. This is accomplished with the help of two numerical simulations of the domain at differing source strengths, allowing the generation of two inverse interpolation functions. These functions in turn are utilized by the predictor step to acquire the plume strength. Finally, the same interpolation functions with the corrections from the plume strength are used to solve for the plume location. Through optimization of the relative location of the sampling points, the minimum number of samples for accurate predictions is reduced to two for the plume strength and three for the plume location. After the optimization, the predictor-corrector method demonstrates global uniqueness of the inverse solution for all test cases. The solution error is less than 1% for both plume strength and plume location. The basic approach could be extended to other inverse convection transport problems, particularly those encountered in environmental flows.

Applied Mathematics in EM Studies with Special Emphasis on an Uncertainty Quantification and 3-D Integral Equation Modelling

NASA Astrophysics Data System (ADS)

Pankratov, Oleg; Kuvshinov, Alexey

2016-01-01

Despite impressive progress in the development and application of electromagnetic (EM) deterministic inverse schemes to map the 3-D distribution of electrical conductivity within the Earth, there is one question which remains poorly addressed—uncertainty quantification of the recovered conductivity models. Apparently, only an inversion based on a statistical approach provides a systematic framework to quantify such uncertainties. The Metropolis-Hastings (M-H) algorithm is the most popular technique for sampling the posterior probability distribution that describes the solution of the statistical inverse problem. However, all statistical inverse schemes require an enormous amount of forward simulations and thus appear to be extremely demanding computationally, if not prohibitive, if a 3-D set up is invoked. This urges development of fast and scalable 3-D modelling codes which can run large-scale 3-D models of practical interest for fractions of a second on high-performance multi-core platforms. But, even with these codes, the challenge for M-H methods is to construct proposal functions that simultaneously provide a good approximation of the target density function while being inexpensive to be sampled. In this paper we address both of these issues. First we introduce a variant of the M-H method which uses information about the local gradient and Hessian of the penalty function. This, in particular, allows us to exploit adjoint-based machinery that has been instrumental for the fast solution of deterministic inverse problems. We explain why this modification of M-H significantly accelerates sampling of the posterior probability distribution. In addition we show how Hessian handling (inverse, square root) can be made practicable by a low-rank approximation using the Lanczos algorithm. Ultimately we discuss uncertainty analysis based on stochastic inversion results. In addition, we demonstrate how this analysis can be performed within a deterministic approach. In the second part, we summarize modern trends in the development of efficient 3-D EM forward modelling schemes with special emphasis on recent advances in the integral equation approach.

Underworld results as a triple (shopping list, posterior, priors)

NASA Astrophysics Data System (ADS)

Quenette, S. M.; Moresi, L. N.; Abramson, D.

2013-12-01

When studying long-term lithosphere deformation and other such large-scale, spatially distinct and behaviour rich problems, there is a natural trade-off between the meaning of a model, the observations used to validate the model and the ability to compute over this space. For example, many models of varying lithologies, rheological properties and underlying physics may reasonably match (or not match) observables. To compound this problem, each realisation is computationally intensive, requiring high resolution, algorithm tuning and code tuning to contemporary computer hardware. It is often intractable to use sampling based assimilation methods, but with better optimisation, the window of tractability becomes wider. The ultimate goal is to find a sweet-spot where a formal assimilation method is used, and where a model affines to observations. Its natural to think of this as an inverse problem, in which the underlying physics may be fixed and the rheological properties and possibly the lithologies themselves are unknown. What happens when we push this approach and treat some portion of the underlying physics as an unknown? At its extreme this is an intractable problem. However, there is an analogy here with how we develop software for these scientific problems. What happens when we treat the changing part of a largely complete code as an unknown, where the changes are working towards this sweet-spot? When posed as a Bayesian inverse problem the result is a triple - the model changes, the real priors and the real posterior. Not only does this give meaning to the process by which a code changes, it forms a mathematical bridge from an inverse problem to compiler optimisations given such changes. As a stepping stone example we show a regional scale heat flow model with constraining observations, and the inverse process including increasingly complexity in the software. The implementation uses Underworld-GT (Underworld plus research extras to import geology and export geothermic measures, etc). Underworld uses StGermain an early (partial) implementation of the theories described here.

Probability density of spatially distributed soil moisture inferred from crosshole georadar traveltime measurements

NASA Astrophysics Data System (ADS)

Linde, N.; Vrugt, J. A.

2009-04-01

Geophysical models are increasingly used in hydrological simulations and inversions, where they are typically treated as an artificial data source with known uncorrelated "data errors". The model appraisal problem in classical deterministic linear and non-linear inversion approaches based on linearization is often addressed by calculating model resolution and model covariance matrices. These measures offer only a limited potential to assign a more appropriate "data covariance matrix" for future hydrological applications, simply because the regularization operators used to construct a stable inverse solution bear a strong imprint on such estimates and because the non-linearity of the geophysical inverse problem is not explored. We present a parallelized Markov Chain Monte Carlo (MCMC) scheme to efficiently derive the posterior spatially distributed radar slowness and water content between boreholes given first-arrival traveltimes. This method is called DiffeRential Evolution Adaptive Metropolis (DREAM_ZS) with snooker updater and sampling from past states. Our inverse scheme does not impose any smoothness on the final solution, and uses uniform prior ranges of the parameters. The posterior distribution of radar slowness is converted into spatially distributed soil moisture values using a petrophysical relationship. To benchmark the performance of DREAM_ZS, we first apply our inverse method to a synthetic two-dimensional infiltration experiment using 9421 traveltimes contaminated with Gaussian errors and 80 different model parameters, corresponding to a model discretization of 0.3 m × 0.3 m. After this, the method is applied to field data acquired in the vadose zone during snowmelt. This work demonstrates that fully non-linear stochastic inversion can be applied with few limiting assumptions to a range of common two-dimensional tomographic geophysical problems. The main advantage of DREAM_ZS is that it provides a full view of the posterior distribution of spatially distributed soil moisture, which is key to appropriately treat geophysical parameter uncertainty and infer hydrologic models.

Extended resolvent and inverse scattering with an application to KPI

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B.

2003-08-01

We present in detail an extended resolvent approach for investigating linear problems associated to 2+1 dimensional integrable equations. Our presentation is based as an example on the nonstationary Schrödinger equation with potential being a perturbation of the one-soliton potential by means of a decaying two-dimensional function. Modification of the inverse scattering theory as well as properties of the Jost solutions and spectral data as follows from the resolvent approach are given.

Identification of the Thermal Conductivity Coefficient for Quasi-Stationary Two-Dimensional Heat Conduction Equations

NASA Astrophysics Data System (ADS)

Matsevityi, Yu. M.; Alekhina, S. V.; Borukhov, V. T.; Zayats, G. M.; Kostikov, A. O.

2017-11-01

The problem of identifying the time-dependent thermal conductivity coefficient in the initial-boundary-value problem for the quasi-stationary two-dimensional heat conduction equation in a bounded cylinder is considered. It is assumed that the temperature field in the cylinder is independent of the angular coordinate. To solve the given problem, which is related to a class of inverse problems, a mathematical approach based on the method of conjugate gradients in a functional form is being developed.

An Inverse Interpolation Method Utilizing In-Flight Strain Measurements for Determining Loads and Structural Response of Aerospace Vehicles

NASA Technical Reports Server (NTRS)

Shkarayev, S.; Krashantisa, R.; Tessler, A.

2004-01-01

An important and challenging technology aimed at the next generation of aerospace vehicles is that of structural health monitoring. The key problem is to determine accurately, reliably, and in real time the applied loads, stresses, and displacements experienced in flight, with such data establishing an information database for structural health monitoring. The present effort is aimed at developing a finite element-based methodology involving an inverse formulation that employs measured surface strains to recover the applied loads, stresses, and displacements in an aerospace vehicle in real time. The computational procedure uses a standard finite element model (i.e., "direct analysis") of a given airframe, with the subsequent application of the inverse interpolation approach. The inverse interpolation formulation is based on a parametric approximation of the loading and is further constructed through a least-squares minimization of calculated and measured strains. This procedure results in the governing system of linear algebraic equations, providing the unknown coefficients that accurately define the load approximation. Numerical simulations are carried out for problems involving various levels of structural approximation. These include plate-loading examples and an aircraft wing box. Accuracy and computational efficiency of the proposed method are discussed in detail. The experimental validation of the methodology by way of structural testing of an aircraft wing is also discussed.

Hamiltonian Monte Carlo Inversion of Seismic Sources in Complex Media

NASA Astrophysics Data System (ADS)

Fichtner, A.; Simutė, S.

2017-12-01

We present a probabilistic seismic source inversion method that properly accounts for 3D heterogeneous Earth structure and provides full uncertainty information on the timing, location and mechanism of the event. Our method rests on two essential elements: (1) reciprocity and spectral-element simulations in complex media, and (2) Hamiltonian Monte Carlo sampling that requires only a small amount of test models. Using spectral-element simulations of 3D, visco-elastic, anisotropic wave propagation, we precompute a data base of the strain tensor in time and space by placing sources at the positions of receivers. Exploiting reciprocity, this receiver-side strain data base can be used to promptly compute synthetic seismograms at the receiver locations for any hypothetical source within the volume of interest. The rapid solution of the forward problem enables a Bayesian solution of the inverse problem. For this, we developed a variant of Hamiltonian Monte Carlo (HMC) sampling. Taking advantage of easily computable derivatives, HMC converges to the posterior probability density with orders of magnitude less samples than derivative-free Monte Carlo methods. (Exact numbers depend on observational errors and the quality of the prior). We apply our method to the Japanese Islands region where we previously constrained 3D structure of the crust and upper mantle using full-waveform inversion with a minimum period of around 15 s.

Review of the inverse scattering problem at fixed energy in quantum mechanics

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.

Warhead verification as inverse problem: Applications of neutron spectrum unfolding from organic-scintillator measurements

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

Lawrence, Chris C.; Flaska, Marek; Pozzi, Sara A.

2016-08-14

Verification of future warhead-dismantlement treaties will require detection of certain warhead attributes without the disclosure of sensitive design information, and this presents an unusual measurement challenge. Neutron spectroscopy—commonly eschewed as an ill-posed inverse problem—may hold special advantages for warhead verification by virtue of its insensitivity to certain neutron-source parameters like plutonium isotopics. In this article, we investigate the usefulness of unfolded neutron spectra obtained from organic-scintillator data for verifying a particular treaty-relevant warhead attribute: the presence of high-explosive and neutron-reflecting materials. Toward this end, several improvements on current unfolding capabilities are demonstrated: deuterated detectors are shown to have superior response-matrixmore » condition to that of standard hydrogen-base scintintillators; a novel data-discretization scheme is proposed which removes important detector nonlinearities; and a technique is described for re-parameterizing the unfolding problem in order to constrain the parameter space of solutions sought, sidestepping the inverse problem altogether. These improvements are demonstrated with trial measurements and verified using accelerator-based time-of-flight calculation of reference spectra. Then, a demonstration is presented in which the elemental compositions of low-Z neutron-attenuating materials are estimated to within 10%. These techniques could have direct application in verifying the presence of high-explosive materials in a neutron-emitting test item, as well as other for treaty verification challenges.« less

Warhead verification as inverse problem: Applications of neutron spectrum unfolding from organic-scintillator measurements

NASA Astrophysics Data System (ADS)

Lawrence, Chris C.; Febbraro, Michael; Flaska, Marek; Pozzi, Sara A.; Becchetti, F. D.

2016-08-01

Verification of future warhead-dismantlement treaties will require detection of certain warhead attributes without the disclosure of sensitive design information, and this presents an unusual measurement challenge. Neutron spectroscopy—commonly eschewed as an ill-posed inverse problem—may hold special advantages for warhead verification by virtue of its insensitivity to certain neutron-source parameters like plutonium isotopics. In this article, we investigate the usefulness of unfolded neutron spectra obtained from organic-scintillator data for verifying a particular treaty-relevant warhead attribute: the presence of high-explosive and neutron-reflecting materials. Toward this end, several improvements on current unfolding capabilities are demonstrated: deuterated detectors are shown to have superior response-matrix condition to that of standard hydrogen-base scintintillators; a novel data-discretization scheme is proposed which removes important detector nonlinearities; and a technique is described for re-parameterizing the unfolding problem in order to constrain the parameter space of solutions sought, sidestepping the inverse problem altogether. These improvements are demonstrated with trial measurements and verified using accelerator-based time-of-flight calculation of reference spectra. Then, a demonstration is presented in which the elemental compositions of low-Z neutron-attenuating materials are estimated to within 10%. These techniques could have direct application in verifying the presence of high-explosive materials in a neutron-emitting test item, as well as other for treaty verification challenges.

Efficient Storage Scheme of Covariance Matrix during Inverse Modeling

NASA Astrophysics Data System (ADS)

Mao, D.; Yeh, T. J.

2013-12-01

During stochastic inverse modeling, the covariance matrix of geostatistical based methods carries the information about the geologic structure. Its update during iterations reflects the decrease of uncertainty with the incorporation of observed data. For large scale problem, its storage and update cost too much memory and computational resources. In this study, we propose a new efficient storage scheme for storage and update. Compressed Sparse Column (CSC) format is utilized to storage the covariance matrix, and users can assign how many data they prefer to store based on correlation scales since the data beyond several correlation scales are usually not very informative for inverse modeling. After every iteration, only the diagonal terms of the covariance matrix are updated. The off diagonal terms are calculated and updated based on shortened correlation scales with a pre-assigned exponential model. The correlation scales are shortened by a coefficient, i.e. 0.95, every iteration to show the decrease of uncertainty. There is no universal coefficient for all the problems and users are encouraged to try several times. This new scheme is tested with 1D examples first. The estimated results and uncertainty are compared with the traditional full storage method. In the end, a large scale numerical model is utilized to validate this new scheme.

Projected Regression Methods for Inverting Fredholm Integrals: Formalism and Application to Analytical Continuation

NASA Astrophysics Data System (ADS)

Arsenault, Louis-Francois; Neuberg, Richard; Hannah, Lauren A.; Millis, Andrew J.

We present a machine learning-based statistical regression approach to the inversion of Fredholm integrals of the first kind by studying an important example for the quantum materials community, the analytical continuation problem of quantum many-body physics. It involves reconstructing the frequency dependence of physical excitation spectra from data obtained at specific points in the complex frequency plane. The approach provides a natural regularization in cases where the inverse of the Fredholm kernel is ill-conditioned and yields robust error metrics. The stability of the forward problem permits the construction of a large database of input-output pairs. Machine learning methods applied to this database generate approximate solutions which are projected onto the subspace of functions satisfying relevant constraints. We show that for low input noise the method performs as well or better than Maximum Entropy (MaxEnt) under standard error metrics, and is substantially more robust to noise. We expect the methodology to be similarly effective for any problem involving a formally ill-conditioned inversion, provided that the forward problem can be efficiently solved. AJM was supported by the Office of Science of the U.S. Department of Energy under Subcontract No. 3F-3138 and LFA by the Columbia Univeristy IDS-ROADS project, UR009033-05 which also provided part support to RN and LH.

Efficient Inversion of Mult-frequency and Multi-Source Electromagnetic Data

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

Gary D. Egbert

2007-03-22

The project covered by this report focused on development of efficient but robust non-linear inversion algorithms for electromagnetic induction data, in particular for data collected with multiple receivers, and multiple transmitters, a situation extremely common in eophysical EM subsurface imaging methods. A key observation is that for such multi-transmitter problems each step in commonly used linearized iterative limited memory search schemes such as conjugate gradients (CG) requires solution of forward and adjoint EM problems for each of the N frequencies or sources, essentially generating data sensitivities for an N dimensional data-subspace. These multiple sensitivities allow a good approximation to themore » full Jacobian of the data mapping to be built up in many fewer search steps than would be required by application of textbook optimization methods, which take no account of the multiplicity of forward problems that must be solved for each search step. We have applied this idea to a develop a hybrid inversion scheme that combines features of the iterative limited memory type methods with a Newton-type approach using a partial calculation of the Jacobian. Initial tests on 2D problems show that the new approach produces results essentially identical to a Newton type Occam minimum structure inversion, while running more rapidly than an iterative (fixed regularization parameter) CG style inversion. Memory requirements, while greater than for something like CG, are modest enough that even in 3D the scheme should allow 3D inverse problems to be solved on a common desktop PC, at least for modest (~ 100 sites, 15-20 frequencies) data sets. A secondary focus of the research has been development of a modular system for EM inversion, using an object oriented approach. This system has proven useful for more rapid prototyping of inversion algorithms, in particular allowing initial development and testing to be conducted with two-dimensional example problems, before approaching more computationally cumbersome three-dimensional problems.« less

Comparison of optimal design methods in inverse problems

NASA Astrophysics Data System (ADS)

Banks, H. T.; Holm, K.; Kappel, F.

2011-07-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).

Inverse regression-based uncertainty quantification algorithms for high-dimensional models: Theory and practice

NASA Astrophysics Data System (ADS)

Li, Weixuan; Lin, Guang; Li, Bing

2016-09-01

Many uncertainty quantification (UQ) approaches suffer from the curse of dimensionality, that is, their computational costs become intractable for problems involving a large number of uncertainty parameters. In these situations, the classic Monte Carlo often remains the preferred method of choice because its convergence rate O (n - 1 / 2), where n is the required number of model simulations, does not depend on the dimension of the problem. However, many high-dimensional UQ problems are intrinsically low-dimensional, because the variation of the quantity of interest (QoI) is often caused by only a few latent parameters varying within a low-dimensional subspace, known as the sufficient dimension reduction (SDR) subspace in the statistics literature. Motivated by this observation, we propose two inverse regression-based UQ algorithms (IRUQ) for high-dimensional problems. Both algorithms use inverse regression to convert the original high-dimensional problem to a low-dimensional one, which is then efficiently solved by building a response surface for the reduced model, for example via the polynomial chaos expansion. The first algorithm, which is for the situations where an exact SDR subspace exists, is proved to converge at rate O (n-1), hence much faster than MC. The second algorithm, which doesn't require an exact SDR, employs the reduced model as a control variate to reduce the error of the MC estimate. The accuracy gain could still be significant, depending on how well the reduced model approximates the original high-dimensional one. IRUQ also provides several additional practical advantages: it is non-intrusive; it does not require computing the high-dimensional gradient of the QoI; and it reports an error bar so the user knows how reliable the result is.

Inverse models: A necessary next step in ground-water modeling

USGS Publications Warehouse

Poeter, E.P.; Hill, M.C.

1997-01-01

Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.

Inverse Electrocardiographic Source Localization of Ischemia: An Optimization Framework and Finite Element Solution

PubMed Central

Wang, Dafang; Kirby, Robert M.; MacLeod, Rob S.; Johnson, Chris R.

2013-01-01

With the goal of non-invasively localizing cardiac ischemic disease using body-surface potential recordings, we attempted to reconstruct the transmembrane potential (TMP) throughout the myocardium with the bidomain heart model. The task is an inverse source problem governed by partial differential equations (PDE). Our main contribution is solving the inverse problem within a PDE-constrained optimization framework that enables various physically-based constraints in both equality and inequality forms. We formulated the optimality conditions rigorously in the continuum before deriving finite element discretization, thereby making the optimization independent of discretization choice. Such a formulation was derived for the L2-norm Tikhonov regularization and the total variation minimization. The subsequent numerical optimization was fulfilled by a primal-dual interior-point method tailored to our problem’s specific structure. Our simulations used realistic, fiber-included heart models consisting of up to 18,000 nodes, much finer than any inverse models previously reported. With synthetic ischemia data we localized ischemic regions with roughly a 10% false-negative rate or a 20% false-positive rate under conditions up to 5% input noise. With ischemia data measured from animal experiments, we reconstructed TMPs with roughly 0.9 correlation with the ground truth. While precisely estimating the TMP in general cases remains an open problem, our study shows the feasibility of reconstructing TMP during the ST interval as a means of ischemia localization. PMID:23913980

Iterative algorithms for a non-linear inverse problem in atmospheric lidar

NASA Astrophysics Data System (ADS)

Denevi, Giulia; Garbarino, Sara; Sorrentino, Alberto

2017-08-01

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms out-perform standard methods in terms of sensitivity to noise and reliability of the estimated profile.

Global Monthly CO2 Flux Inversion Based on Results of Terrestrial Ecosystem Modeling

NASA Astrophysics Data System (ADS)

Deng, F.; Chen, J.; Peters, W.; Krol, M.

2008-12-01

Most of our understanding of the sources and sinks of atmospheric CO2 has come from inverse studies of atmospheric CO2 concentration measurements. However, the number of currently available observation stations and our ability to simulate the diurnal planetary boundary layer evolution over continental regions essentially limit the number of regions that can be reliably inverted globally, especially over continental areas. In order to overcome these restrictions, a nested inverse modeling system was developed based on the Bayesian principle for estimating carbon fluxes of 30 regions in North America and 20 regions for the rest of the globe. Inverse modeling was conducted in monthly steps using CO2 concentration measurements of 5 years (2000 - 2005) with the following two models: (a) An atmospheric transport model (TM5) is used to generate the transport matrix where the diurnal variation n of atmospheric CO2 concentration is considered to enhance the use of the afternoon-hour average CO2 concentration measurements over the continental sites. (b) A process-based terrestrial ecosystem model (BEPS) is used to produce hourly step carbon fluxes, which could minimize the limitation due to our inability to solve the inverse problem in a high resolution, as the background of our inversion. We will present our recent results achieved through a combination of the bottom-up modeling with BEPS and the top-down modeling based on TM5 driven by offline meteorological fields generated by the European Centre for Medium Range Weather Forecast (ECMFW).

Engineering bacteria to solve the Burnt Pancake Problem

PubMed Central

Haynes, Karmella A; Broderick, Marian L; Brown, Adam D; Butner, Trevor L; Dickson, James O; Harden, W Lance; Heard, Lane H; Jessen, Eric L; Malloy, Kelly J; Ogden, Brad J; Rosemond, Sabriya; Simpson, Samantha; Zwack, Erin; Campbell, A Malcolm; Eckdahl, Todd T; Heyer, Laurie J; Poet, Jeffrey L

2008-01-01

Background We investigated the possibility of executing DNA-based computation in living cells by engineering Escherichia coli to address a classic mathematical puzzle called the Burnt Pancake Problem (BPP). The BPP is solved by sorting a stack of distinct objects (pancakes) into proper order and orientation using the minimum number of manipulations. Each manipulation reverses the order and orientation of one or more adjacent objects in the stack. We have designed a system that uses site-specific DNA recombination to mediate inversions of genetic elements that represent pancakes within plasmid DNA. Results Inversions (or "flips") of the DNA fragment pancakes are driven by the Salmonella typhimurium Hin/hix DNA recombinase system that we reconstituted as a collection of modular genetic elements for use in E. coli. Our system sorts DNA segments by inversions to produce different permutations of a promoter and a tetracycline resistance coding region; E. coli cells become antibiotic resistant when the segments are properly sorted. Hin recombinase can mediate all possible inversion operations on adjacent flippable DNA fragments. Mathematical modeling predicts that the system reaches equilibrium after very few flips, where equal numbers of permutations are randomly sorted and unsorted. Semiquantitative PCR analysis of in vivo flipping suggests that inversion products accumulate on a time scale of hours or days rather than minutes. Conclusion The Hin/hix system is a proof-of-concept demonstration of in vivo computation with the potential to be scaled up to accommodate larger and more challenging problems. Hin/hix may provide a flexible new tool for manipulating transgenic DNA in vivo. PMID:18492232

The incomplete inverse and its applications to the linear least squares problem

NASA Technical Reports Server (NTRS)

Morduch, G. E.

1977-01-01

A modified matrix product is explained, and it is shown that this product defiles a group whose inverse is called the incomplete inverse. It was proven that the incomplete inverse of an augmented normal matrix includes all the quantities associated with the least squares solution. An answer is provided to the problem that occurs when the data residuals are too large and when insufficient data to justify augmenting the model are available.

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems

NASA Astrophysics Data System (ADS)

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems.

PubMed

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

On the inversion of geodetic integrals defined over the sphere using 1-D FFT

NASA Astrophysics Data System (ADS)

García, R. V.; Alejo, C. A.

2005-08-01

An iterative method is presented which performs inversion of integrals defined over the sphere. The method is based on one-dimensional fast Fourier transform (1-D FFT) inversion and is implemented with the projected Landweber technique, which is used to solve constrained least-squares problems reducing the associated 1-D cyclic-convolution error. The results obtained are as precise as the direct matrix inversion approach, but with better computational efficiency. A case study uses the inversion of Hotine’s integral to obtain gravity disturbances from geoid undulations. Numerical convergence is also analyzed and comparisons with respect to the direct matrix inversion method using conjugate gradient (CG) iteration are presented. Like the CG method, the number of iterations needed to get the optimum (i.e., small) error decreases as the measurement noise increases. Nevertheless, for discrete data given over a whole parallel band, the method can be applied directly without implementing the projected Landweber method, since no cyclic convolution error exists.

Real-time characterization of partially observed epidemics using surrogate models.

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

Safta, Cosmin; Ray, Jaideep; Lefantzi, Sophia

We present a statistical method, predicated on the use of surrogate models, for the 'real-time' characterization of partially observed epidemics. Observations consist of counts of symptomatic patients, diagnosed with the disease, that may be available in the early epoch of an ongoing outbreak. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information on the dynamics of the etiologic agent in the affected population e.g., the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and epidemiologicalmore » parameters are estimated as distributions using a Markov chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. In some cases, the inverse problem can be computationally expensive, primarily due to the epidemic simulator used inside the inversion algorithm. We present a method, based on replacing the epidemiological model with computationally inexpensive surrogates, that can reduce the computational time to minutes, without a significant loss of accuracy. The surrogates are created by projecting the output of an epidemiological model on a set of polynomial chaos bases; thereafter, computations involving the surrogate model reduce to evaluations of a polynomial. We find that the epidemic characterizations obtained with the surrogate models is very close to that obtained with the original model. We also find that the number of projections required to construct a surrogate model is O(10)-O(10{sup 2}) less than the number of samples required by the MCMC to construct a stationary posterior distribution; thus, depending upon the epidemiological models in question, it may be possible to omit the offline creation and caching of surrogate models, prior to their use in an inverse problem. The technique is demonstrated on synthetic data as well as observations from the 1918 influenza pandemic collected at Camp Custer, Michigan.« less

Analytic semigroups: Applications to inverse problems for flexible structures

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rebnord, D. A.

1990-01-01

Convergence and stability results for least squares inverse problems involving systems described by analytic semigroups are presented. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structures using accelerometer data.

Multi-frequency subspace migration for imaging of perfectly conducting, arc-like cracks in full- and limited-view inverse scattering problems

NASA Astrophysics Data System (ADS)

Park, Won-Kwang

2015-02-01

Multi-frequency subspace migration imaging techniques are usually adopted for the non-iterative imaging of unknown electromagnetic targets, such as cracks in concrete walls or bridges and anti-personnel mines in the ground, in the inverse scattering problems. It is confirmed that this technique is very fast, effective, robust, and can not only be applied to full- but also to limited-view inverse problems if a suitable number of incidents and corresponding scattered fields are applied and collected. However, in many works, the application of such techniques is heuristic. With the motivation of such heuristic application, this study analyzes the structure of the imaging functional employed in the subspace migration imaging technique in two-dimensional full- and limited-view inverse scattering problems when the unknown targets are arbitrary-shaped, arc-like perfectly conducting cracks located in the two-dimensional homogeneous space. In contrast to the statistical approach based on statistical hypothesis testing, our approach is based on the fact that the subspace migration imaging functional can be expressed by a linear combination of the Bessel functions of integer order of the first kind. This is based on the structure of the Multi-Static Response (MSR) matrix collected in the far-field at nonzero frequency in either Transverse Magnetic (TM) mode (Dirichlet boundary condition) or Transverse Electric (TE) mode (Neumann boundary condition). The investigation of the expression of imaging functionals gives us certain properties of subspace migration and explains why multi-frequency enhances imaging resolution. In particular, we carefully analyze the subspace migration and confirm some properties of imaging when a small number of incident fields are applied. Consequently, we introduce a weighted multi-frequency imaging functional and confirm that it is an improved version of subspace migration in TM mode. Various results of numerical simulations performed on the far-field data affected by large amounts of random noise are similar to the analytical results derived in this study, and they provide a direction for future studies.

A modular inverse elastostatics approach to resolve the pressure-induced stress state for in vivo imaging based cardiovascular modeling.

PubMed

Peirlinck, Mathias; De Beule, Matthieu; Segers, Patrick; Rebelo, Nuno

2018-05-28

Patient-specific biomechanical modeling of the cardiovascular system is complicated by the presence of a physiological pressure load given that the imaged tissue is in a pre-stressed and -strained state. Neglect of this prestressed state into solid tissue mechanics models leads to erroneous metrics (e.g. wall deformation, peak stress, wall shear stress) which in their turn are used for device design choices, risk assessment (e.g. procedure, rupture) and surgery planning. It is thus of utmost importance to incorporate this deformed and loaded tissue state into the computational models, which implies solving an inverse problem (calculating an undeformed geometry given the load and the deformed geometry). Methodologies to solve this inverse problem can be categorized into iterative and direct methodologies, both having their inherent advantages and disadvantages. Direct methodologies are typically based on the inverse elastostatics (IE) approach and offer a computationally efficient single shot methodology to compute the in vivo stress state. However, cumbersome and problem-specific derivations of the formulations and non-trivial access to the finite element analysis (FEA) code, especially for commercial products, refrain a broad implementation of these methodologies. For that reason, we developed a novel, modular IE approach and implemented this methodology in a commercial FEA solver with minor user subroutine interventions. The accuracy of this methodology was demonstrated in an arterial tube and porcine biventricular myocardium model. The computational power and efficiency of the methodology was shown by computing the in vivo stress and strain state, and the corresponding unloaded geometry, for two models containing multiple interacting incompressible, anisotropic (fiber-embedded) and hyperelastic material behaviors: a patient-specific abdominal aortic aneurysm and a full 4-chamber heart model. Copyright © 2018 Elsevier Ltd. All rights reserved.

The Inverse Problem in Jet Acoustics

NASA Technical Reports Server (NTRS)

Wooddruff, S. L.; Hussaini, M. Y.

2001-01-01

The inverse problem for jet acoustics, or the determination of noise sources from far-field pressure information, is proposed as a tool for understanding the generation of noise by turbulence and for the improved prediction of jet noise. An idealized version of the problem is investigated first to establish the extent to which information about the noise sources may be determined from far-field pressure data and to determine how a well-posed inverse problem may be set up. Then a version of the industry-standard MGB code is used to predict a jet noise source spectrum from experimental noise data.

ITOUGH2(UNIX). Inverse Modeling for TOUGH2 Family of Multiphase Flow Simulators

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

Finsterle, S.

1999-03-01

ITOUGH2 provides inverse modeling capabilities for the TOUGH2 family of numerical simulators for non-isothermal multiphase flows in fractured-porous media. The ITOUGH2 can be used for estimating parameters by automatic modeling calibration, for sensitivity analyses, and for uncertainity propagation analyses (linear and Monte Carlo simulations). Any input parameter to the TOUGH2 simulator can be estimated based on any type of observation for which a corresponding TOUGH2 output is calculated. ITOUGH2 solves a non-linear least-squares problem using direct or gradient-based minimization algorithms. A detailed residual and error analysis is performed, which includes the evaluation of model identification criteria. ITOUGH2 can also bemore » run in forward mode, solving subsurface flow problems related to nuclear waste isolation, oil, gas, and geothermal resevoir engineering, and vadose zone hydrology.« less

Computational modelling of cellular level metabolism

NASA Astrophysics Data System (ADS)

Calvetti, D.; Heino, J.; Somersalo, E.

2008-07-01

The steady and stationary state inverse problems consist of estimating the reaction and transport fluxes, blood concentrations and possibly the rates of change of some of the concentrations based on data which are often scarce noisy and sampled over a population. The Bayesian framework provides a natural setting for the solution of this inverse problem, because a priori knowledge about the system itself and the unknown reaction fluxes and transport rates can compensate for the insufficiency of measured data, provided that the computational costs do not become prohibitive. This article identifies the computational challenges which have to be met when analyzing the steady and stationary states of multicompartment model for cellular metabolism and suggest stable and efficient ways to handle the computations. The outline of a computational tool based on the Bayesian paradigm for the simulation and analysis of complex cellular metabolic systems is also presented.

Inverse kinematics problem in robotics using neural networks

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.; Lawrence, Charles

1992-01-01

In this paper, Multilayer Feedforward Networks are applied to the robot inverse kinematic problem. The networks are trained with endeffector position and joint angles. After training, performance is measured by having the network generate joint angles for arbitrary endeffector trajectories. A 3-degree-of-freedom (DOF) spatial manipulator is used for the study. It is found that neural networks provide a simple and effective way to both model the manipulator inverse kinematics and circumvent the problems associated with algorithmic solution methods.

Bayesian Inference in Satellite Gravity Inversion

NASA Technical Reports Server (NTRS)

Kis, K. I.; Taylor, Patrick T.; Wittmann, G.; Kim, Hyung Rae; Torony, B.; Mayer-Guerr, T.

2005-01-01

To solve a geophysical inverse problem means applying measurements to determine the parameters of the selected model. The inverse problem is formulated as the Bayesian inference. The Gaussian probability density functions are applied in the Bayes's equation. The CHAMP satellite gravity data are determined at the altitude of 400 kilometer altitude over the South part of the Pannonian basin. The model of interpretation is the right vertical cylinder. The parameters of the model are obtained from the minimum problem solved by the Simplex method.

EDITORIAL: Inverse Problems in Engineering

NASA Astrophysics Data System (ADS)

West, Robert M.; Lesnic, Daniel

2007-01-01

Presented here are 11 noteworthy papers selected from the Fifth International Conference on Inverse Problems in Engineering: Theory and Practice held in Cambridge, UK during 11-15 July 2005. The papers have been peer-reviewed to the usual high standards of this journal and the contributions of reviewers are much appreciated. The conference featured a good balance of the fundamental mathematical concepts of inverse problems with a diverse range of important and interesting applications, which are represented here by the selected papers. Aspects of finite-element modelling and the performance of inverse algorithms are investigated by Autrique et al and Leduc et al. Statistical aspects are considered by Emery et al and Watzenig et al with regard to Bayesian parameter estimation and inversion using particle filters. Electrostatic applications are demonstrated by van Berkel and Lionheart and also Nakatani et al. Contributions to the applications of electrical techniques and specifically electrical tomographies are provided by Wakatsuki and Kagawa, Kim et al and Kortschak et al. Aspects of inversion in optical tomography are investigated by Wright et al and Douiri et al. The authors are representative of the worldwide interest in inverse problems relating to engineering applications and their efforts in producing these excellent papers will be appreciated by many readers of this journal.

Inverse problem for multispecies ferromagneticlike mean-field models in phase space with many states

NASA Astrophysics Data System (ADS)

Fedele, Micaela; Vernia, Cecilia

2017-10-01

In this paper we solve the inverse problem for the Curie-Weiss model and its multispecies version when multiple thermodynamic states are present as in the low temperature phase where the phase space is clustered. The inverse problem consists of reconstructing the model parameters starting from configuration data generated according to the distribution of the model. We demonstrate that, without taking into account the presence of many states, the application of the inversion procedure produces very poor inference results. To overcome this problem, we use the clustering algorithm. When the system has two symmetric states of positive and negative magnetizations, the parameter reconstruction can also be obtained with smaller computational effort simply by flipping the sign of the magnetizations from positive to negative (or vice versa). The parameter reconstruction fails when the system undergoes a phase transition: In that case we give the correct inversion formulas for the Curie-Weiss model and we show that they can be used to measure how close the system gets to being critical.

Domain identification in impedance computed tomography by spline collocation method

NASA Technical Reports Server (NTRS)

Kojima, Fumio

1990-01-01

A method for estimating an unknown domain in elliptic boundary value problems is considered. The problem is formulated as an inverse problem of integral equations of the second kind. A computational method is developed using a splice collocation scheme. The results can be applied to the inverse problem of impedance computed tomography (ICT) for image reconstruction.

Estimation of spatially varying heat transfer coefficient from a flat plate with flush mounted heat sources using Bayesian inference

NASA Astrophysics Data System (ADS)

Jakkareddy, Pradeep S.; Balaji, C.

2016-09-01

This paper employs the Bayesian based Metropolis Hasting - Markov Chain Monte Carlo algorithm to solve inverse heat transfer problem of determining the spatially varying heat transfer coefficient from a flat plate with flush mounted discrete heat sources with measured temperatures at the bottom of the plate. The Nusselt number is assumed to be of the form Nu = aReb(x/l)c . To input reasonable values of ’a’ and ‘b’ into the inverse problem, first limited two dimensional conjugate convection simulations were done with Comsol. Based on the guidance from this different values of ‘a’ and ‘b’ are input to a computationally less complex problem of conjugate conduction in the flat plate (15mm thickness) and temperature distributions at the bottom of the plate which is a more convenient location for measuring the temperatures without disturbing the flow were obtained. Since the goal of this work is to demonstrate the eficiacy of the Bayesian approach to accurately retrieve ‘a’ and ‘b’, numerically generated temperatures with known values of ‘a’ and ‘b’ are treated as ‘surrogate’ experimental data. The inverse problem is then solved by repeatedly using the forward solutions together with the MH-MCMC aprroach. To speed up the estimation, the forward model is replaced by an artificial neural network. The mean, maximum-a-posteriori and standard deviation of the estimated parameters ‘a’ and ‘b’ are reported. The robustness of the proposed method is examined, by synthetically adding noise to the temperatures.

Reconstruction of structural damage based on reflection intensity spectra of fiber Bragg gratings

NASA Astrophysics Data System (ADS)

Huang, Guojun; Wei, Changben; Chen, Shiyuan; Yang, Guowei

2014-12-01

We present an approach for structural damage reconstruction based on the reflection intensity spectra of fiber Bragg gratings (FBGs). Our approach incorporates the finite element method, transfer matrix (T-matrix), and genetic algorithm to solve the inverse photo-elastic problem of damage reconstruction, i.e. to identify the location, size, and shape of a defect. By introducing a parameterized characterization of the damage information, the inverse photo-elastic problem is reduced to an optimization problem, and a relevant computational scheme was developed. The scheme iteratively searches for the solution to the corresponding direct photo-elastic problem until the simulated and measured (or target) reflection intensity spectra of the FBGs near the defect coincide within a prescribed error. Proof-of-concept validations of our approach were performed numerically and experimentally using both holed and cracked plate samples as typical cases of plane-stress problems. The damage identifiability was simulated by changing the deployment of the FBG sensors, including the total number of sensors and their distance to the defect. Both the numerical and experimental results demonstrate that our approach is effective and promising. It provides us with a photo-elastic method for developing a remote, automatic damage-imaging technique that substantially improves damage identification for structural health monitoring.

A Matlab toolkit for three-dimensional electrical impedance tomography: a contribution to the Electrical Impedance and Diffuse Optical Reconstruction Software project

NASA Astrophysics Data System (ADS)

Polydorides, Nick; Lionheart, William R. B.

2002-12-01

The objective of the Electrical Impedance and Diffuse Optical Reconstruction Software project is to develop freely available software that can be used to reconstruct electrical or optical material properties from boundary measurements. Nonlinear and ill posed problems such as electrical impedance and optical tomography are typically approached using a finite element model for the forward calculations and a regularized nonlinear solver for obtaining a unique and stable inverse solution. Most of the commercially available finite element programs are unsuitable for solving these problems because of their conventional inefficient way of calculating the Jacobian, and their lack of accurate electrode modelling. A complete package for the two-dimensional EIT problem was officially released by Vauhkonen et al at the second half of 2000. However most industrial and medical electrical imaging problems are fundamentally three-dimensional. To assist the development we have developed and released a free toolkit of Matlab routines which can be employed to solve the forward and inverse EIT problems in three dimensions based on the complete electrode model along with some basic visualization utilities, in the hope that it will stimulate further development. We also include a derivation of the formula for the Jacobian (or sensitivity) matrix based on the complete electrode model.

Time-lapse three-dimensional inversion of complex conductivity data using an active time constrained (ATC) approach

USGS Publications Warehouse

Karaoulis, M.; Revil, A.; Werkema, D.D.; Minsley, B.J.; Woodruff, W.F.; Kemna, A.

2011-01-01

Induced polarization (more precisely the magnitude and phase of impedance of the subsurface) is measured using a network of electrodes located at the ground surface or in boreholes. This method yields important information related to the distribution of permeability and contaminants in the shallow subsurface. We propose a new time-lapse 3-D modelling and inversion algorithm to image the evolution of complex conductivity over time. We discretize the subsurface using hexahedron cells. Each cell is assigned a complex resistivity or conductivity value. Using the finite-element approach, we model the in-phase and out-of-phase (quadrature) electrical potentials on the 3-D grid, which are then transformed into apparent complex resistivity. Inhomogeneous Dirichlet boundary conditions are used at the boundary of the domain. The calculation of the Jacobian matrix is based on the principles of reciprocity. The goal of time-lapse inversion is to determine the change in the complex resistivity of each cell of the spatial grid as a function of time. Each model along the time axis is called a 'reference space model'. This approach can be simplified into an inverse problem looking for the optimum of several reference space models using the approximation that the material properties vary linearly in time between two subsequent reference models. Regularizations in both space domain and time domain reduce inversion artefacts and improve the stability of the inversion problem. In addition, the use of the time-lapse equations allows the simultaneous inversion of data obtained at different times in just one inversion step (4-D inversion). The advantages of this new inversion algorithm are demonstrated on synthetic time-lapse data resulting from the simulation of a salt tracer test in a heterogeneous random material described by an anisotropic semi-variogram. ?? 2011 The Authors Geophysical Journal International ?? 2011 RAS.

Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

NASA Astrophysics Data System (ADS)

Sun, Yong; Meng, Zhaohai; Li, Fengting

2018-03-01

Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.

A sparse reconstruction method for the estimation of multiresolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2014-08-20

We present a sparse reconstruction scheme that can also be used to ensure non-negativity when fitting wavelet-based random field models to limited observations in non-rectangular geometries. The method is relevant when multiresolution fields are estimated using linear inverse problems. Examples include the estimation of emission fields for many anthropogenic pollutants using atmospheric inversion or hydraulic conductivity in aquifers from flow measurements. The scheme is based on three new developments. Firstly, we extend an existing sparse reconstruction method, Stagewise Orthogonal Matching Pursuit (StOMP), to incorporate prior information on the target field. Secondly, we develop an iterative method that uses StOMP tomore » impose non-negativity on the estimated field. Finally, we devise a method, based on compressive sensing, to limit the estimated field within an irregularly shaped domain. We demonstrate the method on the estimation of fossil-fuel CO 2 (ffCO 2) emissions in the lower 48 states of the US. The application uses a recently developed multiresolution random field model and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of two. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

A Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment

PubMed Central

Burton, Brett M; Tate, Jess D; Erem, Burak; Swenson, Darrell J; Wang, Dafang F; Steffen, Michael; Brooks, Dana H; van Dam, Peter M; Macleod, Rob S

2012-01-01

Computational modeling in electrocardiography often requires the examination of cardiac forward and inverse problems in order to non-invasively analyze physiological events that are otherwise inaccessible or unethical to explore. The study of these models can be performed in the open-source SCIRun problem solving environment developed at the Center for Integrative Biomedical Computing (CIBC). A new toolkit within SCIRun provides researchers with essential frameworks for constructing and manipulating electrocardiographic forward and inverse models in a highly efficient and interactive way. The toolkit contains sample networks, tutorials and documentation which direct users through SCIRun-specific approaches in the assembly and execution of these specific problems. PMID:22254301

Inversion of residual stress profiles from ultrasonic Rayleigh wave dispersion data

NASA Astrophysics Data System (ADS)

Mora, P.; Spies, M.

2018-05-01

We investigate theoretically and with synthetic data the performance of several inversion methods to infer a residual stress state from ultrasonic surface wave dispersion data. We show that this particular problem may reveal in relevant materials undesired behaviors for some methods that could be reliably applied to infer other properties. We focus on two methods, one based on a Taylor-expansion, and another one based on a piecewise linear expansion regularized by a singular value decomposition. We explain the instabilities of the Taylor-based method by highlighting singularities in the series of coefficients. At the same time, we show that the other method can successfully provide performances which only weakly depend on the material.

Numerical inverse Laplace transformation for determining the system response of linear systems in the time domain

NASA Technical Reports Server (NTRS)

Friedrich, R.; Drewelow, W.

1978-01-01

An algorithm is described that is based on the method of breaking the Laplace transform down into partial fractions which are then inverse-transformed separately. The sum of the resulting partial functions is the wanted time function. Any problems caused by equation system forms are largely limited by appropriate normalization using an auxiliary parameter. The practical limits of program application are reached when the degree of the denominator of the Laplace transform is seven to eight.

Destructive materials thermal characteristics determination with application for spacecraft structures testing

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Budnik, S. A.; Nenarokomov, A. V.; Netelev, A. V.; Titov, D. M.

2013-04-01

In many practical situations it is impossible to measure directly thermal and thermokinetic properties of analyzed composite materials. The only way that can often be used to overcome these difficulties is indirect measurements. This type of measurements is usually formulated as the solution of inverse heat transfer problems. Such problems are ill-posed in mathematical sense and their main feature shows itself in the solution instabilities. That is why special regularizing methods are needed to solve them. The general method of iterative regularization is concerned with application to the estimation of materials properties. The objective of this paper is to estimate thermal and thermokinetic properties of advanced materials using the approach based on inverse methods. An experimental-computational system is presented for investigating the thermal and kinetics properties of composite materials by methods of inverse heat transfer problems and which is developed at the Thermal Laboratory of Department Space Systems Engineering, of Moscow Aviation Institute (MAI). The system is aimed at investigating the materials in conditions of unsteady contact and/or radiation heating over a wide range of temperature changes and heating rates in a vacuum, air and inert gas medium.

Plasma homovanillic acid correlates inversely with history of learning problems in healthy volunteer and personality disordered subjects.

PubMed

Coccaro, Emil F; Hirsch, Sharon L; Stein, Mark A

2007-01-15

Central dopaminergic activity is critical to the functioning of both motor and cognitive systems. Based on the therapeutic action of dopaminergic agents in treating attention deficit hyperactivity disorder (ADHD), ADHD symptoms may be related to a reduction in central dopaminergic activity. We tested the hypothesis that dopaminergic activity, as reflected by plasma homovanillic acid (pHVA), may be related to dimensional aspects of ADHD in adults. Subjects were 30 healthy volunteer and 39 personality disordered subjects, in whom morning basal pHVA concentration and a dimensional measure of childhood ADHD symptoms (Wender Utah Rating Scale: WURS) were obtained. A significant inverse correlation was found between WURS Total score and pHVA concentration in the total sample. Among WURS factor scores, a significant inverse relationship was noted between pHVA and history of "childhood learning problems". Consistent with the dopaminergic dysfunction hypothesis of ADHD and of cognitive function, pHVA concentrations were correlated with childhood history of ADHD symptoms in general and with history of "learning problems" in non-ADHD psychiatric patients and controls. Replication is needed in treated and untreated ADHD samples to confirm these initial results.

Singularity and Nonnormality in the Classification of Compositional Data

USGS Publications Warehouse

Bohling, Geoffrey C.; Davis, J.C.; Olea, R.A.; Harff, Jan

1998-01-01

Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore-Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.

The role of simulated small-scale ocean variability in inverse computations for ocean acoustic tomography.

PubMed

Dushaw, Brian D; Sagen, Hanne

2017-12-01

Ocean acoustic tomography depends on a suitable reference ocean environment with which to set the basic parameters of the inverse problem. Some inverse problems may require a reference ocean that includes the small-scale variations from internal waves, small mesoscale, or spice. Tomographic inversions that employ data of stable shadow zone arrivals, such as those that have been observed in the North Pacific and Canary Basin, are an example. Estimating temperature from the unique acoustic data that have been obtained in Fram Strait is another example. The addition of small-scale variability to augment a smooth reference ocean is essential to understanding the acoustic forward problem in these cases. Rather than a hindrance, the stochastic influences of the small scale can be exploited to obtain accurate inverse estimates. Inverse solutions are readily obtained, and they give computed arrival patterns that matched the observations. The approach is not ad hoc, but universal, and it has allowed inverse estimates for ocean temperature variations in Fram Strait to be readily computed on several acoustic paths for which tomographic data were obtained.

Wavelet-sparsity based regularization over time in the inverse problem of electrocardiography.

PubMed

Cluitmans, Matthijs J M; Karel, Joël M H; Bonizzi, Pietro; Volders, Paul G A; Westra, Ronald L; Peeters, Ralf L M

2013-01-01

Noninvasive, detailed assessment of electrical cardiac activity at the level of the heart surface has the potential to revolutionize diagnostics and therapy of cardiac pathologies. Due to the requirement of noninvasiveness, body-surface potentials are measured and have to be projected back to the heart surface, yielding an ill-posed inverse problem. Ill-posedness ensures that there are non-unique solutions to this problem, resulting in a problem of choice. In the current paper, it is proposed to restrict this choice by requiring that the time series of reconstructed heart-surface potentials is sparse in the wavelet domain. A local search technique is introduced that pursues a sparse solution, using an orthogonal wavelet transform. Epicardial potentials reconstructed from this method are compared to those from existing methods, and validated with actual intracardiac recordings. The new technique improves the reconstructions in terms of smoothness and recovers physiologically meaningful details. Additionally, reconstruction of activation timing seems to be improved when pursuing sparsity of the reconstructed signals in the wavelet domain.

Reduction of Dynamic Loads in Mine Lifting Installations

NASA Astrophysics Data System (ADS)

Kuznetsov, N. K.; Eliseev, S. V.; Perelygina, A. Yu

2018-01-01

Article is devoted to a problem of decrease in the dynamic loadings arising in transitional operating modes of the mine lifting installations leading to heavy oscillating motions of lifting vessels and decrease in efficiency and reliability of work. The known methods and means of decrease in dynamic loadings and oscillating motions of the similar equipment are analysed. It is shown that an approach based on the concept of the inverse problems of dynamics can be effective method of the solution of this problem. The article describes the design model of a one-ended lifting installation in the form of a two-mass oscillation system, in which the inertial elements are the mass of the lifting vessel and the reduced mass of the engine, reducer, drum and pulley. The simplified mathematical model of this system and results of an efficiency research of an active way of reduction of dynamic loadings of lifting installation on the basis of the concept of the inverse problems of dynamics are given.

The inverse problem of using the information of historical data to estimate model errors is one of the science frontier research topics. In this study, we investigate such a problem using the classic Lorenz (1963) equation as a prediction model.

NASA Astrophysics Data System (ADS)

Wan, S.; He, W.

2016-12-01

The inverse problem of using the information of historical data to estimate model errors is one of the science frontier research topics. In this study, we investigate such a problem using the classic Lorenz (1963) equation as a prediction model and the Lorenz equation with a periodic evolutionary function as an accurate representation of reality to generate "observational data." On the basis of the intelligent features of evolutionary modeling (EM), including self-organization, self-adaptive and self-learning, the dynamic information contained in the historical data can be identified and extracted by computer automatically. Thereby, a new approach is proposed to estimate model errors based on EM in the present paper. Numerical tests demonstrate the ability of the new approach to correct model structural errors. In fact, it can actualize the combination of the statistics and dynamics to certain extent.

An inverse dynamics approach to trajectory optimization and guidance for an aerospace plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1992-01-01

The optimal ascent problem for an aerospace planes is formulated as an optimal inverse dynamic problem. Both minimum-fuel and minimax type of performance indices are considered. Some important features of the optimal trajectory and controls are used to construct a nonlinear feedback midcourse controller, which not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suited for onboard implementation. Robust ascent guidance is obtained by using combination of feedback compensation and onboard generation of control through the inverse dynamics approach. Accurate orbital insertion can be achieved with near-optimal control of the rocket through inverse dynamics even in the presence of disturbances.

INFO-RNA--a fast approach to inverse RNA folding.

PubMed

Busch, Anke; Backofen, Rolf

2006-08-01

The structure of RNA molecules is often crucial for their function. Therefore, secondary structure prediction has gained much interest. Here, we consider the inverse RNA folding problem, which means designing RNA sequences that fold into a given structure. We introduce a new algorithm for the inverse folding problem (INFO-RNA) that consists of two parts; a dynamic programming method for good initial sequences and a following improved stochastic local search that uses an effective neighbor selection method. During the initialization, we design a sequence that among all sequences adopts the given structure with the lowest possible energy. For the selection of neighbors during the search, we use a kind of look-ahead of one selection step applying an additional energy-based criterion. Afterwards, the pre-ordered neighbors are tested using the actual optimization criterion of minimizing the structure distance between the target structure and the mfe structure of the considered neighbor. We compared our algorithm to RNAinverse and RNA-SSD for artificial and biological test sets. Using INFO-RNA, we performed better than RNAinverse and in most cases, we gained better results than RNA-SSD, the probably best inverse RNA folding tool on the market. www.bioinf.uni-freiburg.de?Subpages/software.html.

Dynamic Shape Reconstruction of Three-Dimensional Frame Structures Using the Inverse Finite Element Method

NASA Technical Reports Server (NTRS)

Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander

2011-01-01

A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.

On uncertainty quantification in hydrogeology and hydrogeophysics

NASA Astrophysics Data System (ADS)

Linde, Niklas; Ginsbourger, David; Irving, James; Nobile, Fabio; Doucet, Arnaud

2017-12-01

Recent advances in sensor technologies, field methodologies, numerical modeling, and inversion approaches have contributed to unprecedented imaging of hydrogeological properties and detailed predictions at multiple temporal and spatial scales. Nevertheless, imaging results and predictions will always remain imprecise, which calls for appropriate uncertainty quantification (UQ). In this paper, we outline selected methodological developments together with pioneering UQ applications in hydrogeology and hydrogeophysics. The applied mathematics and statistics literature is not easy to penetrate and this review aims at helping hydrogeologists and hydrogeophysicists to identify suitable approaches for UQ that can be applied and further developed to their specific needs. To bypass the tremendous computational costs associated with forward UQ based on full-physics simulations, we discuss proxy-modeling strategies and multi-resolution (Multi-level Monte Carlo) methods. We consider Bayesian inversion for non-linear and non-Gaussian state-space problems and discuss how Sequential Monte Carlo may become a practical alternative. We also describe strategies to account for forward modeling errors in Bayesian inversion. Finally, we consider hydrogeophysical inversion, where petrophysical uncertainty is often ignored leading to overconfident parameter estimation. The high parameter and data dimensions encountered in hydrogeological and geophysical problems make UQ a complicated and important challenge that has only been partially addressed to date.

Optimal design of piezoelectric transformers: a rational approach based on an analytical model and a deterministic global optimization.

PubMed

Pigache, Francois; Messine, Frédéric; Nogarede, Bertrand

2007-07-01

This paper deals with a deterministic and rational way to design piezoelectric transformers in radial mode. The proposed approach is based on the study of the inverse problem of design and on its reformulation as a mixed constrained global optimization problem. The methodology relies on the association of the analytical models for describing the corresponding optimization problem and on an exact global optimization software, named IBBA and developed by the second author to solve it. Numerical experiments are presented and compared in order to validate the proposed approach.

A Strassen-Newton algorithm for high-speed parallelizable matrix inversion

NASA Technical Reports Server (NTRS)

Bailey, David H.; Ferguson, Helaman R. P.

1988-01-01

Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.

Optimisation in radiotherapy. III: Stochastic optimisation algorithms and conclusions.

PubMed

Ebert, M

1997-12-01

This is the final article in a three part examination of optimisation in radiotherapy. Previous articles have established the bases and form of the radiotherapy optimisation problem, and examined certain types of optimisation algorithm, namely, those which perform some form of ordered search of the solution space (mathematical programming), and those which attempt to find the closest feasible solution to the inverse planning problem (deterministic inversion). The current paper examines algorithms which search the space of possible irradiation strategies by stochastic methods. The resulting iterative search methods move about the solution space by sampling random variates, which gradually become more constricted as the algorithm converges upon the optimal solution. This paper also discusses the implementation of optimisation in radiotherapy practice.

A physiologically motivated sparse, compact, and smooth (SCS) approach to EEG source localization.

PubMed

Cao, Cheng; Akalin Acar, Zeynep; Kreutz-Delgado, Kenneth; Makeig, Scott

2012-01-01

Here, we introduce a novel approach to the EEG inverse problem based on the assumption that principal cortical sources of multi-channel EEG recordings may be assumed to be spatially sparse, compact, and smooth (SCS). To enforce these characteristics of solutions to the EEG inverse problem, we propose a correlation-variance model which factors a cortical source space covariance matrix into the multiplication of a pre-given correlation coefficient matrix and the square root of the diagonal variance matrix learned from the data under a Bayesian learning framework. We tested the SCS method using simulated EEG data with various SNR and applied it to a real ECOG data set. We compare the results of SCS to those of an established SBL algorithm.

Recovering an elastic obstacle containing embedded objects by the acoustic far-field measurements

NASA Astrophysics Data System (ADS)

Qu, Fenglong; Yang, Jiaqing; Zhang, Bo

2018-01-01

Consider the inverse scattering problem of time-harmonic acoustic waves by a 3D bounded elastic obstacle which may contain embedded impenetrable obstacles inside. We propose a novel and simple technique to show that the elastic obstacle can be uniquely recovered by the acoustic far-field pattern at a fixed frequency, disregarding its contents. Our method is based on constructing a well-posed modified interior transmission problem on a small domain and makes use of an a priori estimate for both the acoustic and elastic wave fields in the usual H 1-norm. In the case when there is no obstacle embedded inside the elastic body, our method gives a much simpler proof for the uniqueness result obtained previously in the literature (Natroshvili et al 2000 Rend. Mat. Serie VII 20 57-92 Monk and Selgas 2009 Inverse Problems Imaging 3 173-98).

Inverse random source scattering for the Helmholtz equation in inhomogeneous media

NASA Astrophysics Data System (ADS)

Li, Ming; Chen, Chuchu; Li, Peijun

2018-01-01

This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.

Graph-cut based discrete-valued image reconstruction.

PubMed

Tuysuzoglu, Ahmet; Karl, W Clem; Stojanovic, Ivana; Castañòn, David; Ünlü, M Selim

2015-05-01

Efficient graph-cut methods have been used with great success for labeling and denoising problems occurring in computer vision. Unfortunately, the presence of linear image mappings has prevented the use of these techniques in most discrete-amplitude image reconstruction problems. In this paper, we develop a graph-cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations. We first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph-cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator. We then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph-cut frameworks. We use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems. We first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter. Then we focus on nonlocal, tomographic examples where we consider limited-angle data problems. We compare our technique with state-of-the-art discrete and continuous image reconstruction techniques. Experiments show that the proposed method outperforms state-of-the-art techniques in challenging scenarios involving discrete valued unknowns.

LS-APC v1.0: a tuning-free method for the linear inverse problem and its application to source-term determination

NASA Astrophysics Data System (ADS)

Tichý, Ondřej; Šmídl, Václav; Hofman, Radek; Stohl, Andreas

2016-11-01

Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values) as a product of the source-receptor sensitivity (SRS) matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX) where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.

PREFACE: First International Congress of the International Association of Inverse Problems (IPIA): Applied Inverse Problems 2007: Theoretical and Computational Aspects

NASA Astrophysics Data System (ADS)

Uhlmann, Gunther

2008-07-01

This volume represents the proceedings of the fourth Applied Inverse Problems (AIP) international conference and the first congress of the Inverse Problems International Association (IPIA) which was held in Vancouver, Canada, June 25 29, 2007. The organizing committee was formed by Uri Ascher, University of British Columbia, Richard Froese, University of British Columbia, Gary Margrave, University of Calgary, and Gunther Uhlmann, University of Washington, chair. The conference was part of the activities of the Pacific Institute of Mathematical Sciences (PIMS) Collaborative Research Group on inverse problems (http://www.pims.math.ca/scientific/collaborative-research-groups/past-crgs). This event was also supported by grants from NSF and MITACS. Inverse Problems (IP) are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. The enormous increase in computing power and the development of powerful algorithms have made it possible to apply the techniques of IP to real-world problems of growing complexity. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth's substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences. The series of Applied Inverse Problems (AIP) Conferences aims to provide a primary international forum for academic and industrial researchers working on all aspects of inverse problems, such as mathematical modelling, functional analytic methods, computational approaches, numerical algorithms etc. The steering committee of the AIP conferences consists of Heinz Engl (Johannes Kepler Universität, Austria), Joyce McLaughlin (RPI, USA), William Rundell (Texas A&M, USA), Erkki Somersalo (Helsinki University of Technology, Finland), Masahiro Yamamoto (University of Tokyo, Japan), Gunther Uhlmann (University of Washington) and Jun Zou (Chinese University of Hong Kong). IPIA is a recently formed organization that intends to promote the field of inverse problem at all levels. See http://www.inverse-problems.net/. IPIA awarded the first Calderón prize at the opening of the conference to Matti Lassas (see first article in the Proceedings). There was also a general meeting of IPIA during the workshop. This was probably the largest conference ever on IP with 350 registered participants. The program consisted of 18 invited speakers and the Calderón Prize Lecture given by Matti Lassas. Another integral part of the program was the more than 60 mini-symposia that covered a broad spectrum of the theory and applications of inverse problems, focusing on recent developments in medical imaging, seismic exploration, remote sensing, industrial applications, numerical and regularization methods in inverse problems. Another important related topic was image processing in particular the advances which have allowed for significant enhancement of widely used imaging techniques. For more details on the program see the web page: http://www.pims.math.ca/science/2007/07aip. These proceedings reflect the broad spectrum of topics covered in AIP 2007. The conference and these proceedings would not have happened without the contributions of many people. I thank all my fellow organizers, the invited speakers, the speakers and organizers of mini-symposia for making this an exciting and vibrant event. I also thank PIMS, NSF and MITACS for their generous financial support. I take this opportunity to thank the PIMS staff, particularly Ken Leung, for making the local arrangements. Also thanks are due to Stephen McDowall for his help in preparing the schedule of the conference and Xiaosheng Li for the help in preparing these proceedings. I also would like to thank the contributors of this volume and the referees. Finally, many thanks are due to Graham Douglas and Elaine Longden-Chapman for suggesting publication in Journal of Physics: Conference Series.

Modular Approaches to Earth Science Scientific Computing: 3D Electromagnetic Induction Modeling as an Example

NASA Astrophysics Data System (ADS)

Tandon, K.; Egbert, G.; Siripunvaraporn, W.

2003-12-01

We are developing a modular system for three-dimensional inversion of electromagnetic (EM) induction data, using an object oriented programming approach. This approach allows us to modify the individual components of the inversion scheme proposed, and also reuse the components for variety of problems in earth science computing howsoever diverse they might be. In particular, the modularity allows us to (a) change modeling codes independently of inversion algorithm details; (b) experiment with new inversion algorithms; and (c) modify the way prior information is imposed in the inversion to test competing hypothesis and techniques required to solve an earth science problem. Our initial code development is for EM induction equations on a staggered grid, using iterative solution techniques in 3D. An example illustrated here is an experiment with the sensitivity of 3D magnetotelluric inversion to uncertainties in the boundary conditions required for regional induction problems. These boundary conditions should reflect the large-scale geoelectric structure of the study area, which is usually poorly constrained. In general for inversion of MT data, one fixes boundary conditions at the edge of the model domain, and adjusts the earth?s conductivity structure within the modeling domain. Allowing for errors in specification of the open boundary values is simple in principle, but no existing inversion codes that we are aware of have this feature. Adding a feature such as this is straightforward within the context of the modular approach. More generally, a modular approach provides an efficient methodology for setting up earth science computing problems to test various ideas. As a concrete illustration relevant to EM induction problems, we investigate the sensitivity of MT data near San Andreas Fault at Parkfield (California) to uncertainties in the regional geoelectric structure.

The Iterative Reweighted Mixed-Norm Estimate for Spatio-Temporal MEG/EEG Source Reconstruction.

PubMed

Strohmeier, Daniel; Bekhti, Yousra; Haueisen, Jens; Gramfort, Alexandre

2016-10-01

Source imaging based on magnetoencephalography (MEG) and electroencephalography (EEG) allows for the non-invasive analysis of brain activity with high temporal and good spatial resolution. As the bioelectromagnetic inverse problem is ill-posed, constraints are required. For the analysis of evoked brain activity, spatial sparsity of the neuronal activation is a common assumption. It is often taken into account using convex constraints based on the l 1 -norm. The resulting source estimates are however biased in amplitude and often suboptimal in terms of source selection due to high correlations in the forward model. In this work, we demonstrate that an inverse solver based on a block-separable penalty with a Frobenius norm per block and a l 0.5 -quasinorm over blocks addresses both of these issues. For solving the resulting non-convex optimization problem, we propose the iterative reweighted Mixed Norm Estimate (irMxNE), an optimization scheme based on iterative reweighted convex surrogate optimization problems, which are solved efficiently using a block coordinate descent scheme and an active set strategy. We compare the proposed sparse imaging method to the dSPM and the RAP-MUSIC approach based on two MEG data sets. We provide empirical evidence based on simulations and analysis of MEG data that the proposed method improves on the standard Mixed Norm Estimate (MxNE) in terms of amplitude bias, support recovery, and stability.

On the Duality of Forward and Inverse Light Transport.

PubMed

Chandraker, Manmohan; Bai, Jiamin; Ng, Tian-Tsong; Ramamoorthi, Ravi

2011-10-01

Inverse light transport seeks to undo global illumination effects, such as interreflections, that pervade images of most scenes. This paper presents the theoretical and computational foundations for inverse light transport as a dual of forward rendering. Mathematically, this duality is established through the existence of underlying Neumann series expansions. Physically, it can be shown that each term of our inverse series cancels an interreflection bounce, just as the forward series adds them. While the convergence properties of the forward series are well known, we show that the oscillatory convergence of the inverse series leads to more interesting conditions on material reflectance. Conceptually, the inverse problem requires the inversion of a large light transport matrix, which is impractical for realistic resolutions using standard techniques. A natural consequence of our theoretical framework is a suite of fast computational algorithms for light transport inversion--analogous to finite element radiosity, Monte Carlo and wavelet-based methods in forward rendering--that rely at most on matrix-vector multiplications. We demonstrate two practical applications, namely, separation of individual bounces of the light transport and fast projector radiometric compensation, to display images free of global illumination artifacts in real-world environments.

On the optimization of electromagnetic geophysical data: Application of the PSO algorithm

NASA Astrophysics Data System (ADS)

Godio, A.; Santilano, A.

2018-01-01

Particle Swarm optimization (PSO) algorithm resolves constrained multi-parameter problems and is suitable for simultaneous optimization of linear and nonlinear problems, with the assumption that forward modeling is based on good understanding of ill-posed problem for geophysical inversion. We apply PSO for solving the geophysical inverse problem to infer an Earth model, i.e. the electrical resistivity at depth, consistent with the observed geophysical data. The method doesn't require an initial model and can be easily constrained, according to external information for each single sounding. The optimization process to estimate the model parameters from the electromagnetic soundings focuses on the discussion of the objective function to be minimized. We discuss the possibility to introduce in the objective function vertical and lateral constraints, with an Occam-like regularization. A sensitivity analysis allowed us to check the performance of the algorithm. The reliability of the approach is tested on synthetic, real Audio-Magnetotelluric (AMT) and Long Period MT data. The method appears able to solve complex problems and allows us to estimate the a posteriori distribution of the model parameters.

Joint Model and Parameter Dimension Reduction for Bayesian Inversion Applied to an Ice Sheet Flow Problem

NASA Astrophysics Data System (ADS)

Ghattas, O.; Petra, N.; Cui, T.; Marzouk, Y.; Benjamin, P.; Willcox, K.

2016-12-01

Model-based projections of the dynamics of the polar ice sheets play a central role in anticipating future sea level rise. However, a number of mathematical and computational challenges place significant barriers on improving predictability of these models. One such challenge is caused by the unknown model parameters (e.g., in the basal boundary conditions) that must be inferred from heterogeneous observational data, leading to an ill-posed inverse problem and the need to quantify uncertainties in its solution. In this talk we discuss the problem of estimating the uncertainty in the solution of (large-scale) ice sheet inverse problems within the framework of Bayesian inference. Computing the general solution of the inverse problem--i.e., the posterior probability density--is intractable with current methods on today's computers, due to the expense of solving the forward model (3D full Stokes flow with nonlinear rheology) and the high dimensionality of the uncertain parameters (which are discretizations of the basal sliding coefficient field). To overcome these twin computational challenges, it is essential to exploit problem structure (e.g., sensitivity of the data to parameters, the smoothing property of the forward model, and correlations in the prior). To this end, we present a data-informed approach that identifies low-dimensional structure in both parameter space and the forward model state space. This approach exploits the fact that the observations inform only a low-dimensional parameter space and allows us to construct a parameter-reduced posterior. Sampling this parameter-reduced posterior still requires multiple evaluations of the forward problem, therefore we also aim to identify a low dimensional state space to reduce the computational cost. To this end, we apply a proper orthogonal decomposition (POD) approach to approximate the state using a low-dimensional manifold constructed using ``snapshots'' from the parameter reduced posterior, and the discrete empirical interpolation method (DEIM) to approximate the nonlinearity in the forward problem. We show that using only a limited number of forward solves, the resulting subspaces lead to an efficient method to explore the high-dimensional posterior.

Phases, periphases, and interphases equilibrium by molecular modeling. I. Mass equilibrium by the semianalytical stochastic perturbations method and application to a solution between (120) gypsum faces

NASA Astrophysics Data System (ADS)

Pedesseau, Laurent; Jouanna, Paul

2004-12-01

The SASP (semianalytical stochastic perturbations) method is an original mixed macro-nano-approach dedicated to the mass equilibrium of multispecies phases, periphases, and interphases. This general method, applied here to the reflexive relation Ck⇔μk between the concentrations Ck and the chemical potentials μk of k species within a fluid in equilibrium, leads to the distribution of the particles at the atomic scale. The macroaspects of the method, based on analytical Taylor's developments of chemical potentials, are intimately mixed with the nanoaspects of molecular mechanics computations on stochastically perturbed states. This numerical approach, directly linked to definitions, is universal by comparison with current approaches, DLVO Derjaguin-Landau-Verwey-Overbeek, grand canonical Monte Carlo, etc., without any restriction on the number of species, concentrations, or boundary conditions. The determination of the relation Ck⇔μk implies in fact two problems: a direct problem Ck⇒μk and an inverse problem μk⇒Ck. Validation of the method is demonstrated in case studies A and B which treat, respectively, a direct problem and an inverse problem within a free saturated gypsum solution. The flexibility of the method is illustrated in case study C dealing with an inverse problem within a solution interphase, confined between two (120) gypsum faces, remaining in connection with a reference solution. This last inverse problem leads to the mass equilibrium of ions and water molecules within a 3 Å thick gypsum interface. The major unexpected observation is the repulsion of SO42- ions towards the reference solution and the attraction of Ca2+ ions from the reference solution, the concentration being 50 times higher within the interphase as compared to the free solution. The SASP method is today the unique approach able to tackle the simulation of the number and distribution of ions plus water molecules in such extreme confined conditions. This result is of prime importance for all coupled chemical-mechanical problems dealing with interfaces, and more generally for a wide variety of applications such as phase changes, osmotic equilibrium, surface energy, etc., in complex chemical-physics situations.

The novel high-performance 3-D MT inverse solver

NASA Astrophysics Data System (ADS)

Kruglyakov, Mikhail; Geraskin, Alexey; Kuvshinov, Alexey

2016-04-01

We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse solver. The solver is written in multi-language paradigm to make it as efficient, readable and maintainable as possible. Separation of concerns and single responsibility concepts go through implementation of the solver. As a forward modelling engine a modern scalable solver extrEMe, based on contracting integral equation approach, is used. Iterative gradient-type (quasi-Newton) optimization scheme is invoked to search for (regularized) inverse problem solution, and adjoint source approach is used to calculate efficiently the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT responses, and supports massive parallelization. Moreover, different parallelization strategies implemented in the code allow optimal usage of available computational resources for a given problem statement. To parameterize an inverse domain the so-called mask parameterization is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to HPC Piz Daint (6th supercomputer in the world) demonstrate practically linear scalability of the code up to thousands of nodes.

Characterizing open and non-uniform vertical heat sources: towards the identification of real vertical cracks in vibrothermography experiments

NASA Astrophysics Data System (ADS)

Castelo, A.; Mendioroz, A.; Celorrio, R.; Salazar, A.; López de Uralde, P.; Gorosmendi, I.; Gorostegui-Colinas, E.

2017-05-01

Lock-in vibrothermography is used to characterize vertical kissing and open cracks in metals. In this technique the crack heats up during ultrasound excitation due mainly to friction between the defect's faces. We have solved the inverse problem, consisting in determining the heat source distribution produced at cracks under amplitude modulated ultrasound excitation, which is an ill-posed inverse problem. As a consequence the minimization of the residual is unstable. We have stabilized the algorithm introducing a penalty term based on Total Variation functional. In the inversion, we combine amplitude and phase surface temperature data obtained at several modulation frequencies. Inversions of synthetic data with added noise indicate that compact heat sources are characterized accurately and that the particular upper contours can be retrieved for shallow heat sources. The overall shape of open and homogeneous semicircular strip-shaped heat sources representing open half-penny cracks can also be retrieved but the reconstruction of the deeper end of the heat source loses contrast. Angle-, radius- and depth-dependent inhomogeneous heat flux distributions within these semicircular strips can also be qualitatively characterized. Reconstructions of experimental data taken on samples containing calibrated heat sources confirm the predictions from reconstructions of synthetic data. We also present inversions of experimental data obtained from a real welded Inconel 718 specimen. The results are in good qualitative agreement with the results of liquids penetrants testing.

Efficient 3D inversions using the Richards equation

NASA Astrophysics Data System (ADS)

Cockett, Rowan; Heagy, Lindsey J.; Haber, Eldad

2018-07-01

Fluid flow in the vadose zone is governed by the Richards equation; it is parameterized by hydraulic conductivity, which is a nonlinear function of pressure head. Investigations in the vadose zone typically require characterizing distributed hydraulic properties. Water content or pressure head data may include direct measurements made from boreholes. Increasingly, proxy measurements from hydrogeophysics are being used to supply more spatially and temporally dense data sets. Inferring hydraulic parameters from such datasets requires the ability to efficiently solve and optimize the nonlinear time domain Richards equation. This is particularly important as the number of parameters to be estimated in a vadose zone inversion continues to grow. In this paper, we describe an efficient technique to invert for distributed hydraulic properties in 1D, 2D, and 3D. Our technique does not store the Jacobian matrix, but rather computes its product with a vector. Existing literature for the Richards equation inversion explicitly calculates the sensitivity matrix using finite difference or automatic differentiation, however, for large scale problems these methods are constrained by computation and/or memory. Using an implicit sensitivity algorithm enables large scale inversion problems for any distributed hydraulic parameters in the Richards equation to become tractable on modest computational resources. We provide an open source implementation of our technique based on the SimPEG framework, and show it in practice for a 3D inversion of saturated hydraulic conductivity using water content data through time.

Inversions of the Ledoux discriminant: a closer look at the tachocline

NASA Astrophysics Data System (ADS)

Buldgen, Gaël; Salmon, S. J. A. J.; Godart, M.; Noels, A.; Scuflaire, R.; Dupret, M. A.; Reese, D. R.; Colgan, J.; Fontes, C. J.; Eggenberger, P.; Hakel, P.; Kilcrease, D. P.; Richard, O.

2017-11-01

Modelling the base of the solar convective envelope is a tedious problem. Since the first rotation inversions, solar modellers are confronted with the fact that a region of very limited extent has an enormous physical impact on the Sun. Indeed, it is the transition region from differential to solid body rotation, the tachocline, which furthermore is influenced by turbulence and is also supposed to be the seat of the solar magnetic dynamo. Moreover, solar models show significant disagreement with the sound-speed profile in this region. In this Letter, we show how helioseismology can provide further constraints on this region by carrying out an inversion of the Ledoux discriminant. We compare these inversions for standard solar sodels built using various opacity tables and chemical abundances and discuss the origins of the discrepancies between solar models and the Sun.

Inverse scattering approach to improving pattern recognition

NASA Astrophysics Data System (ADS)

Chapline, George; Fu, Chi-Yung

2005-05-01

The Helmholtz machine provides what may be the best existing model for how the mammalian brain recognizes patterns. Based on the observation that the "wake-sleep" algorithm for training a Helmholtz machine is similar to the problem of finding the potential for a multi-channel Schrodinger equation, we propose that the construction of a Schrodinger potential using inverse scattering methods can serve as a model for how the mammalian brain learns to extract essential information from sensory data. In particular, inverse scattering theory provides a conceptual framework for imagining how one might use EEG and MEG observations of brain-waves together with sensory feedback to improve human learning and pattern recognition. Longer term, implementation of inverse scattering algorithms on a digital or optical computer could be a step towards mimicking the seamless information fusion of the mammalian brain.

Inverse Scattering Approach to Improving Pattern Recognition

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

Chapline, G; Fu, C

2005-02-15

The Helmholtz machine provides what may be the best existing model for how the mammalian brain recognizes patterns. Based on the observation that the ''wake-sleep'' algorithm for training a Helmholtz machine is similar to the problem of finding the potential for a multi-channel Schrodinger equation, we propose that the construction of a Schrodinger potential using inverse scattering methods can serve as a model for how the mammalian brain learns to extract essential information from sensory data. In particular, inverse scattering theory provides a conceptual framework for imagining how one might use EEG and MEG observations of brain-waves together with sensorymore » feedback to improve human learning and pattern recognition. Longer term, implementation of inverse scattering algorithms on a digital or optical computer could be a step towards mimicking the seamless information fusion of the mammalian brain.« less

The importance of coherence in inverse problems in optics

NASA Astrophysics Data System (ADS)

Ferwerda, H. A.; Baltes, H. P.; Glass, A. S.; Steinle, B.

1981-12-01

Current inverse problems of statistical optics are presented with a guide to relevant literature. The inverse problems are categorized into four groups, and the Van Cittert-Zernike theorem and its generalization are discussed. The retrieval of structural information from the far-zone degree of coherence and the time-averaged intensity distribution of radiation scattered by a superposition of random and periodic scatterers are also discussed. In addition, formulas for the calculation of far-zone properties are derived within the framework of scalar optics, and results are applied to two examples.

Comparison of iterative inverse coarse-graining methods

NASA Astrophysics Data System (ADS)

Rosenberger, David; Hanke, Martin; van der Vegt, Nico F. A.

2016-10-01

Deriving potentials for coarse-grained Molecular Dynamics (MD) simulations is frequently done by solving an inverse problem. Methods like Iterative Boltzmann Inversion (IBI) or Inverse Monte Carlo (IMC) have been widely used to solve this problem. The solution obtained by application of these methods guarantees a match in the radial distribution function (RDF) between the underlying fine-grained system and the derived coarse-grained system. However, these methods often fail in reproducing thermodynamic properties. To overcome this deficiency, additional thermodynamic constraints such as pressure or Kirkwood-Buff integrals (KBI) may be added to these methods. In this communication we test the ability of these methods to converge to a known solution of the inverse problem. With this goal in mind we have studied a binary mixture of two simple Lennard-Jones (LJ) fluids, in which no actual coarse-graining is performed. We further discuss whether full convergence is actually needed to achieve thermodynamic representability.

Variable-permittivity linear inverse problem for the H(sub z)-polarized case

NASA Technical Reports Server (NTRS)

Moghaddam, M.; Chew, W. C.

1993-01-01

The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.

Ground-based microwave radiometric remote sensing of the tropical atmosphere

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

Han, Yong.

1992-01-01

A partially developed 9-channel ground-based microwave radiometer for the Department of Meteorology at Penn State was completed and tested. Complementary units were added, corrections to both hardware and software were made, and system software was corrected and upgraded. Measurements from this radiometer were used to infer tropospheric temperature, water vapor and cloud liquid water. The various weighting functions at each of the 9 channels were calculated and analyzed to estimate the sensitivities of the brightness temperature to the desired atmospheric variables. The mathematical inversion problem, in a linear form, was viewed in terms of the theory of linear algebra. Severalmore » methods for solving the inversion problem were reviewed. Radiometric observations were conducted during the 1990 Tropical Cyclone Motion Experiment. The radiometer was installed on the island of Saipan in a tropical region. The radiometer was calibrated using tipping curve and radiosonde data as well as measurements of the radiation from a blackbody absorber. A linear statistical method was applied for the data inversion. The inversion coefficients in the equation were obtained using a large number of radiosonde profiles from Guam and a radiative transfer model. Retrievals were compared with those from local, Saipan, radiosonde measurements. Water vapor profiles, integrated water vapor, and integrated liquid water were retrieved successfully. For temperature profile retrievals, however, the radiometric measurements with experimental noises added no more profile information to the inversion than that they were determined mainly by the surface pressure measurements. A method was developed to derive the integrated water vapor and liquid water from combined radiometer and ceilometer measurements. Significant improvement on radiometric measurements of the integrated liquid water can be gained with this method.« less

On computational experiments in some inverse problems of heat and mass transfer

NASA Astrophysics Data System (ADS)

Bilchenko, G. G.; Bilchenko, N. G.

2016-11-01

The results of mathematical modeling of effective heat and mass transfer on hypersonic aircraft permeable surfaces are considered. The physic-chemical processes (the dissociation and the ionization) in laminar boundary layer of compressible gas are appreciated. Some algorithms of control restoration are suggested for the interpolation and approximation statements of heat and mass transfer inverse problems. The differences between the methods applied for the problem solutions search for these statements are discussed. Both the algorithms are realized as programs. Many computational experiments were accomplished with the use of these programs. The parameters of boundary layer obtained by means of the A.A.Dorodnicyn's generalized integral relations method from solving the direct problems have been used to obtain the inverse problems solutions. Two types of blowing laws restoration for the inverse problem in interpolation statement are presented as the examples. The influence of the temperature factor on the blowing restoration is investigated. The different character of sensitivity of controllable parameters (the local heat flow and local tangent friction) respectively to step (discrete) changing of control (the blowing) and the switching point position is studied.

TOMO3D: 3-D joint refraction and reflection traveltime tomography parallel code for active-source seismic data—synthetic test

NASA Astrophysics Data System (ADS)

Meléndez, A.; Korenaga, J.; Sallarès, V.; Miniussi, A.; Ranero, C. R.

2015-10-01

We present a new 3-D traveltime tomography code (TOMO3D) for the modelling of active-source seismic data that uses the arrival times of both refracted and reflected seismic phases to derive the velocity distribution and the geometry of reflecting boundaries in the subsurface. This code is based on its popular 2-D version TOMO2D from which it inherited the methods to solve the forward and inverse problems. The traveltime calculations are done using a hybrid ray-tracing technique combining the graph and bending methods. The LSQR algorithm is used to perform the iterative regularized inversion to improve the initial velocity and depth models. In order to cope with an increased computational demand due to the incorporation of the third dimension, the forward problem solver, which takes most of the run time (˜90 per cent in the test presented here), has been parallelized with a combination of multi-processing and message passing interface standards. This parallelization distributes the ray-tracing and traveltime calculations among available computational resources. The code's performance is illustrated with a realistic synthetic example, including a checkerboard anomaly and two reflectors, which simulates the geometry of a subduction zone. The code is designed to invert for a single reflector at a time. A data-driven layer-stripping strategy is proposed for cases involving multiple reflectors, and it is tested for the successive inversion of the two reflectors. Layers are bound by consecutive reflectors, and an initial velocity model for each inversion step incorporates the results from previous steps. This strategy poses simpler inversion problems at each step, allowing the recovery of strong velocity discontinuities that would otherwise be smoothened.

Solving constrained inverse problems for waveform tomography with Salvus

NASA Astrophysics Data System (ADS)

Boehm, C.; Afanasiev, M.; van Driel, M.; Krischer, L.; May, D.; Rietmann, M.; Fichtner, A.

2016-12-01

Finding a good balance between flexibility and performance is often difficult within domain-specific software projects. To achieve this balance, we introduce Salvus: an open-source high-order finite element package built upon PETSc and Eigen, that focuses on large-scale full-waveform modeling and inversion. One of the key features of Salvus is its modular design, based on C++ mixins, that separates the physical equations from the numerical discretization and the mathematical optimization. In this presentation we focus on solving inverse problems with Salvus and discuss (i) dealing with inexact derivatives resulting, e.g., from lossy wavefield compression, (ii) imposing additional constraints on the model parameters, e.g., from effective medium theory, and (iii) integration with a workflow management tool. We present a feasible-point trust-region method for PDE-constrained inverse problems that can handle inexactly computed derivatives. The level of accuracy in the approximate derivatives is controlled by localized error estimates to ensure global convergence of the method. Additional constraints on the model parameters are typically cheap to compute without the need for further simulations. Hence, including them in the trust-region subproblem introduces only a small computational overhead, but ensures feasibility of the model in every iteration. We show examples with homogenization constraints derived from effective medium theory (i.e. all fine-scale updates must upscale to a physically meaningful long-wavelength model). Salvus has a built-in workflow management framework to automate the inversion with interfaces to user-defined misfit functionals and data structures. This significantly reduces the amount of manual user interaction and enhances reproducibility which we demonstrate for several applications from the laboratory to global scale.

An iterative particle filter approach for coupled hydro-geophysical inversion of a controlled infiltration experiment

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

Manoli, Gabriele, E-mail: manoli@dmsa.unipd.it; Nicholas School of the Environment, Duke University, Durham, NC 27708; Rossi, Matteo

The modeling of unsaturated groundwater flow is affected by a high degree of uncertainty related to both measurement and model errors. Geophysical methods such as Electrical Resistivity Tomography (ERT) can provide useful indirect information on the hydrological processes occurring in the vadose zone. In this paper, we propose and test an iterated particle filter method to solve the coupled hydrogeophysical inverse problem. We focus on an infiltration test monitored by time-lapse ERT and modeled using Richards equation. The goal is to identify hydrological model parameters from ERT electrical potential measurements. Traditional uncoupled inversion relies on the solution of two sequentialmore » inverse problems, the first one applied to the ERT measurements, the second one to Richards equation. This approach does not ensure an accurate quantitative description of the physical state, typically violating mass balance. To avoid one of these two inversions and incorporate in the process more physical simulation constraints, we cast the problem within the framework of a SIR (Sequential Importance Resampling) data assimilation approach that uses a Richards equation solver to model the hydrological dynamics and a forward ERT simulator combined with Archie's law to serve as measurement model. ERT observations are then used to update the state of the system as well as to estimate the model parameters and their posterior distribution. The limitations of the traditional sequential Bayesian approach are investigated and an innovative iterative approach is proposed to estimate the model parameters with high accuracy. The numerical properties of the developed algorithm are verified on both homogeneous and heterogeneous synthetic test cases based on a real-world field experiment.« less

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

Ray, Jaideep; Lee, Jina; Lefantzi, Sophia

The estimation of fossil-fuel CO2 emissions (ffCO2) from limited ground-based and satellite measurements of CO2 concentrations will form a key component of the monitoring of treaties aimed at the abatement of greenhouse gas emissions. To that end, we construct a multiresolution spatial parametrization for fossil-fuel CO2 emissions (ffCO2), to be used in atmospheric inversions. Such a parametrization does not currently exist. The parametrization uses wavelets to accurately capture the multiscale, nonstationary nature of ffCO2 emissions and employs proxies of human habitation, e.g., images of lights at night and maps of built-up areas to reduce the dimensionality of the multiresolution parametrization.more » The parametrization is used in a synthetic data inversion to test its suitability for use in atmospheric inverse problem. This linear inverse problem is predicated on observations of ffCO2 concentrations collected at measurement towers. We adapt a convex optimization technique, commonly used in the reconstruction of compressively sensed images, to perform sparse reconstruction of the time-variant ffCO2 emission field. We also borrow concepts from compressive sensing to impose boundary conditions i.e., to limit ffCO2 emissions within an irregularly shaped region (the United States, in our case). We find that the optimization algorithm performs a data-driven sparsification of the spatial parametrization and retains only of those wavelets whose weights could be estimated from the observations. Further, our method for the imposition of boundary conditions leads to a 10computational saving over conventional means of doing so. We conclude with a discussion of the accuracy of the estimated emissions and the suitability of the spatial parametrization for use in inverse problems with a significant degree of regularization.« less

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.

An Inverse Neural Controller Based on the Applicability Domain of RBF Network Models

PubMed Central

Alexandridis, Alex; Stogiannos, Marios; Papaioannou, Nikolaos; Zois, Elias; Sarimveis, Haralambos

2018-01-01

This paper presents a novel methodology of generic nature for controlling nonlinear systems, using inverse radial basis function neural network models, which may combine diverse data originating from various sources. The algorithm starts by applying the particle swarm optimization-based non-symmetric variant of the fuzzy means (PSO-NSFM) algorithm so that an approximation of the inverse system dynamics is obtained. PSO-NSFM offers models of high accuracy combined with small network structures. Next, the applicability domain concept is suitably tailored and embedded into the proposed control structure in order to ensure that extrapolation is avoided in the controller predictions. Finally, an error correction term, estimating the error produced by the unmodeled dynamics and/or unmeasured external disturbances, is included to the control scheme to increase robustness. The resulting controller guarantees bounded input-bounded state (BIBS) stability for the closed loop system when the open loop system is BIBS stable. The proposed methodology is evaluated on two different control problems, namely, the control of an experimental armature-controlled direct current (DC) motor and the stabilization of a highly nonlinear simulated inverted pendulum. For each one of these problems, appropriate case studies are tested, in which a conventional neural controller employing inverse models and a PID controller are also applied. The results reveal the ability of the proposed control scheme to handle and manipulate diverse data through a data fusion approach and illustrate the superiority of the method in terms of faster and less oscillatory responses. PMID:29361781

Content based image retrieval for matching images of improvised explosive devices in which snake initialization is viewed as an inverse problem

NASA Astrophysics Data System (ADS)

Acton, Scott T.; Gilliam, Andrew D.; Li, Bing; Rossi, Adam

2008-02-01

Improvised explosive devices (IEDs) are common and lethal instruments of terrorism, and linking a terrorist entity to a specific device remains a difficult task. In the effort to identify persons associated with a given IED, we have implemented a specialized content based image retrieval system to search and classify IED imagery. The system makes two contributions to the art. First, we introduce a shape-based matching technique exploiting shape, color, and texture (wavelet) information, based on novel vector field convolution active contours and a novel active contour initialization method which treats coarse segmentation as an inverse problem. Second, we introduce a unique graph theoretic approach to match annotated printed circuit board images for which no schematic or connectivity information is available. The shape-based image retrieval method, in conjunction with the graph theoretic tool, provides an efficacious system for matching IED images. For circuit imagery, the basic retrieval mechanism has a precision of 82.1% and the graph based method has a precision of 98.1%. As of the fall of 2007, the working system has processed over 400,000 case images.

Filtering techniques for efficient inversion of two-dimensional Nuclear Magnetic Resonance data

NASA Astrophysics Data System (ADS)

Bortolotti, V.; Brizi, L.; Fantazzini, P.; Landi, G.; Zama, F.

2017-10-01

The inversion of two-dimensional Nuclear Magnetic Resonance (NMR) data requires the solution of a first kind Fredholm integral equation with a two-dimensional tensor product kernel and lower bound constraints. For the solution of this ill-posed inverse problem, the recently presented 2DUPEN algorithm [V. Bortolotti et al., Inverse Problems, 33(1), 2016] uses multiparameter Tikhonov regularization with automatic choice of the regularization parameters. In this work, I2DUPEN, an improved version of 2DUPEN that implements Mean Windowing and Singular Value Decomposition filters, is deeply tested. The reconstruction problem with filtered data is formulated as a compressed weighted least squares problem with multi-parameter Tikhonov regularization. Results on synthetic and real 2D NMR data are presented with the main purpose to deeper analyze the separate and combined effects of these filtering techniques on the reconstructed 2D distribution.

Regularization Reconstruction Method for Imaging Problems in Electrical Capacitance Tomography

NASA Astrophysics Data System (ADS)

Chu, Pan; Lei, Jing

2017-11-01

The electrical capacitance tomography (ECT) is deemed to be a powerful visualization measurement technique for the parametric measurement in a multiphase flow system. The inversion task in the ECT technology is an ill-posed inverse problem, and seeking for an efficient numerical method to improve the precision of the reconstruction images is important for practical measurements. By the introduction of the Tikhonov regularization (TR) methodology, in this paper a loss function that emphasizes the robustness of the estimation and the low rank property of the imaging targets is put forward to convert the solution of the inverse problem in the ECT reconstruction task into a minimization problem. Inspired by the split Bregman (SB) algorithm, an iteration scheme is developed for solving the proposed loss function. Numerical experiment results validate that the proposed inversion method not only reconstructs the fine structures of the imaging targets, but also improves the robustness.

Termination Proofs for String Rewriting Systems via Inverse Match-Bounds

NASA Technical Reports Server (NTRS)

Butler, Ricky (Technical Monitor); Geser, Alfons; Hofbauer, Dieter; Waldmann, Johannes

2004-01-01

Annotating a letter by a number, one can record information about its history during a reduction. A string rewriting system is called match-bounded if there is a global upper bound to these numbers. In earlier papers we established match-boundedness as a strong sufficient criterion for both termination and preservation of regular languages. We show now that the string rewriting system whose inverse (left and right hand sides exchanged) is match-bounded, also have exceptional properties, but slightly different ones. Inverse match-bounded systems effectively preserve context-free languages; their sets of normalized strings and their sets of immortal strings are effectively regular. These sets of strings can be used to decide the normalization, the termination and the uniform termination problems of inverse match-bounded systems. We also show that the termination problem is decidable in linear time, and that a certain strong reachability problem is deciable, thus solving two open problems of McNaughton's.

Assimilating data into open ocean tidal models

NASA Astrophysics Data System (ADS)

Kivman, Gennady A.

The problem of deriving tidal fields from observations by reason of incompleteness and imperfectness of every data set practically available has an infinitely large number of allowable solutions fitting the data within measurement errors and hence can be treated as ill-posed. Therefore, interpolating the data always relies on some a priori assumptions concerning the tides, which provide a rule of sampling or, in other words, a regularization of the ill-posed problem. Data assimilation procedures used in large scale tide modeling are viewed in a common mathematical framework as such regularizations. It is shown that they all (basis functions expansion, parameter estimation, nudging, objective analysis, general inversion, and extended general inversion), including those (objective analysis and general inversion) originally formulated in stochastic terms, may be considered as utilizations of one of the three general methods suggested by the theory of ill-posed problems. The problem of grid refinement critical for inverse methods and nudging is discussed.

Multi-level damage identification with response reconstruction

NASA Astrophysics Data System (ADS)

Zhang, Chao-Dong; Xu, You-Lin

2017-10-01

Damage identification through finite element (FE) model updating usually forms an inverse problem. Solving the inverse identification problem for complex civil structures is very challenging since the dimension of potential damage parameters in a complex civil structure is often very large. Aside from enormous computation efforts needed in iterative updating, the ill-condition and non-global identifiability features of the inverse problem probably hinder the realization of model updating based damage identification for large civil structures. Following a divide-and-conquer strategy, a multi-level damage identification method is proposed in this paper. The entire structure is decomposed into several manageable substructures and each substructure is further condensed as a macro element using the component mode synthesis (CMS) technique. The damage identification is performed at two levels: the first is at macro element level to locate the potentially damaged region and the second is over the suspicious substructures to further locate as well as quantify the damage severity. In each level's identification, the damage searching space over which model updating is performed is notably narrowed down, not only reducing the computation amount but also increasing the damage identifiability. Besides, the Kalman filter-based response reconstruction is performed at the second level to reconstruct the response of the suspicious substructure for exact damage quantification. Numerical studies and laboratory tests are both conducted on a simply supported overhanging steel beam for conceptual verification. The results demonstrate that the proposed multi-level damage identification via response reconstruction does improve the identification accuracy of damage localization and quantization considerably.

A genetic algorithm approach to estimate glacier mass variations from GRACE data

NASA Astrophysics Data System (ADS)

Reimond, Stefan; Klinger, Beate; Krauss, Sandro; Mayer-Gürr, Torsten

2017-04-01

The application of a genetic algorithm (GA) to the inference of glacier mass variations with a point-mass modeling method is described. GRACE K-band ranging data (available since April 2002) processed at the Graz University of Technology serve as input for this study. The reformulation of the point-mass inversion method in terms of an optimization problem is motivated by two reasons: first, an improved choice of the positions of the modeled point-masses (with a particular focus on the depth parameter) is expected to increase the signal-to-noise ratio. Considering these coordinates as additional unknown parameters (besides from the mass change magnitudes) results in a highly non-linear optimization problem. The second reason is that the mass inversion from satellite tracking data is an ill-posed problem, and hence regularization becomes necessary. The main task in this context is the determination of the regularization parameter, which is typically done by means of heuristic selection rules like, e.g., the L-curve criterion. In this study, however, the challenge of selecting a suitable balancing parameter (or even a matrix) is tackled by introducing regularization to the overall optimization problem. Based on this novel approach, estimations of ice-mass changes in various alpine glacier systems (e.g. Svalbard) are presented and compared to existing results and alternative inversion methods.

Modification of the nuclear landscape in the inverse problem framework using the generalized Bethe-Weizsäcker mass formula

NASA Astrophysics Data System (ADS)

Mavrodiev, S. Cht.; Deliyergiyev, M. A.

We formalized the nuclear mass problem in the inverse problem framework. This approach allows us to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. The inverse problem was formulated for the numerically generalized semi-empirical mass formula of Bethe and von Weizsäcker. It was solved in a step-by-step way based on the AME2012 nuclear database. The established parametrization describes the measured nuclear masses of 2564 isotopes with a maximum deviation less than 2.6MeV, starting from the number of protons and number of neutrons equal to 1. The explicit form of unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified least χ2 procedure, that realized in the algorithms which were developed by Lubomir Aleksandrov to solve the nonlinear systems of equations via the Gauss-Newton method, lets us to choose the better one between two functions with same χ2. In the obtained generalized model, the corrections to the binding energy depend on nine proton (2, 8, 14, 20, 28, 50, 82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic numbers as well on the asymptotic boundaries of their influence. The obtained results were compared with the predictions of other models.

Minimizing EIT image artefacts from mesh variability in finite element models.

PubMed

Adler, Andy; Lionheart, William R B

2011-07-01

Electrical impedance tomography (EIT) solves an inverse problem to estimate the conductivity distribution within a body from electrical simulation and measurements at the body surface, where the inverse problem is based on a solution of Laplace's equation in the body. Most commonly, a finite element model (FEM) is used, largely because of its ability to describe irregular body shapes. In this paper, we show that simulated variations in the positions of internal nodes within a FEM can result in serious image artefacts in the reconstructed images. Such variations occur when designing FEM meshes to conform to conductivity targets, but the effects may also be seen in other applications of absolute and difference EIT. We explore the hypothesis that these artefacts result from changes in the projection of the anisotropic conductivity tensor onto the FEM system matrix, which introduces anisotropic components into the simulated voltages, which cannot be reconstructed onto an isotropic image, and appear as artefacts. The magnitude of the anisotropic effect is analysed for a small regular FEM, and shown to be proportional to the relative node movement as a fraction of element size. In order to address this problem, we show that it is possible to incorporate a FEM node movement component into the formulation of the inverse problem. These results suggest that it is important to consider artefacts due to FEM mesh geometry in EIT image reconstruction.

Identification of Bouc-Wen hysteretic parameters based on enhanced response sensitivity approach

NASA Astrophysics Data System (ADS)

Wang, Li; Lu, Zhong-Rong

2017-05-01

This paper aims to identify parameters of Bouc-Wen hysteretic model using time-domain measured data. It follows a general inverse identification procedure, that is, identifying model parameters is treated as an optimization problem with the nonlinear least squares objective function. Then, the enhanced response sensitivity approach, which has been shown convergent and proper for such kind of problems, is adopted to solve the optimization problem. Numerical tests are undertaken to verify the proposed identification approach.

A theoretical Deduction from the Hubble law based on a Modified Newtonian Dynamics with field of Yukawa inverse

NASA Astrophysics Data System (ADS)

Falcon, N.

2017-07-01

At cosmic scales the dynamics of the Universe are almost exclusively prescribed by the force of gravity; however the assumption of the law of gravitation, depending on the inverse of the distance, leads to the known problems of the rotation curves of galaxies and missing mass (dark matter). The problem of the coupling of gravity to changes in scale and deviations from the law of the inverse square is an old problem (Laplace, 1805; Seeliger 1898), which has motivated alternatives to Newtonian dynamics compatible with observations. The present paper postulates a modified Newtonian dynamics by adding an inverse Yukawa potential: U(r)≡U0(M)(r-r0)e-α/r is the the potential per unit mass (in N/kg) as a function of the barionic mass that causes the field, r0 is of the order of 50h-1 Mpc and alpha is a coupling constant of the order of 2.5 h-1 Mpc. This potential is zero within the solar system, slightly attractive at interstellar distances, very attractive in galactic range and repulsive at cosmic scales. Its origin is the barionic matter, it allows to include the Milgrow MoND theory to explain the rotation curves, it is compatible with the experiments Eovos type, and allows to deduce the law of Hubble to cosmic scales, in the form H0=100h km/s Mpc≍U0(M)/c, where U0(M)≍ 4pi×6.67 10-11m/s2, is obtained from the Laplace's equation, assuming that the gravitational force is the law of the inverse of the square plus a non-linear term type Yukawa inverse. It is concluded that the modification of the law of gravity with nonlinear terms, allows to model the dynamics of the Universe on a large scale and include non-locality without dark matter. (See Falcon et al. 2014, International Journal of Astronomy and Astrophysics, 4, 551-559).

A function space framework for structural total variation regularization with applications in inverse problems

NASA Astrophysics Data System (ADS)

Hintermüller, Michael; Holler, Martin; Papafitsoros, Kostas

2018-06-01

In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semi-continuous envelope (relaxation) of a suitable TV type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted TV for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddle-point problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson log-likelihood data discrepancy terms. Finally, we provide proof-of-concept numerical examples where we solve the saddle-point problem for weighted TV denoising as well as for MR guided PET image reconstruction.

Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R2 = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.

Convex blind image deconvolution with inverse filtering

NASA Astrophysics Data System (ADS)

Lv, Xiao-Guang; Li, Fang; Zeng, Tieyong

2018-03-01

Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption.

Parana Basin Structure from Multi-Objective Inversion of Surface Wave and Receiver Function by Competent Genetic Algorithm

NASA Astrophysics Data System (ADS)

An, M.; Assumpcao, M.

2003-12-01

The joint inversion of receiver function and surface wave is an effective way to diminish the influences of the strong tradeoff among parameters and the different sensitivity to the model parameters in their respective inversions, but the inversion problem becomes more complex. Multi-objective problems can be much more complicated than single-objective inversion in the model selection and optimization. If objectives are involved and conflicting, models can be ordered only partially. In this case, Pareto-optimal preference should be used to select solutions. On the other hand, the inversion to get only a few optimal solutions can not deal properly with the strong tradeoff between parameters, the uncertainties in the observation, the geophysical complexities and even the incompetency of the inversion technique. The effective way is to retrieve the geophysical information statistically from many acceptable solutions, which requires more competent global algorithms. Competent genetic algorithms recently proposed are far superior to the conventional genetic algorithm and can solve hard problems quickly, reliably and accurately. In this work we used one of competent genetic algorithms, Bayesian Optimization Algorithm as the main inverse procedure. This algorithm uses Bayesian networks to draw out inherited information and can use Pareto-optimal preference in the inversion. With this algorithm, the lithospheric structure of Paran"› basin is inverted to fit both the observations of inter-station surface wave dispersion and receiver function.

Problem-Based Learning for Didactic Presentation to Baccalaureate Nursing Students.

PubMed

Montenery, Susan

2017-05-01

Nursing judgment is an essential component in the delivery of safe, quality patient care. Nurses must have the knowledge and skills to question authority, make judgments, substantiate evidence, and advocate for the patient. Traditional pedagogy in content-laden courses remains primarily lecture based. Incorporating active strategies to strengthen professional practice is essential. A pilot study assessed senior baccalaureate nursing students' perceptions of problem-based learning (PBL) and their readiness for self-directed learning. In addition, the authors analyzed the relationship between readiness for self-directed learning and course content mastery using PBL. Students completed the Self-directed Learning Readiness Scale, the Problem-Based Learning Environment Inventory, and course content mastery exams. Students reported positive experiences with PBL and readiness for self-directed learning. Readiness for self-directed learning and 2 of 5 exam scores were inversely, significantly related. Students' perceptions of their readiness for self-directed learning did not always correspond with course content mastery. Specifically, some students who perceived themselves as ready for self-directed learning did not perform well on course content exams. This inverse relationship has not been reported by other researchers and brings an interesting perspective to student perceptions and actual performance. Four themes emerged from students' narrative responses: Prepared Me for Real Life Professional Situations, Stimulated My Critical Thinking, Promoted Independent Problem Solving, and Supported Learning Retention. PBL as a pedagogical approach provides opportunities for nursing students to explore their professional independence while attempting to master content.

Self-constrained inversion of potential fields

NASA Astrophysics Data System (ADS)

Paoletti, V.; Ialongo, S.; Florio, G.; Fedi, M.; Cella, F.

2013-11-01

We present a potential-field-constrained inversion procedure based on a priori information derived exclusively from the analysis of the gravity and magnetic data (self-constrained inversion). The procedure is designed to be applied to underdetermined problems and involves scenarios where the source distribution can be assumed to be of simple character. To set up effective constraints, we first estimate through the analysis of the gravity or magnetic field some or all of the following source parameters: the source depth-to-the-top, the structural index, the horizontal position of the source body edges and their dip. The second step is incorporating the information related to these constraints in the objective function as depth and spatial weighting functions. We show, through 2-D and 3-D synthetic and real data examples, that potential field-based constraints, for example, structural index, source boundaries and others, are usually enough to obtain substantial improvement in the density and magnetization models.

High effective inverse dynamics modelling for dual-arm robot

NASA Astrophysics Data System (ADS)

Shen, Haoyu; Liu, Yanli; Wu, Hongtao

2018-05-01

To deal with the problem of inverse dynamics modelling for dual arm robot, a recursive inverse dynamics modelling method based on decoupled natural orthogonal complement is presented. In this model, the concepts and methods of Decoupled Natural Orthogonal Complement matrices are used to eliminate the constraint forces in the Newton-Euler kinematic equations, and the screws is used to express the kinematic and dynamics variables. On this basis, the paper has developed a special simulation program with symbol software of Mathematica and conducted a simulation research on the a dual-arm robot. Simulation results show that the proposed method based on decoupled natural orthogonal complement can save an enormous amount of CPU time that was spent in computing compared with the recursive Newton-Euler kinematic equations and the results is correct and reasonable, which can verify the reliability and efficiency of the method.

Diagnostic methods for atmospheric inversions of long-lived greenhouse gases

NASA Astrophysics Data System (ADS)

Michalak, Anna M.; Randazzo, Nina A.; Chevallier, Frédéric

2017-06-01

The ability to predict the trajectory of climate change requires a clear understanding of the emissions and uptake (i.e., surface fluxes) of long-lived greenhouse gases (GHGs). Furthermore, the development of climate policies is driving a need to constrain the budgets of anthropogenic GHG emissions. Inverse problems that couple atmospheric observations of GHG concentrations with an atmospheric chemistry and transport model have increasingly been used to gain insights into surface fluxes. Given the inherent technical challenges associated with their solution, it is imperative that objective approaches exist for the evaluation of such inverse problems. Because direct observation of fluxes at compatible spatiotemporal scales is rarely possible, diagnostics tools must rely on indirect measures. Here we review diagnostics that have been implemented in recent studies and discuss their use in informing adjustments to model setup. We group the diagnostics along a continuum starting with those that are most closely related to the scientific question being targeted, and ending with those most closely tied to the statistical and computational setup of the inversion. We thus begin with diagnostics based on assessments against independent information (e.g., unused atmospheric observations, large-scale scientific constraints), followed by statistical diagnostics of inversion results, diagnostics based on sensitivity tests, and analyses of robustness (e.g., tests focusing on the chemistry and transport model, the atmospheric observations, or the statistical and computational framework), and close with the use of synthetic data experiments (i.e., observing system simulation experiments, OSSEs). We find that existing diagnostics provide a crucial toolbox for evaluating and improving flux estimates but, not surprisingly, cannot overcome the fundamental challenges associated with limited atmospheric observations or the lack of direct flux measurements at compatible scales. As atmospheric inversions are increasingly expected to contribute to national reporting of GHG emissions, the need for developing and implementing robust and transparent evaluation approaches will only grow.

A robust method of computing finite difference coefficients based on Vandermonde matrix

NASA Astrophysics Data System (ADS)

Zhang, Yijie; Gao, Jinghuai; Peng, Jigen; Han, Weimin

2018-05-01

When the finite difference (FD) method is employed to simulate the wave propagation, high-order FD method is preferred in order to achieve better accuracy. However, if the order of FD scheme is high enough, the coefficient matrix of the formula for calculating finite difference coefficients is close to be singular. In this case, when the FD coefficients are computed by matrix inverse operator of MATLAB, inaccuracy can be produced. In order to overcome this problem, we have suggested an algorithm based on Vandermonde matrix in this paper. After specified mathematical transformation, the coefficient matrix is transformed into a Vandermonde matrix. Then the FD coefficients of high-order FD method can be computed by the algorithm of Vandermonde matrix, which prevents the inverse of the singular matrix. The dispersion analysis and numerical results of a homogeneous elastic model and a geophysical model of oil and gas reservoir demonstrate that the algorithm based on Vandermonde matrix has better accuracy compared with matrix inverse operator of MATLAB.

Directional Slack-Based Measure for the Inverse Data Envelopment Analysis

PubMed Central

Abu Bakar, Mohd Rizam; Lee, Lai Soon; Jaafar, Azmi B.; Heydar, Maryam

2014-01-01

A novel technique has been introduced in this research which lends its basis to the Directional Slack-Based Measure for the inverse Data Envelopment Analysis. In practice, the current research endeavors to elucidate the inverse directional slack-based measure model within a new production possibility set. On one occasion, there is a modification imposed on the output (input) quantities of an efficient decision making unit. In detail, the efficient decision making unit in this method was omitted from the present production possibility set but substituted by the considered efficient decision making unit while its input and output quantities were subsequently modified. The efficiency score of the entire DMUs will be retained in this approach. Also, there would be an improvement in the efficiency score. The proposed approach was investigated in this study with reference to a resource allocation problem. It is possible to simultaneously consider any upsurges (declines) of certain outputs associated with the efficient decision making unit. The significance of the represented model is accentuated by presenting numerical examples. PMID:24883350

Technical Note: Approximate Bayesian parameterization of a complex tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2013-08-01

Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can successfully be applied to process-based models of high complexity. The methodology is particularly suited to heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models in ecology and evolution.

IPDO-2007: Inverse Problems, Design and Optimization Symposium

DTIC Science & Technology

2007-08-01

Kanevce, G. H., Kanevce, Lj. P., and Mitrevski , V. B.), International Symposium on Inverse Problems, Design and Optimization (IPDO-2007), (eds...107 Gligor Kanevce Ljubica Kanevce Vangelce Mitrevski George Dulikravich 108 Gligor Kanevce Ljubica Kanevce Igor Andreevski George Dulikravich

On the recovery of missing low and high frequency information from bandlimited reflectivity data

NASA Astrophysics Data System (ADS)

Sacchi, M. D.; Ulrych, T. J.

2007-12-01

During the last two decades, an important effort in the seismic exploration community has been made to retrieve broad-band seismic data by means of deconvolution and inversion. In general, the problem can be stated as a spectral reconstruction problem. In other words, given limited spectral information about the earth's reflectivity sequence, one attempts to create a broadband estimate of the Fourier spectra of the unknown reflectivity. Techniques based on the principle of parsimony can be effectively used to retrieve a sparse spike sequence and, consequently, a broad band signal. Alternatively, continuation methods, e.g., autoregressive modeling, can be used to extrapolate the recorded bandwidth of the seismic signal. The goal of this paper is to examine under what conditions the recovery of low and high frequencies from band-limited and noisy signals is possible. At the heart of the methods we discuss, is the celebrated non-Gaussian assumption so important in many modern signal processing methods, such as ICA, for example. Spectral recovery from limited information tends to work when the reflectivity consist of a few well isolated events. Results degrade with the number of reflectors, decreasing SNR and decreasing bandwidth of the source wavelet. Constrains and information-based priors can be used to stabilize the recovery but, as in all inverse problems, the solution is nonunique and effort is required to understand the level of recovery that is achievable, always keeping the physics of the problem in mind. We provide in this paper, a survey of methods to recover broad-band reflectivity sequences and examine the role that these techniques can play in the processing and inversion as applied to exploration and global seismology.

Approximate non-linear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-03-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-waves scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform (GRT). After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic non-linear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P-wave and S-wave information.

Approximate nonlinear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-07-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-wave scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform. After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic nonlinear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P- and S-wave information.

Analysis of Tube Hydroforming by means of an Inverse Approach

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

Nguyen, Ba Nghiep; Johnson, Kenneth I.; Khaleel, Mohammad A.

2003-05-01

This paper presents a computational tool for the analysis of freely hydroformed tubes by means of an inverse approach. The formulation of the inverse method developed by Guo et al. is adopted and extended to the tube hydrofoming problems in which the initial geometry is a round tube submitted to hydraulic pressure and axial feed at the tube ends (end-feed). A simple criterion based on a forming limit diagram is used to predict the necking regions in the deformed workpiece. Although the developed computational tool is a stand-alone code, it has been linked to the Marc finite element code formore » meshing and visualization of results. The application of the inverse approach to tube hydroforming is illustrated through the analyses of the aluminum alloy AA6061-T4 seamless tubes under free hydroforming conditions. The results obtained are in good agreement with those issued from a direct incremental approach. However, the computational time in the inverse procedure is much less than that in the incremental method.« less

A preprocessing strategy for helioseismic inversions

NASA Astrophysics Data System (ADS)

Christensen-Dalsgaard, J.; Thompson, M. J.

1993-05-01

Helioseismic inversion in general involves considerable computational expense, due to the large number of modes that is typically considered. This is true in particular of the widely used optimally localized averages (OLA) inversion methods, which require the inversion of one or more matrices whose order is the number of modes in the set. However, the number of practically independent pieces of information that a large helioseismic mode set contains is very much less than the number of modes, suggesting that the set might first be reduced before the expensive inversion is performed. We demonstrate with a model problem that by first performing a singular value decomposition the original problem may be transformed into a much smaller one, reducing considerably the cost of the OLA inversion and with no significant loss of information.

Comparing multiple statistical methods for inverse prediction in nuclear forensics applications

DOE PAGES

Lewis, John R.; Zhang, Adah; Anderson-Cook, Christine Michaela

2017-10-29

Forensic science seeks to predict source characteristics using measured observables. Statistically, this objective can be thought of as an inverse problem where interest is in the unknown source characteristics or factors ( X) of some underlying causal model producing the observables or responses (Y = g ( X) + error). Here, this paper reviews several statistical methods for use in inverse problems and demonstrates that comparing results from multiple methods can be used to assess predictive capability. Motivation for assessing inverse predictions comes from the desired application to historical and future experiments involving nuclear material production for forensics research inmore » which inverse predictions, along with an assessment of predictive capability, are desired.« less

Comparing multiple statistical methods for inverse prediction in nuclear forensics applications

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

Lewis, John R.; Zhang, Adah; Anderson-Cook, Christine Michaela

Forensic science seeks to predict source characteristics using measured observables. Statistically, this objective can be thought of as an inverse problem where interest is in the unknown source characteristics or factors ( X) of some underlying causal model producing the observables or responses (Y = g ( X) + error). Here, this paper reviews several statistical methods for use in inverse problems and demonstrates that comparing results from multiple methods can be used to assess predictive capability. Motivation for assessing inverse predictions comes from the desired application to historical and future experiments involving nuclear material production for forensics research inmore » which inverse predictions, along with an assessment of predictive capability, are desired.« less

3D lens-free time-lapse microscopy for 3D cell culture

NASA Astrophysics Data System (ADS)

Berdeu, Anthony; Momey, Fabien; Laperrousaz, Bastien; Bordy, Thomas; Gidrol, Xavier; Dinten, Jean-Marc; Picollet-D'hahan, Nathalie; Allier, Cédric

2017-07-01

We propose a new imaging platform based on lens-free time-lapse microscopy for 3D cell culture and its dedicated algorithm lying on a fully 3D regularized inverse problem approach. First 3D+t results are presented

Final Report: Resolving and Discriminating Overlapping Anomalies from Multiple Objects in Cluttered Environments

DTIC Science & Technology

2015-12-15

UXO community . NAME Total Number: PERCENT_SUPPORTEDNAME FTE Equivalent: Total Number: Irma Shamatava 0.50 0.50 1 Resolving and Discriminating...Distinguishing an object of interest from innocuous items is the main problem that the UXO community is facing currently. This inverse problem...innocuous items is the main problem that the UXO community is facing currently. This inverse problem demands fast and accurate representation of

Bilinear Inverse Problems: Theory, Algorithms, and Applications

NASA Astrophysics Data System (ADS)

Ling, Shuyang

We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical guarantees and stability theory are derived and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

Reflection full-waveform inversion using a modified phase misfit function

NASA Astrophysics Data System (ADS)

Cui, Chao; Huang, Jian-Ping; Li, Zhen-Chun; Liao, Wen-Yuan; Guan, Zhe

2017-09-01

Reflection full-waveform inversion (RFWI) updates the low- and highwavenumber components, and yields more accurate initial models compared with conventional full-waveform inversion (FWI). However, there is strong nonlinearity in conventional RFWI because of the lack of low-frequency data and the complexity of the amplitude. The separation of phase and amplitude information makes RFWI more linear. Traditional phase-calculation methods face severe phase wrapping. To solve this problem, we propose a modified phase-calculation method that uses the phase-envelope data to obtain the pseudo phase information. Then, we establish a pseudophase-information-based objective function for RFWI, with the corresponding source and gradient terms. Numerical tests verify that the proposed calculation method using the phase-envelope data guarantees the stability and accuracy of the phase information and the convergence of the objective function. The application on a portion of the Sigsbee2A model and comparison with inversion results of the improved RFWI and conventional FWI methods verify that the pseudophase-based RFWI produces a highly accurate and efficient velocity model. Moreover, the proposed method is robust to noise and high frequency.

Multidimensional NMR inversion without Kronecker products: Multilinear inversion

NASA Astrophysics Data System (ADS)

Medellín, David; Ravi, Vivek R.; Torres-Verdín, Carlos

2016-08-01

Multidimensional NMR inversion using Kronecker products poses several challenges. First, kernel compression is only possible when the kernel matrices are separable, and in recent years, there has been an increasing interest in NMR sequences with non-separable kernels. Second, in three or more dimensions, the singular value decomposition is not unique; therefore kernel compression is not well-defined for higher dimensions. Without kernel compression, the Kronecker product yields matrices that require large amounts of memory, making the inversion intractable for personal computers. Finally, incorporating arbitrary regularization terms is not possible using the Lawson-Hanson (LH) or the Butler-Reeds-Dawson (BRD) algorithms. We develop a minimization-based inversion method that circumvents the above problems by using multilinear forms to perform multidimensional NMR inversion without using kernel compression or Kronecker products. The new method is memory efficient, requiring less than 0.1% of the memory required by the LH or BRD methods. It can also be extended to arbitrary dimensions and adapted to include non-separable kernels, linear constraints, and arbitrary regularization terms. Additionally, it is easy to implement because only a cost function and its first derivative are required to perform the inversion.

Application of L1-norm regularization to epicardial potential reconstruction based on gradient projection.

PubMed

Wang, Liansheng; Qin, Jing; Wong, Tien Tsin; Heng, Pheng Ann

2011-10-07

The epicardial potential (EP)-targeted inverse problem of electrocardiography (ECG) has been widely investigated as it is demonstrated that EPs reflect underlying myocardial activity. It is a well-known ill-posed problem as small noises in input data may yield a highly unstable solution. Traditionally, L2-norm regularization methods have been proposed to solve this ill-posed problem. But the L2-norm penalty function inherently leads to considerable smoothing of the solution, which reduces the accuracy of distinguishing abnormalities and locating diseased regions. Directly using the L1-norm penalty function, however, may greatly increase computational complexity due to its non-differentiability. We propose an L1-norm regularization method in order to reduce the computational complexity and make rapid convergence possible. Variable splitting is employed to make the L1-norm penalty function differentiable based on the observation that both positive and negative potentials exist on the epicardial surface. Then, the inverse problem of ECG is further formulated as a bound-constrained quadratic problem, which can be efficiently solved by gradient projection in an iterative manner. Extensive experiments conducted on both synthetic data and real data demonstrate that the proposed method can handle both measurement noise and geometry noise and obtain more accurate results than previous L2- and L1-norm regularization methods, especially when the noises are large.

Regularized minimum I-divergence methods for the inverse blackbody radiation problem

NASA Astrophysics Data System (ADS)

Choi, Kerkil; Lanterman, Aaron D.; Shin, Jaemin

2006-08-01

This paper proposes iterative methods for estimating the area temperature distribution of a blackbody from its total radiated power spectrum measurements. This is called the inverse blackbody radiation problem. This problem is inherently ill-posed due to the characteristics of the kernel in the underlying integral equation given by Planck's law. The functions involved in the problem are all non-negative. Csiszár's I-divergence is an information-theoretic discrepancy measure between two non-negative functions. We derive iterative methods for minimizing Csiszár's I-divergence between the measured power spectrum and the power spectrum arising from the estimate according to the integral equation. Due to the ill-posedness of the problem, unconstrained algorithms often produce poor estimates, especially when the measurements are corrupted by noise. To alleviate this difficulty, we apply regularization methods to our algorithms. Penalties based on Shannon's entropy, the L1-norm and Good's roughness are chosen to suppress the undesirable artefacts. When a penalty is applied, the pertinent optimization that needs to be performed at each iteration is no longer trivial. In particular, Good's roughness causes couplings between estimate components. To handle this issue, we adapt Green's one-step-late method. This choice is based on the important fact that our minimum I-divergence algorithms can be interpreted as asymptotic forms of certain expectation-maximization algorithms. The effectiveness of our methods is illustrated via various numerical experiments.

The inverse problem of sensing the mass and force induced by an adsorbate on a beam nanomechanical resonator

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

Liu, Yun; Zhang, Yin

2016-06-08

The mass sensing superiority of a micro/nanomechanical resonator sensor over conventional mass spectrometry has been, or at least, is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors such as position and axial force can also cause the shifts of resonant frequencies. The in-situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as smallmore » as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of mechanical resonator sensor on two things: reducing extra experimental equipments and achieving better mass sensing by considering more factors.« less

Trajectory Correction and Locomotion Analysis of a Hexapod Walking Robot with Semi-Round Rigid Feet

PubMed Central

Zhu, Yaguang; Jin, Bo; Wu, Yongsheng; Guo, Tong; Zhao, Xiangmo

2016-01-01

Aimed at solving the misplaced body trajectory problem caused by the rolling of semi-round rigid feet when a robot is walking, a legged kinematic trajectory correction methodology based on the Least Squares Support Vector Machine (LS-SVM) is proposed. The concept of ideal foothold is put forward for the three-dimensional kinematic model modification of a robot leg, and the deviation value between the ideal foothold and real foothold is analyzed. The forward/inverse kinematic solutions between the ideal foothold and joint angular vectors are formulated and the problem of direct/inverse kinematic nonlinear mapping is solved by using the LS-SVM. Compared with the previous approximation method, this correction methodology has better accuracy and faster calculation speed with regards to inverse kinematics solutions. Experiments on a leg platform and a hexapod walking robot are conducted with multi-sensors for the analysis of foot tip trajectory, base joint vibration, contact force impact, direction deviation, and power consumption, respectively. The comparative analysis shows that the trajectory correction methodology can effectively correct the joint trajectory, thus eliminating the contact force influence of semi-round rigid feet, significantly improving the locomotion of the walking robot and reducing the total power consumption of the system. PMID:27589766

Feasibility of waveform inversion of Rayleigh waves for shallow shear-wave velocity using a genetic algorithm

USGS Publications Warehouse

Zeng, C.; Xia, J.; Miller, R.D.; Tsoflias, G.P.

2011-01-01

Conventional surface wave inversion for shallow shear (S)-wave velocity relies on the generation of dispersion curves of Rayleigh waves. This constrains the method to only laterally homogeneous (or very smooth laterally heterogeneous) earth models. Waveform inversion directly fits waveforms on seismograms, hence, does not have such a limitation. Waveforms of Rayleigh waves are highly related to S-wave velocities. By inverting the waveforms of Rayleigh waves on a near-surface seismogram, shallow S-wave velocities can be estimated for earth models with strong lateral heterogeneity. We employ genetic algorithm (GA) to perform waveform inversion of Rayleigh waves for S-wave velocities. The forward problem is solved by finite-difference modeling in the time domain. The model space is updated by generating offspring models using GA. Final solutions can be found through an iterative waveform-fitting scheme. Inversions based on synthetic records show that the S-wave velocities can be recovered successfully with errors no more than 10% for several typical near-surface earth models. For layered earth models, the proposed method can generate one-dimensional S-wave velocity profiles without the knowledge of initial models. For earth models containing lateral heterogeneity in which case conventional dispersion-curve-based inversion methods are challenging, it is feasible to produce high-resolution S-wave velocity sections by GA waveform inversion with appropriate priori information. The synthetic tests indicate that the GA waveform inversion of Rayleigh waves has the great potential for shallow S-wave velocity imaging with the existence of strong lateral heterogeneity. ?? 2011 Elsevier B.V.

Numerical simulations of induction and MWD logging tools and data inversion method with X-window interface on a UNIX workstation

NASA Astrophysics Data System (ADS)

Tian, Xiang-Dong

The purpose of this research is to simulate induction and measuring-while-drilling (MWD) logs. In simulation of logs, there are two tasks. The first task, the forward modeling procedure, is to compute the logs from known formation. The second task, the inversion procedure, is to determine the unknown properties of the formation from the measured field logs. In general, the inversion procedure requires the solution of a forward model. In this study, a stable numerical method to simulate induction and MWD logs is presented. The proposed algorithm is based on a horizontal eigenmode expansion method. Vertical propagation of modes is modeled by a three-layer module. The multilayer cases are treated as a cascade of these modules. The mode tracing algorithm possesses stable characteristics that are superior to other methods. This method is applied to simulate the logs in the formations with both vertical and horizontal layers, and also used to study the groove effects of the MWD tool. The results are very good. Two-dimensional inversion of induction logs is an nonlinear problem. Nonlinear functions of the apparent conductivity are expanded into a Taylor series. After truncating the high order terms in this Taylor series, the nonlinear functions are linearized. An iterative procedure is then devised to solve the inversion problem. In each iteration, the Jacobian matrix is calculated, and a small variation computed using the least-squares method is used to modify the background medium. Finally, the inverted medium is obtained. The horizontal eigenstate method is used to solve the forward problem. It is found that a good inverted formation can be obtained by using measurements. In order to help the user simulate the induction logs conveniently, a Wellog Simulator, based on the X-window system, is developed. The application software (FORTRAN codes) embedded in the Simulator is designed to simulate the responses of the induction tools in the layered formation with dipping beds. The graphic user-interface part of the Wellog Simulator is implemented with C and Motif. Through the user interface, the user can prepare the simulation data, select the tools, simulate the logs and plot the results.

Pulse-Inversion Subharmonic Ultrafast Active Cavitation Imaging in Tissue Using Fast Eigenspace-Based Adaptive Beamforming and Cavitation Deconvolution.

PubMed

Bai, Chen; Xu, Shanshan; Duan, Junbo; Jing, Bowen; Yang, Miao; Wan, Mingxi

2017-08-01

Pulse-inversion subharmonic (PISH) imaging can display information relating to pure cavitation bubbles while excluding that of tissue. Although plane-wave-based ultrafast active cavitation imaging (UACI) can monitor the transient activities of cavitation bubbles, its resolution and cavitation-to-tissue ratio (CTR) are barely satisfactory but can be significantly improved by introducing eigenspace-based (ESB) adaptive beamforming. PISH and UACI are a natural combination for imaging of pure cavitation activity in tissue; however, it raises two problems: 1) the ESB beamforming is hard to implement in real time due to the enormous amount of computation associated with the covariance matrix inversion and eigendecomposition and 2) the narrowband characteristic of the subharmonic filter will incur a drastic degradation in resolution. Thus, in order to jointly address these two problems, we propose a new PISH-UACI method using novel fast ESB (F-ESB) beamforming and cavitation deconvolution for nonlinear signals. This method greatly reduces the computational complexity by using F-ESB beamforming through dimensionality reduction based on principal component analysis, while maintaining the high quality of ESB beamforming. The degraded resolution is recovered using cavitation deconvolution through a modified convolution model and compressive deconvolution. Both simulations and in vitro experiments were performed to verify the effectiveness of the proposed method. Compared with the ESB-based PISH-UACI, the entire computation of our proposed approach was reduced by 99%, while the axial resolution gain and CTR were increased by 3 times and 2 dB, respectively, confirming that satisfactory performance can be obtained for monitoring pure cavitation bubbles in tissue erosion.

Computing Fourier integral operators with caustics

NASA Astrophysics Data System (ADS)

Caday, Peter

2016-12-01

Fourier integral operators (FIOs) have widespread applications in imaging, inverse problems, and PDEs. An implementation of a generic algorithm for computing FIOs associated with canonical graphs is presented, based on a recent paper of de Hoop et al. Given the canonical transformation and principal symbol of the operator, a preprocessing step reduces application of an FIO approximately to multiplications, pushforwards and forward and inverse discrete Fourier transforms, which can be computed in O({N}n+(n-1)/2{log}N) time for an n-dimensional FIO. The same preprocessed data also allows computation of the inverse and transpose of the FIO, with identical runtime. Examples demonstrate the algorithm’s output, and easily extendible MATLAB/C++ source code is available from the author.

Viscoelastic material inversion using Sierra-SD and ROL

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

Walsh, Timothy; Aquino, Wilkins; Ridzal, Denis

2014-11-01

In this report we derive frequency-domain methods for inverse characterization of the constitutive parameters of viscoelastic materials. The inverse problem is cast in a PDE-constrained optimization framework with efficient computation of gradients and Hessian vector products through matrix free operations. The abstract optimization operators for first and second derivatives are derived from first principles. Various methods from the Rapid Optimization Library (ROL) are tested on the viscoelastic inversion problem. The methods described herein are applied to compute the viscoelastic bulk and shear moduli of a foam block model, which was recently used in experimental testing for viscoelastic property characterization.

Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction

NASA Astrophysics Data System (ADS)

Qiao, Baijie; Zhang, Xingwu; Gao, Jiawei; Liu, Ruonan; Chen, Xuefeng

2017-01-01

Most previous regularization methods for solving the inverse problem of force reconstruction are to minimize the l2-norm of the desired force. However, these traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition, commonly fail to solve the large-scale ill-posed inverse problem in moderate computational cost. In this paper, taking into account the sparse characteristic of impact force, the idea of sparse deconvolution is first introduced to the field of impact force reconstruction and a general sparse deconvolution model of impact force is constructed. Second, a novel impact force reconstruction method based on the primal-dual interior point method (PDIPM) is proposed to solve such a large-scale sparse deconvolution model, where minimizing the l2-norm is replaced by minimizing the l1-norm. Meanwhile, the preconditioned conjugate gradient algorithm is used to compute the search direction of PDIPM with high computational efficiency. Finally, two experiments including the small-scale or medium-scale single impact force reconstruction and the relatively large-scale consecutive impact force reconstruction are conducted on a composite wind turbine blade and a shell structure to illustrate the advantage of PDIPM. Compared with Tikhonov regularization, PDIPM is more efficient, accurate and robust whether in the single impact force reconstruction or in the consecutive impact force reconstruction.

Simulation of Constrained Musculoskeletal Systems in Task Space.

PubMed

Stanev, Dimitar; Moustakas, Konstantinos

2018-02-01

This paper proposes an operational task space formalization of constrained musculoskeletal systems, motivated by its promising results in the field of robotics. The change of representation requires different algorithms for solving the inverse and forward dynamics simulation in the task space domain. We propose an extension to the direct marker control and an adaptation of the computed muscle control algorithms for solving the inverse kinematics and muscle redundancy problems, respectively. Experimental evaluation demonstrates that this framework is not only successful in dealing with the inverse dynamics problem, but also provides an intuitive way of studying and designing simulations, facilitating assessment prior to any experimental data collection. The incorporation of constraints in the derivation unveils an important extension of this framework toward addressing systems that use absolute coordinates and topologies that contain closed kinematic chains. Task space projection reveals a more intuitive encoding of the motion planning problem, allows for better correspondence between observed and estimated variables, provides the means to effectively study the role of kinematic redundancy, and most importantly, offers an abstract point of view and control, which can be advantageous toward further integration with high level models of the precommand level. Task-based approaches could be adopted in the design of simulation related to the study of constrained musculoskeletal systems.

The Priority Inversion Problem and Real-Time Symbolic Model Checking

DTIC Science & Technology

1993-04-23

real time systems unpredictable in subtle ways. This makes it more difficult to implement and debug such systems. Our work discusses this problem and presents one possible solution. The solution is formalized and verified using temporal logic model checking techniques. In order to perform the verification, the BDD-based symbolic model checking algorithm given in previous works was extended to handle real-time properties using the bounded until operator. We believe that this algorithm, which is based on discrete time, is able to handle many real-time properties

Imaging model for the scintillator and its application to digital radiography image enhancement.

PubMed

Wang, Qian; Zhu, Yining; Li, Hongwei

2015-12-28

Digital Radiography (DR) images obtained by OCD-based (optical coupling detector) Micro-CT system usually suffer from low contrast. In this paper, a mathematical model is proposed to describe the image formation process in scintillator. By solving the correlative inverse problem, the quality of DR images is improved, i.e. higher contrast and spatial resolution. By analyzing the radiative transfer process of visible light in scintillator, scattering is recognized as the main factor leading to low contrast. Moreover, involved blurring effect is also concerned and described as point spread function (PSF). Based on these physical processes, the scintillator imaging model is then established. When solving the inverse problem, pre-correction to the intensity of x-rays, dark channel prior based haze removing technique, and an effective blind deblurring approach are employed. Experiments on a variety of DR images show that the proposed approach could improve the contrast of DR images dramatically as well as eliminate the blurring vision effectively. Compared with traditional contrast enhancement methods, such as CLAHE, our method could preserve the relative absorption values well.

RNAfbinv: an interactive Java application for fragment-based design of RNA sequences.

PubMed

Weinbrand, Lina; Avihoo, Assaf; Barash, Danny

2013-11-15

In RNA design problems, it is plausible to assume that the user would be interested in preserving a particular RNA secondary structure motif, or fragment, for biological reasons. The preservation could be in structure or sequence, or both. Thus, the inverse RNA folding problem could benefit from considering fragment constraints. We have developed a new interactive Java application called RNA fragment-based inverse that allows users to insert an RNA secondary structure in dot-bracket notation. It then performs sequence design that conforms to the shape of the input secondary structure, the specified thermodynamic stability, the specified mutational robustness and the user-selected fragment after shape decomposition. In this shape-based design approach, specific RNA structural motifs with known biological functions are strictly enforced, while others can possess more flexibility in their structure in favor of preserving physical attributes and additional constraints. RNAfbinv is freely available for download on the web at http://www.cs.bgu.ac.il/~RNAexinv/RNAfbinv. The site contains a help file with an explanation regarding the exact use.

An optimization method for the problems of thermal cloaking of material bodies

NASA Astrophysics Data System (ADS)

Alekseev, G. V.; Levin, V. A.

2016-11-01

Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.

Complete Sets of Radiating and Nonradiating Parts of a Source and Their Fields with Applications in Inverse Scattering Limited-Angle Problems

PubMed Central

Louis, A. K.

2006-01-01

Many algorithms applied in inverse scattering problems use source-field systems instead of the direct computation of the unknown scatterer. It is well known that the resulting source problem does not have a unique solution, since certain parts of the source totally vanish outside of the reconstruction area. This paper provides for the two-dimensional case special sets of functions, which include all radiating and all nonradiating parts of the source. These sets are used to solve an acoustic inverse problem in two steps. The problem under discussion consists of determining an inhomogeneous obstacle supported in a part of a disc, from data, known for a subset of a two-dimensional circle. In a first step, the radiating parts are computed by solving a linear problem. The second step is nonlinear and consists of determining the nonradiating parts. PMID:23165060

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

ERIC Educational Resources Information Center

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Parameter Estimation for Geoscience Applications Using a Measure-Theoretic Approach

NASA Astrophysics Data System (ADS)

Dawson, C.; Butler, T.; Mattis, S. A.; Graham, L.; Westerink, J. J.; Vesselinov, V. V.; Estep, D.

2016-12-01

Effective modeling of complex physical systems arising in the geosciences is dependent on knowing parameters which are often difficult or impossible to measure in situ. In this talk we focus on two such problems, estimating parameters for groundwater flow and contaminant transport, and estimating parameters within a coastal ocean model. The approach we will describe, proposed by collaborators D. Estep, T. Butler and others, is based on a novel stochastic inversion technique based on measure theory. In this approach, given a probability space on certain observable quantities of interest, one searches for the sets of highest probability in parameter space which give rise to these observables. When viewed as mappings between sets, the stochastic inversion problem is well-posed in certain settings, but there are computational challenges related to the set construction. We will focus the talk on estimating scalar parameters and fields in a contaminant transport setting, and in estimating bottom friction in a complicated near-shore coastal application.

Inverse Source Data-Processing Strategies for Radio-Frequency Localization in Indoor Environments.

PubMed

Gennarelli, Gianluca; Al Khatib, Obada; Soldovieri, Francesco

2017-10-27

Indoor positioning of mobile devices plays a key role in many aspects of our daily life. These include real-time people tracking and monitoring, activity recognition, emergency detection, navigation, and numerous location based services. Despite many wireless technologies and data-processing algorithms have been developed in recent years, indoor positioning is still a problem subject of intensive research. This paper deals with the active radio-frequency (RF) source localization in indoor scenarios. The localization task is carried out at the physical layer thanks to receiving sensor arrays which are deployed on the border of the surveillance region to record the signal emitted by the source. The localization problem is formulated as an imaging one by taking advantage of the inverse source approach. Different measurement configurations and data-processing/fusion strategies are examined to investigate their effectiveness in terms of localization accuracy under both line-of-sight (LOS) and non-line of sight (NLOS) conditions. Numerical results based on full-wave synthetic data are reported to support the analysis.

Inverse Source Data-Processing Strategies for Radio-Frequency Localization in Indoor Environments

PubMed Central

Gennarelli, Gianluca; Al Khatib, Obada; Soldovieri, Francesco

2017-01-01

Indoor positioning of mobile devices plays a key role in many aspects of our daily life. These include real-time people tracking and monitoring, activity recognition, emergency detection, navigation, and numerous location based services. Despite many wireless technologies and data-processing algorithms have been developed in recent years, indoor positioning is still a problem subject of intensive research. This paper deals with the active radio-frequency (RF) source localization in indoor scenarios. The localization task is carried out at the physical layer thanks to receiving sensor arrays which are deployed on the border of the surveillance region to record the signal emitted by the source. The localization problem is formulated as an imaging one by taking advantage of the inverse source approach. Different measurement configurations and data-processing/fusion strategies are examined to investigate their effectiveness in terms of localization accuracy under both line-of-sight (LOS) and non-line of sight (NLOS) conditions. Numerical results based on full-wave synthetic data are reported to support the analysis. PMID:29077071

Parameter Identification Of Multilayer Thermal Insulation By Inverse Problems

NASA Astrophysics Data System (ADS)

Nenarokomov, Aleksey V.; Alifanov, Oleg M.; Gonzalez, Vivaldo M.

2012-07-01

The purpose of this paper is to introduce an iterative regularization method in the research of radiative and thermal properties of materials with further applications in the design of Thermal Control Systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (heat capacity, emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the (TCS) for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the Inverse Heat Transfer Problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the IHTP, based on sensitivity function approach, is presented too. The practical testing was performed for specimen of the real MLI. This paper consists of recent researches, which developed the approach suggested at [1].

Frechet derivatives for shallow water ocean acoustic inverse problems

NASA Astrophysics Data System (ADS)

Odom, Robert I.

2003-04-01

For any inverse problem, finding a model fitting the data is only half the problem. Most inverse problems of interest in ocean acoustics yield nonunique model solutions, and involve inevitable trade-offs between model and data resolution and variance. Problems of uniqueness and resolution and variance trade-offs can be addressed by examining the Frechet derivatives of the model-data functional with respect to the model variables. Tarantola [Inverse Problem Theory (Elsevier, Amsterdam, 1987), p. 613] published analytical formulas for the basic derivatives, e.g., derivatives of pressure with respect to elastic moduli and density. Other derivatives of interest, such as the derivative of transmission loss with respect to attenuation, can be easily constructed using the chain rule. For a range independent medium the analytical formulas involve only the Green's function and the vertical derivative of the Green's function for the medium. A crucial advantage of the analytical formulas for the Frechet derivatives over numerical differencing is that they can be computed with a single pass of any program which supplies the Green's function. Various derivatives of interest in shallow water ocean acoustics are presented and illustrated by an application to the sensitivity of measured pressure to shallow water sediment properties. [Work supported by ONR.

Comparing implementations of penalized weighted least-squares sinogram restoration.

PubMed

Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick

2010-11-01

A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix inversion into smaller coupled problems and exploited sparseness to minimize matrix operations. For the conjugate-gradient approach, the authors exploited sparseness and preconditioned the problem to speed up convergence. All methods produced qualitatively and quantitatively similar images as measured by resolution-variance tradeoffs and difference images. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approaches, with a computational burden higher by an order of magnitude or more. The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of the authors' previous penalized-likelihood implementation. Iterative conjugate-gradient based PWLS sinogram restoration with careful matrix optimizations has computational advantages over direct matrix PWLS inversion and over penalized-likelihood sinogram restoration and can be considered a good alternative in standard-dose regimes.

An approach to quantum-computational hydrologic inverse analysis

DOE PAGES

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

An approach to quantum-computational hydrologic inverse analysis.

PubMed

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.

Coupling of Large Amplitude Inversion with Other States

NASA Astrophysics Data System (ADS)

Pearson, John; Yu, Shanshan

2016-06-01

The coupling of a large amplitude motion with a small amplitude vibration remains one of the least well characterized problems in molecular physics. Molecular inversion poses a few unique and not intuitively obvious challenges to the large amplitude motion problem. In spite of several decades of theoretical work numerous challenges in calculation of transition frequencies and more importantly intensities persist. The most challenging aspect of this problem is that the inversion coordinate is a unique function of the overall vibrational state including both the large and small amplitude modes. As a result, the r-axis system and the meaning of the K-quantum number in the rotational basis set are unique to each vibrational state of large or small amplitude motion. This unfortunate reality has profound consequences to calculation of intensities and the coupling of nearly degenerate vibrational states. The case of NH3 inversion and inversion through a plane of symmetry in alcohols will be examined to find a general path forward.

An approach to quantum-computational hydrologic inverse analysis

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

O'Malley, Daniel

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

Stability and uncertainty of finite-fault slip inversions: Application to the 2004 Parkfield, California, earthquake

USGS Publications Warehouse

Hartzell, S.; Liu, P.; Mendoza, C.; Ji, C.; Larson, K.M.

2007-01-01

The 2004 Parkfield, California, earthquake is used to investigate stability and uncertainty aspects of the finite-fault slip inversion problem with different a priori model assumptions. We utilize records from 54 strong ground motion stations and 13 continuous, 1-Hz sampled, geodetic instruments. Two inversion procedures are compared: a linear least-squares subfault-based methodology and a nonlinear global search algorithm. These two methods encompass a wide range of the different approaches that have been used to solve the finite-fault slip inversion problem. For the Parkfield earthquake and the inversion of velocity or displacement waveforms, near-surface related site response (top 100 m, frequencies above 1 Hz) is shown to not significantly affect the solution. Results are also insensitive to selection of slip rate functions with similar duration and to subfault size if proper stabilizing constraints are used. The linear and nonlinear formulations yield consistent results when the same limitations in model parameters are in place and the same inversion norm is used. However, the solution is sensitive to the choice of inversion norm, the bounds on model parameters, such as rake and rupture velocity, and the size of the model fault plane. The geodetic data set for Parkfield gives a slip distribution different from that of the strong-motion data, which may be due to the spatial limitation of the geodetic stations and the bandlimited nature of the strong-motion data. Cross validation and the bootstrap method are used to set limits on the upper bound for rupture velocity and to derive mean slip models and standard deviations in model parameters. This analysis shows that slip on the northwestern half of the Parkfield rupture plane from the inversion of strong-motion data is model dependent and has a greater uncertainty than slip near the hypocenter.

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

Cerebellum-inspired neural network solution of the inverse kinematics problem.

PubMed

Asadi-Eydivand, Mitra; Ebadzadeh, Mohammad Mehdi; Solati-Hashjin, Mehran; Darlot, Christian; Abu Osman, Noor Azuan

2015-12-01

The demand today for more complex robots that have manipulators with higher degrees of freedom is increasing because of technological advances. Obtaining the precise movement for a desired trajectory or a sequence of arm and positions requires the computation of the inverse kinematic (IK) function, which is a major problem in robotics. The solution of the IK problem leads robots to the precise position and orientation of their end-effector. We developed a bioinspired solution comparable with the cerebellar anatomy and function to solve the said problem. The proposed model is stable under all conditions merely by parameter determination, in contrast to recursive model-based solutions, which remain stable only under certain conditions. We modified the proposed model for the simple two-segmented arm to prove the feasibility of the model under a basic condition. A fuzzy neural network through its learning method was used to compute the parameters of the system. Simulation results show the practical feasibility and efficiency of the proposed model in robotics. The main advantage of the proposed model is its generalizability and potential use in any robot.

An alternative empirical likelihood method in missing response problems and causal inference.

PubMed

Ren, Kaili; Drummond, Christopher A; Brewster, Pamela S; Haller, Steven T; Tian, Jiang; Cooper, Christopher J; Zhang, Biao

2016-11-30

Missing responses are common problems in medical, social, and economic studies. When responses are missing at random, a complete case data analysis may result in biases. A popular debias method is inverse probability weighting proposed by Horvitz and Thompson. To improve efficiency, Robins et al. proposed an augmented inverse probability weighting method. The augmented inverse probability weighting estimator has a double-robustness property and achieves the semiparametric efficiency lower bound when the regression model and propensity score model are both correctly specified. In this paper, we introduce an empirical likelihood-based estimator as an alternative to Qin and Zhang (2007). Our proposed estimator is also doubly robust and locally efficient. Simulation results show that the proposed estimator has better performance when the propensity score is correctly modeled. Moreover, the proposed method can be applied in the estimation of average treatment effect in observational causal inferences. Finally, we apply our method to an observational study of smoking, using data from the Cardiovascular Outcomes in Renal Atherosclerotic Lesions clinical trial. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

The Natural-CCD Algorithm, a Novel Method to Solve the Inverse Kinematics of Hyper-redundant and Soft Robots.

PubMed

Martín, Andrés; Barrientos, Antonio; Del Cerro, Jaime

2018-03-22

This article presents a new method to solve the inverse kinematics problem of hyper-redundant and soft manipulators. From an engineering perspective, this kind of robots are underdetermined systems. Therefore, they exhibit an infinite number of solutions for the inverse kinematics problem, and to choose the best one can be a great challenge. A new algorithm based on the cyclic coordinate descent (CCD) and named as natural-CCD is proposed to solve this issue. It takes its name as a result of generating very harmonious robot movements and trajectories that also appear in nature, such as the golden spiral. In addition, it has been applied to perform continuous trajectories, to develop whole-body movements, to analyze motion planning in complex environments, and to study fault tolerance, even for both prismatic and rotational joints. The proposed algorithm is very simple, precise, and computationally efficient. It works for robots either in two or three spatial dimensions and handles a large amount of degrees-of-freedom. Because of this, it is aimed to break down barriers between discrete hyper-redundant and continuum soft robots.

Learning the inverse kinetics of an octopus-like manipulator in three-dimensional space.

PubMed

Giorelli, M; Renda, F; Calisti, M; Arienti, A; Ferri, G; Laschi, C

2015-05-13

This work addresses the inverse kinematics problem of a bioinspired octopus-like manipulator moving in three-dimensional space. The bioinspired manipulator has a conical soft structure that confers the ability of twirling around objects as a real octopus arm does. Despite the simple design, the soft conical shape manipulator driven by cables is described by nonlinear differential equations, which are difficult to solve analytically. Since exact solutions of the equations are not available, the Jacobian matrix cannot be calculated analytically and the classical iterative methods cannot be used. To overcome the intrinsic problems of methods based on the Jacobian matrix, this paper proposes a neural network learning the inverse kinematics of a soft octopus-like manipulator driven by cables. After the learning phase, a feed-forward neural network is able to represent the relation between manipulator tip positions and forces applied to the cables. Experimental results show that a desired tip position can be achieved in a short time, since heavy computations are avoided, with a degree of accuracy of 8% relative average error with respect to the total arm length.

a Novel Discrete Optimal Transport Method for Bayesian Inverse Problems

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Myers, A.; Wang, K.; Thiery, A.

2017-12-01

We present the Augmented Ensemble Transform (AET) method for generating approximate samples from a high-dimensional posterior distribution as a solution to Bayesian inverse problems. Solving large-scale inverse problems is critical for some of the most relevant and impactful scientific endeavors of our time. Therefore, constructing novel methods for solving the Bayesian inverse problem in more computationally efficient ways can have a profound impact on the science community. This research derives the novel AET method for exploring a posterior by solving a sequence of linear programming problems, resulting in a series of transport maps which map prior samples to posterior samples, allowing for the computation of moments of the posterior. We show both theoretical and numerical results, indicating this method can offer superior computational efficiency when compared to other SMC methods. Most of this efficiency is derived from matrix scaling methods to solve the linear programming problem and derivative-free optimization for particle movement. We use this method to determine inter-well connectivity in a reservoir and the associated uncertainty related to certain parameters. The attached file shows the difference between the true parameter and the AET parameter in an example 3D reservoir problem. The error is within the Morozov discrepancy allowance with lower computational cost than other particle methods.

Seismic waveform inversion best practices: regional, global and exploration test cases

NASA Astrophysics Data System (ADS)

Modrak, Ryan; Tromp, Jeroen

2016-09-01

Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions. We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.

Analytical and experimental studies on detection of longitudinal, L and inverted T cracks in isotropic and bi-material beams based on changes in natural frequencies

NASA Astrophysics Data System (ADS)

Ravi, J. T.; Nidhan, S.; Muthu, N.; Maiti, S. K.

2018-02-01

An analytical method for determination of dimensions of longitudinal crack in monolithic beams, based on frequency measurements, has been extended to model L and inverted T cracks. Such cracks including longitudinal crack arise in beams made of layered isotropic or composite materials. A new formulation for modelling cracks in bi-material beams is presented. Longitudinal crack segment sizes, for L and inverted T cracks, varying from 2.7% to 13.6% of length of Euler-Bernoulli beams are considered. Both forward and inverse problems have been examined. In the forward problems, the analytical results are compared with finite element (FE) solutions. In the inverse problems, the accuracy of prediction of crack dimensions is verified using FE results as input for virtual testing. The analytical results show good agreement with the actual crack dimensions. Further, experimental studies have been done to verify the accuracy of the analytical method for prediction of dimensions of three types of crack in isotropic and bi-material beams. The results show that the proposed formulation is reliable and can be employed for crack detection in slender beam like structures in practice.

Coupled Hydrogeophysical Inversion and Hydrogeological Data Fusion

NASA Astrophysics Data System (ADS)

Cirpka, O. A.; Schwede, R. L.; Li, W.

2012-12-01

Tomographic geophysical monitoring methods give the opportunity to observe hydrogeological tests at higher spatial resolution than is possible with classical hydraulic monitoring tools. This has been demonstrated in a substantial number of studies in which electrical resistivity tomography (ERT) has been used to monitor salt-tracer experiments. It is now accepted that inversion of such data sets requires a fully coupled framework, explicitly accounting for the hydraulic processes (groundwater flow and solute transport), the relationship between solute and geophysical properties (petrophysical relationship such as Archie's law), and the governing equations of the geophysical surveying techniques (e.g., the Poisson equation) as consistent coupled system. These data sets can be amended with data from other - more direct - hydrogeological tests to infer the distribution of hydraulic aquifer parameters. In the inversion framework, meaningful condensation of data does not only contribute to inversion efficiency but also increases the stability of the inversion. In particular, transient concentration data themselves only weakly depend on hydraulic conductivity, and model improvement using gradient-based methods is only possible when a substantial agreement between measurements and model output already exists. The latter also holds when concentrations are monitored by ERT. Tracer arrival times, by contrast, show high sensitivity and a more monotonic dependence on hydraulic conductivity than concentrations themselves. Thus, even without using temporal-moment generating equations, inverting travel times rather than concentrations or related geoelectrical signals themselves is advantageous. We have applied this approach to concentrations measured directly or via ERT, and to heat-tracer data. We present a consistent inversion framework including temporal moments of concentrations, geoelectrical signals obtained during salt-tracer tests, drawdown data from hydraulic tomography and flowmeter measurements to identify mainly the hydraulic-conductivity distribution. By stating the inversion as geostatistical conditioning problem, we obtain parameter sets together with their correlated uncertainty. While we have applied the quasi-linear geostatistical approach as inverse kernel, other methods - such as ensemble Kalman methods - may suit the same purpose, particularly when many data points are to be included. In order to identify 3-D fields, discretized by about 50 million grid points, we use the high-performance-computing framework DUNE to solve the involved partial differential equations on midrange computer cluster. We have quantified the worth of different data types in these inference problems. In practical applications, the constitutive relationships between geophysical, thermal, and hydraulic properties can pose a problem, requiring additional inversion. However, not well constrained transient boundary conditions may put inversion efforts on larger (e.g. regional) scales even more into question. We envision that future hydrogeophysical inversion efforts will target boundary conditions, such as groundwater recharge rates, in conjunction with - or instead of - aquifer parameters. By this, the distinction between data assimilation and parameter estimation will gradually vanish.

Prize for Industrial Applications of Physics Talk: The Inverse Scattering Problem and the role of measurements in its solution

NASA Astrophysics Data System (ADS)

Wyatt, Philip

2009-03-01

The electromagnetic inverse scattering problem suggests that if a homogeneous and non-absorbing object be illuminated with a monochromatic light source and if the far field scattered light intensity is known at sufficient scattering angles, then, in principle, one could derive the dielectric structure of the scattering object. In general, this is an ill-posed problem and methods must be developed to regularize the search for unique solutions. An iterative procedure often begins with a model of the scattering object, solves the forward scattering problem using this model, and then compares these calculated results with the measured values. Key to any such solution is instrumentation capable of providing adequate data. To this end, the development of the first laser based absolute light scattering photometers is described together with their continuing evolution and some of the remarkable discoveries made with them. For particles much smaller than the wavelength of the incident light (e.g. macromolecules), the inverse scattering problems are easily solved. Among the many solutions derived with this instrumentation are the in situ structure of bacterial cells, new drug delivery mechanisms, the development of new vaccines and other biologicals, characterization of wines, the possibility of custom chemotherapy, development of new polymeric materials, identification of protein crystallization conditions, and a variety discoveries concerning protein interactions. A new form of the problem is described to address bioterrorist threats. Over the many years of development and refinement, one element stands out as essential for the successes that followed: the R and D teams were always directed and executed by physics trained theorists and experimentalists. 14 Ph. D. physicists each made his/her unique contribution to the development of these evolving instruments and the interpretation of their results.

Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods.

PubMed

Gramfort, Alexandre; Kowalski, Matthieu; Hämäläinen, Matti

2012-04-07

Magneto- and electroencephalography (M/EEG) measure the electromagnetic fields produced by the neural electrical currents. Given a conductor model for the head, and the distribution of source currents in the brain, Maxwell's equations allow one to compute the ensuing M/EEG signals. Given the actual M/EEG measurements and the solution of this forward problem, one can localize, in space and in time, the brain regions that have produced the recorded data. However, due to the physics of the problem, the limited number of sensors compared to the number of possible source locations, and measurement noise, this inverse problem is ill-posed. Consequently, additional constraints are needed. Classical inverse solvers, often called minimum norm estimates (MNE), promote source estimates with a small ℓ₂ norm. Here, we consider a more general class of priors based on mixed norms. Such norms have the ability to structure the prior in order to incorporate some additional assumptions about the sources. We refer to such solvers as mixed-norm estimates (MxNE). In the context of M/EEG, MxNE can promote spatially focal sources with smooth temporal estimates with a two-level ℓ₁/ℓ₂ mixed-norm, while a three-level mixed-norm can be used to promote spatially non-overlapping sources between different experimental conditions. In order to efficiently solve the optimization problems of MxNE, we introduce fast first-order iterative schemes that for the ℓ₁/ℓ₂ norm give solutions in a few seconds making such a prior as convenient as the simple MNE. Furthermore, thanks to the convexity of the optimization problem, we can provide optimality conditions that guarantee global convergence. The utility of the methods is demonstrated both with simulations and experimental MEG data.

Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods

PubMed Central

Gramfort, Alexandre; Kowalski, Matthieu; Hämäläinen, Matti

2012-01-01

Magneto- and electroencephalography (M/EEG) measure the electromagnetic fields produced by the neural electrical currents. Given a conductor model for the head, and the distribution of source currents in the brain, Maxwell’s equations allow one to compute the ensuing M/EEG signals. Given the actual M/EEG measurements and the solution of this forward problem, one can localize, in space and in time, the brain regions than have produced the recorded data. However, due to the physics of the problem, the limited number of sensors compared to the number of possible source locations, and measurement noise, this inverse problem is ill-posed. Consequently, additional constraints are needed. Classical inverse solvers, often called Minimum Norm Estimates (MNE), promote source estimates with a small ℓ2 norm. Here, we consider a more general class of priors based on mixed-norms. Such norms have the ability to structure the prior in order to incorporate some additional assumptions about the sources. We refer to such solvers as Mixed-Norm Estimates (MxNE). In the context of M/EEG, MxNE can promote spatially focal sources with smooth temporal estimates with a two-level ℓ1/ℓ2 mixed-norm, while a three-level mixed-norm can be used to promote spatially non-overlapping sources between different experimental conditions. In order to efficiently solve the optimization problems of MxNE, we introduce fast first-order iterative schemes that for the ℓ1/ℓ2 norm give solutions in a few seconds making such a prior as convenient as the simple MNE. Furhermore, thanks to the convexity of the optimization problem, we can provide optimality conditions that guarantee global convergence. The utility of the methods is demonstrated both with simulations and experimental MEG data. PMID:22421459

Control and System Theory, Optimization, Inverse and Ill-Posed Problems

DTIC Science & Technology

1988-09-14

Justlfleatlen Distribut ion/ Availability Codes # AFOSR-87-0350 Avat’ and/or1987-1988 Dist Special *CONTROL AND SYSTEM THEORY , ~ * OPTIMIZATION, * INVERSE...considerable va- riety of research investigations within the grant areas (Control and system theory , Optimization, and Ill-posed problems]. The

Behavioral pattern identification for structural health monitoring in complex systems

NASA Astrophysics Data System (ADS)

Gupta, Shalabh

Estimation of structural damage and quantification of structural integrity are critical for safe and reliable operation of human-engineered complex systems, such as electromechanical, thermofluid, and petrochemical systems. Damage due to fatigue crack is one of the most commonly encountered sources of structural degradation in mechanical systems. Early detection of fatigue damage is essential because the resulting structural degradation could potentially cause catastrophic failures, leading to loss of expensive equipment and human life. Therefore, for reliable operation and enhanced availability, it is necessary to develop capabilities for prognosis and estimation of impending failures, such as the onset of wide-spread fatigue crack damage in mechanical structures. This dissertation presents information-based online sensing of fatigue damage using the analytical tools of symbolic time series analysis ( STSA). Anomaly detection using STSA is a pattern recognition method that has been recently developed based upon a fixed-structure, fixed-order Markov chain. The analysis procedure is built upon the principles of Symbolic Dynamics, Information Theory and Statistical Pattern Recognition. The dissertation demonstrates real-time fatigue damage monitoring based on time series data of ultrasonic signals. Statistical pattern changes are measured using STSA to monitor the evolution of fatigue damage. Real-time anomaly detection is presented as a solution to the forward (analysis) problem and the inverse (synthesis) problem. (1) the forward problem - The primary objective of the forward problem is identification of the statistical changes in the time series data of ultrasonic signals due to gradual evolution of fatigue damage. (2) the inverse problem - The objective of the inverse problem is to infer the anomalies from the observed time series data in real time based on the statistical information generated during the forward problem. A computer-controlled special-purpose fatigue test apparatus, equipped with multiple sensing devices (e.g., ultrasonics and optical microscope) for damage analysis, has been used to experimentally validate the STSA method for early detection of anomalous behavior. The sensor information is integrated with a software module consisting of the STSA algorithm for real-time monitoring of fatigue damage. Experiments have been conducted under different loading conditions on specimens constructed from the ductile aluminium alloy 7075 - T6. The dissertation has also investigated the application of the STSA method for early detection of anomalies in other engineering disciplines. Two primary applications include combustion instability in a generic thermal pulse combustor model and whirling phenomenon in a typical misaligned shaft.

Solution of internal ballistic problem for SRM with grain of complex shape during main firing phase

NASA Astrophysics Data System (ADS)

Kiryushkin, A. E.; Minkov, L. L.

2017-10-01

Solid rocket motor (SRM) internal ballistics problems are related to the problems with moving boundaries. The algorithm able to solve similar problems in axisymmetric formulation on Cartesian mesh with an arbitrary order of accuracy is considered in this paper. The base of this algorithm is the ghost point extrapolation using inverse Lax-Wendroff procedure. Level set method is used as an implicit representation of the domain boundary. As an example, the internal ballistics problem for SRM with umbrella type grain was solved during the main firing phase. In addition, flow parameters distribution in the combustion chamber was obtained for different time moments.

Pareto joint inversion of 2D magnetotelluric and gravity data

NASA Astrophysics Data System (ADS)

Miernik, Katarzyna; Bogacz, Adrian; Kozubal, Adam; Danek, Tomasz; Wojdyła, Marek

2015-04-01

In this contribution, the first results of the "Innovative technology of petrophysical parameters estimation of geological media using joint inversion algorithms" project were described. At this stage of the development, Pareto joint inversion scheme for 2D MT and gravity data was used. Additionally, seismic data were provided to set some constrains for the inversion. Sharp Boundary Interface(SBI) approach and description model with set of polygons were used to limit the dimensionality of the solution space. The main engine was based on modified Particle Swarm Optimization(PSO). This algorithm was properly adapted to handle two or more target function at once. Additional algorithm was used to eliminate non- realistic solution proposals. Because PSO is a method of stochastic global optimization, it requires a lot of proposals to be evaluated to find a single Pareto solution and then compose a Pareto front. To optimize this stage parallel computing was used for both inversion engine and 2D MT forward solver. There are many advantages of proposed solution of joint inversion problems. First of all, Pareto scheme eliminates cumbersome rescaling of the target functions, that can highly affect the final solution. Secondly, the whole set of solution is created in one optimization run, providing a choice of the final solution. This choice can be based off qualitative data, that are usually very hard to be incorporated into the regular inversion schema. SBI parameterisation not only limits the problem of dimensionality, but also makes constraining of the solution easier. At this stage of work, decision to test the approach using MT and gravity data was made, because this combination is often used in practice. It is important to mention, that the general solution is not limited to this two methods and it is flexible enough to be used with more than two sources of data. Presented results were obtained for synthetic models, imitating real geological conditions, where interesting density distributions are relatively shallow and resistivity changes are related to deeper parts. This kind of conditions are well suited for joint inversion of MT and gravity data. In the next stage of the solution development of further code optimization and extensive tests for real data will be realized. Presented work was supported by Polish National Centre for Research and Development under the contract number POIG.01.04.00-12-279/13

Novel Scalable 3-D MT Inverse Solver

NASA Astrophysics Data System (ADS)

Kuvshinov, A. V.; Kruglyakov, M.; Geraskin, A.

2016-12-01

We present a new, robust and fast, three-dimensional (3-D) magnetotelluric (MT) inverse solver. As a forward modelling engine a highly-scalable solver extrEMe [1] is used. The (regularized) inversion is based on an iterative gradient-type optimization (quasi-Newton method) and exploits adjoint sources approach for fast calculation of the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT (single-site and/or inter-site) responses, and supports massive parallelization. Different parallelization strategies implemented in the code allow for optimal usage of available computational resources for a given problem set up. To parameterize an inverse domain a mask approach is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to high-performance clusters demonstrate practically linear scalability of the code up to thousands of nodes. 1. Kruglyakov, M., A. Geraskin, A. Kuvshinov, 2016. Novel accurate and scalable 3-D MT forward solver based on a contracting integral equation method, Computers and Geosciences, in press.

IFSM fractal image compression with entropy and sparsity constraints: A sequential quadratic programming approach

NASA Astrophysics Data System (ADS)

Kunze, Herb; La Torre, Davide; Lin, Jianyi

2017-01-01

We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point f ¯ is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.

The shifting zoom: new possibilities for inverse scattering on electrically large domains

NASA Astrophysics Data System (ADS)

Persico, Raffaele; Ludeno, Giovanni; Soldovieri, Francesco; De Coster, Alberic; Lambot, Sebastien

2017-04-01

Inverse scattering is a subject of great interest in diagnostic problems, which are in their turn of interest for many applicative problems as investigation of cultural heritage, characterization of foundations or subservices, identification of unexploded ordnances and so on [1-4]. In particular, GPR data are usually focused by means of migration algorithms, essentially based on a linear approximation of the scattering phenomenon. Migration algorithms are popular because they are computationally efficient and do not require the inversion of a matrix, neither the calculation of the elements of a matrix. In fact, they are essentially based on the adjoint of the linearised scattering operator, which allows in the end to write the inversion formula as a suitably weighted integral of the data [5]. In particular, this makes a migration algorithm more suitable than a linear microwave tomography inversion algorithm for the reconstruction of an electrically large investigation domain. However, this computational challenge can be overcome by making use of investigation domains joined side by side, as proposed e.g. in ref. [3]. This allows to apply a microwave tomography algorithm even to large investigation domains. However, the joining side by side of sequential investigation domains introduces a problem of limited (and asymmetric) maximum view angle with regard to the targets occurring close to the edges between two adjacent domains, or possibly crossing these edges. The shifting zoom is a method that allows to overcome this difficulty by means of overlapped investigation and observation domains [6-7]. It requires more sequential inversion with respect to adjacent investigation domains, but the really required extra-time is minimal because the matrix to be inverted is calculated ones and for all, as well as its singular value decomposition: what is repeated more time is only a fast matrix-vector multiplication. References [1] M. Pieraccini, L. Noferini, D. Mecatti, C. Atzeni, R. Persico, F. Soldovieri, Advanced Processing Techniques for Step-frequency Continuous-Wave Penetrating Radar: the Case Study of "Palazzo Vecchio" Walls (Firenze, Italy), Research on Nondestructive Evaluation, vol. 17, pp. 71-83, 2006. [2] N. Masini, R. Persico, E. Rizzo, A. Calia, M. T. Giannotta, G. Quarta, A. Pagliuca, "Integrated Techniques for Analysis and Monitoring of Historical Monuments: the case of S.Giovanni al Sepolcro in Brindisi (Southern Italy)." Near Surface Geophysics, vol. 8 (5), pp. 423-432, 2010. [3] E. Pettinelli, A. Di Matteo, E. Mattei, L. Crocco, F. Soldovieri, J. D. Redman, and A. P. Annan, "GPR response from buried pipes: Measurement on field site and tomographic reconstructions", IEEE Transactions on Geoscience and Remote Sensing, vol. 47, n. 8, 2639-2645, Aug. 2009. [4] O. Lopera, E. C. Slob, N. Milisavljevic and S. Lambot, "Filtering soil surface and antenna effects from GPR data to enhance landmine detection", IEEE Transactions on Geoscience and Remote Sensing, vol. 45, n. 3, pp.707-717, 2007. [5] R. Persico, "Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing". Wiley, 2014. [6] R. Persico, J. Sala, "The problem of the investigation domain subdivision in 2D linear inversions for large scale GPR data", IEEE Geoscience and Remote Sensing Letters, vol. 11, n. 7, pp. 1215-1219, doi 10.1109/LGRS.2013.2290008, July 2014. [7] R. Persico, F. Soldovieri, S. Lambot, Shifting zoom in 2D linear inversions performed on GPR data gathered along an electrically large investigation domain, Proc. 16th International Conference on Ground Penetrating Radar GPR2016, Honk-Kong, June 13-16, 2016