Stochastic Gabor reflectivity and acoustic impedance inversion

NASA Astrophysics Data System (ADS)

Hariri Naghadeh, Diako; Morley, Christopher Keith; Ferguson, Angus John

2018-02-01

To delineate subsurface lithology to estimate petrophysical properties of a reservoir, it is possible to use acoustic impedance (AI) which is the result of seismic inversion. To change amplitude to AI, removal of wavelet effects from the seismic signal in order to get a reflection series, and subsequently transforming those reflections to AI, is vital. To carry out seismic inversion correctly it is important to not assume that the seismic signal is stationary. However, all stationary deconvolution methods are designed following that assumption. To increase temporal resolution and interpretation ability, amplitude compensation and phase correction are inevitable. Those are pitfalls of stationary reflectivity inversion. Although stationary reflectivity inversion methods are trying to estimate reflectivity series, because of incorrect assumptions their estimations will not be correct, but may be useful. Trying to convert those reflection series to AI, also merging with the low frequency initial model, can help us. The aim of this study was to apply non-stationary deconvolution to eliminate time variant wavelet effects from the signal and to convert the estimated reflection series to the absolute AI by getting bias from well logs. To carry out this aim, stochastic Gabor inversion in the time domain was used. The Gabor transform derived the signal’s time-frequency analysis and estimated wavelet properties from different windows. Dealing with different time windows gave an ability to create a time-variant kernel matrix, which was used to remove matrix effects from seismic data. The result was a reflection series that does not follow the stationary assumption. The subsequent step was to convert those reflections to AI using well information. Synthetic and real data sets were used to show the ability of the introduced method. The results highlight that the time cost to get seismic inversion is negligible related to general Gabor inversion in the frequency domain. Also, obtaining bias could help the method to estimate reliable AI. To justify the effect of random noise on deterministic and stochastic inversion results, a stationary noisy trace with signal-to-noise ratio equal to 2 was used. The results highlight the inability of deterministic inversion in dealing with a noisy data set even using a high number of regularization parameters. Also, despite the low level of signal, stochastic Gabor inversion not only can estimate correctly the wavelet’s properties but also, because of bias from well logs, the inversion result is very close to the real AI. Comparing deterministic and introduced inversion results on a real data set shows that low resolution results, especially in the deeper parts of seismic sections using deterministic inversion, creates significant reliability problems for seismic prospects, but this pitfall is solved completely using stochastic Gabor inversion. The estimated AI using Gabor inversion in the time domain is much better and faster than general Gabor inversion in the frequency domain. This is due to the extra number of windows required to analyze the time-frequency information and also the amount of temporal increment between windows. In contrast, stochastic Gabor inversion can estimate trustable physical properties close to the real characteristics. Applying to a real data set could give an ability to detect the direction of volcanic intrusion and the ability of lithology distribution delineation along the fan. Comparing the inversion results highlights the efficiency of stochastic Gabor inversion to delineate lateral lithology changes because of the improved frequency content and zero phasing of the final inversion volume.

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.

Isotropic probability measures in infinite dimensional spaces: Inverse problems/prior information/stochastic inversion

NASA Technical Reports Server (NTRS)

Backus, George

1987-01-01

Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub n :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity)(P sub n to the -1(B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.

A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization

NASA Astrophysics Data System (ADS)

Liu, Shuang; Hu, Xiangyun; Liu, Tianyou

2014-07-01

Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.

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.

Stochastic Seismic Inversion and Migration for Offshore Site Investigation in the Northern Gulf of Mexico

NASA Astrophysics Data System (ADS)

Son, J.; Medina-Cetina, Z.

2017-12-01

We discuss the comparison between deterministic and stochastic optimization approaches to the nonlinear geophysical full-waveform inverse problem, based on the seismic survey data from Mississippi Canyon in the Northern Gulf of Mexico. Since the subsea engineering and offshore construction projects actively require reliable ground models from various site investigations, the primary goal of this study is to reconstruct the accurate subsurface information of the soil and rock material profiles under the seafloor. The shallow sediment layers have naturally formed heterogeneous formations which may cause unwanted marine landslides or foundation failures of underwater infrastructure. We chose the quasi-Newton and simulated annealing as deterministic and stochastic optimization algorithms respectively. Seismic forward modeling based on finite difference method with absorbing boundary condition implements the iterative simulations in the inverse modeling. We briefly report on numerical experiments using a synthetic data as an offshore ground model which contains shallow artificial target profiles of geomaterials under the seafloor. We apply the seismic migration processing and generate Voronoi tessellation on two-dimensional space-domain to improve the computational efficiency of the imaging stratigraphical velocity model reconstruction. We then report on the detail of a field data implementation, which shows the complex geologic structures in the Northern Gulf of Mexico. Lastly, we compare the new inverted image of subsurface site profiles in the space-domain with the previously processed seismic image in the time-domain at the same location. Overall, stochastic optimization for seismic inversion with migration and Voronoi tessellation show significant promise to improve the subsurface imaging of ground models and improve the computational efficiency required for the full waveform inversion. We anticipate that by improving the inversion process of shallow layers from geophysical data will better support the offshore site investigation.

Inverse problems and computational cell metabolic models: a statistical approach

NASA Astrophysics Data System (ADS)

Calvetti, D.; Somersalo, E.

2008-07-01

In this article, we give an overview of the Bayesian modelling of metabolic systems at the cellular and subcellular level. The models are based on detailed description of key biochemical reactions occurring in tissue, which may in turn be compartmentalized into cytosol and mitochondria, and of transports between the compartments. The classical deterministic approach which models metabolic systems as dynamical systems with Michaelis-Menten kinetics, is replaced by a stochastic extension where the model parameters are interpreted as random variables with an appropriate probability density. The inverse problem of cell metabolism in this setting consists of estimating the density of the model parameters. After discussing some possible approaches to solving the problem, we address the issue of how to assess the reliability of the predictions of a stochastic model by proposing an output analysis in terms of model uncertainties. Visualization modalities for organizing the large amount of information provided by the Bayesian dynamic sensitivity analysis are also illustrated.

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)].

Teaching Tip: When a Matrix and Its Inverse Are Stochastic

ERIC Educational Resources Information Center

Ding, J.; Rhee, N. H.

2013-01-01

A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.

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.

Online learning in optical tomography: a stochastic approach

NASA Astrophysics Data System (ADS)

Chen, Ke; Li, Qin; Liu, Jian-Guo

2018-07-01

We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the incoming–outgoing pair of light intensity. We formulate it as a PDE-constraint optimization problem, where the mismatch of computed and measured outgoing data is minimized with same initial data and RTE constraint. The memory and computation cost it requires, however, is typically prohibitive, especially in high dimensional space. Smart iterative solvers that only use partial information in each step is called for thereafter. Stochastic gradient descent method is an online learning algorithm that randomly selects data for minimizing the mismatch. It requires minimum memory and computation, and advances fast, therefore perfectly serves the purpose. In this paper we formulate the problem, in both nonlinear and its linearized setting, apply SGD algorithm and analyze the convergence performance.

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.

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.

An Inverse Problem Formulation Methodology for Stochastic Models

DTIC Science & Technology

2010-05-02

form the surveillance data Infection control measures were implemented in the form of health care worker hand - hygiene before and after patients contact...manuscript derives from our interest in understanding the spread of infectious diseases in particular, nosocomial infections , in order to prevent major...given by the inverse of the parameter of the exponential distribution. A hand - hygiene policy applied to health care workers on isolated VRE colonized

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.

Stochastic Evolutionary Algorithms for Planning Robot Paths

NASA Technical Reports Server (NTRS)

Fink, Wolfgang; Aghazarian, Hrand; Huntsberger, Terrance; Terrile, Richard

2006-01-01

A computer program implements stochastic evolutionary algorithms for planning and optimizing collision-free paths for robots and their jointed limbs. Stochastic evolutionary algorithms can be made to produce acceptably close approximations to exact, optimal solutions for path-planning problems while often demanding much less computation than do exhaustive-search and deterministic inverse-kinematics algorithms that have been used previously for this purpose. Hence, the present software is better suited for application aboard robots having limited computing capabilities (see figure). The stochastic aspect lies in the use of simulated annealing to (1) prevent trapping of an optimization algorithm in local minima of an energy-like error measure by which the fitness of a trial solution is evaluated while (2) ensuring that the entire multidimensional configuration and parameter space of the path-planning problem is sampled efficiently with respect to both robot joint angles and computation time. Simulated annealing is an established technique for avoiding local minima in multidimensional optimization problems, but has not, until now, been applied to planning collision-free robot paths by use of low-power computers.

M-matrices with prescribed elementary divisors

NASA Astrophysics Data System (ADS)

Soto, Ricardo L.; Díaz, Roberto C.; Salas, Mario; Rojo, Oscar

2017-09-01

A real matrix A is said to be an M-matrix if it is of the form A=α I-B, where B is a nonnegative matrix with Perron eigenvalue ρ (B), and α ≥slant ρ (B) . This paper provides sufficient conditions for the existence and construction of an M-matrix A with prescribed elementary divisors, which are the characteristic polynomials of the Jordan blocks of the Jordan canonical form of A. This inverse problem on M-matrices has not been treated until now. We solve the inverse elementary divisors problem for diagonalizable M-matrices and the symmetric generalized doubly stochastic inverse M-matrix problem for lists of real numbers and for lists of complex numbers of the form Λ =\\{λ 1, a+/- bi, \\ldots, a+/- bi\\} . The constructive nature of our results allows for the computation of a solution matrix. The paper also discusses an application of M-matrices to a capacity problem in wireless communications.

The isolation limits of stochastic vibration

NASA Technical Reports Server (NTRS)

Knopse, C. R.; Allaire, P. E.

1993-01-01

The vibration isolation problem is formulated as a 1D kinematic problem. The geometry of the stochastic wall trajectories arising from the stroke constraint is defined in terms of their significant extrema. An optimal control solution for the minimum acceleration return path determines a lower bound on platform mean square acceleration. This bound is expressed in terms of the probability density function on the significant maxima and the conditional fourth moment of the first passage time inverse. The first of these is found analytically while the second is found using a Monte Carlo simulation. The rms acceleration lower bound as a function of available space is then determined through numerical quadrature.

Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

NASA Astrophysics Data System (ADS)

Avdyushev, Victor A.

2017-12-01

Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the method of disturbed observations, we conclude that it practically should be still entirely acceptable to adequately describe the orbital uncertainty since, from a geometrical point of view, the efficiency of the method directly depends only on the nonflatness of the estimation subspace and it gets higher as the nonflatness decreases.

GARCH modelling of covariance in dynamical estimation of inverse solutions

NASA Astrophysics Data System (ADS)

Galka, Andreas; Yamashita, Okito; Ozaki, Tohru

2004-12-01

The problem of estimating unobserved states of spatially extended dynamical systems poses an inverse problem, which can be solved approximately by a recently developed variant of Kalman filtering; in order to provide the model of the dynamics with more flexibility with respect to space and time, we suggest to combine the concept of GARCH modelling of covariance, well known in econometrics, with Kalman filtering. We formulate this algorithm for spatiotemporal systems governed by stochastic diffusion equations and demonstrate its feasibility by presenting a numerical simulation designed to imitate the situation of the generation of electroencephalographic recordings by the human cortex.

Particle Swarm Optimization algorithms for geophysical inversion, practical hints

NASA Astrophysics Data System (ADS)

Garcia Gonzalo, E.; Fernandez Martinez, J.; Fernandez Alvarez, J.; Kuzma, H.; Menendez Perez, C.

2008-12-01

PSO is a stochastic optimization technique that has been successfully used in many different engineering fields. PSO algorithm can be physically interpreted as a stochastic damped mass-spring system (Fernandez Martinez and Garcia Gonzalo 2008). Based on this analogy we present a whole family of PSO algorithms and their respective first order and second order stability regions. Their performance is also checked using synthetic functions (Rosenbrock and Griewank) showing a degree of ill-posedness similar to that found in many geophysical inverse problems. Finally, we present the application of these algorithms to the analysis of a Vertical Electrical Sounding inverse problem associated to a seawater intrusion in a coastal aquifer in South Spain. We analyze the role of PSO parameters (inertia, local and global accelerations and discretization step), both in convergence curves and in the a posteriori sampling of the depth of an intrusion. Comparison is made with binary genetic algorithms and simulated annealing. As result of this analysis, practical hints are given to select the correct algorithm and to tune the corresponding PSO parameters. Fernandez Martinez, J.L., Garcia Gonzalo, E., 2008a. The generalized PSO: a new door to PSO evolution. Journal of Artificial Evolution and Applications. DOI:10.1155/2008/861275.

Stochastic inversion of time-lapse geophysical data to characterize the vadose zone at the Arrenaes field site (Denmark)

NASA Astrophysics Data System (ADS)

Marie, S.; Irving, J. D.; Looms, M. C.; Nielsen, L.; Holliger, K.

2011-12-01

Geophysical methods such as ground-penetrating radar (GPR) can provide valuable information on the hydrological properties of the vadose zone. In particular, there is evidence to suggest that the stochastic inversion of such data may allow for significant reductions in uncertainty regarding subsurface van-Genuchten-Mualem (VGM) parameters, which characterize unsaturated hydrodynamic behaviour as defined by the combination of the water retention and hydraulic conductivity functions. A significant challenge associated with the use of geophysical methods in a hydrological context is that they generally exhibit an indirect and/or weak sensitivity to the hydraulic parameters of interest. A novel and increasingly popular means of addressing this issue involves the acquisition of geophysical data in a time-lapse fashion while changes occur in the hydrological condition of the probed subsurface region. Another significant challenge when attempting to use geophysical data for the estimation of subsurface hydrological properties is the inherent non-linearity and non-uniqueness of the corresponding inverse problems. Stochastic inversion approaches have the advantage of providing a comprehensive exploration of the model space, which makes them ideally suited for addressing such issues. In this work, we present the stochastic inversion of time-lapse zero-offset-profile (ZOP) crosshole GPR traveltime data, collected during a forced infiltration experiment at the Arreneas field site in Denmark, in order to estimate subsurface VGM parameters and their corresponding uncertainties. We do this using a Bayesian Markov-chain-Monte-Carlo (MCMC) inversion approach. We find that the Bayesian-MCMC methodology indeed allows for a substantial refinement in the inferred posterior parameter distributions of the VGM parameters as compared to the corresponding priors. To further understand the potential impact on capturing the underlying hydrological behaviour, we also explore how the posterior VGM parameter distributions affect the hydrodynamic characteristics. In doing so, we find clear evidence that the approach pursued in this study allows for effective characterization of the hydrological behaviour of the probed subsurface region.

Mathematic and the Quest for Fundamental Principles of Biology

DTIC Science & Technology

2017-05-05

stochasticity as part of the process, rather than as extrinsic noise. In some sense, like all organisms, we must continually solve inverse problems...predictions that could not be made before, ideally while simultaneously elucidating new mechanisms and proposing new experiments. The meeting concluded with

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.

A stochastic vortex structure method for interacting particles in turbulent shear flows

NASA Astrophysics Data System (ADS)

Dizaji, Farzad F.; Marshall, Jeffrey S.; Grant, John R.

2018-01-01

In a recent study, we have proposed a new synthetic turbulence method based on stochastic vortex structures (SVSs), and we have demonstrated that this method can accurately predict particle transport, collision, and agglomeration in homogeneous, isotropic turbulence in comparison to direct numerical simulation results. The current paper extends the SVS method to non-homogeneous, anisotropic turbulence. The key element of this extension is a new inversion procedure, by which the vortex initial orientation can be set so as to generate a prescribed Reynolds stress field. After validating this inversion procedure for simple problems, we apply the SVS method to the problem of interacting particle transport by a turbulent planar jet. Measures of the turbulent flow and of particle dispersion, clustering, and collision obtained by the new SVS simulations are shown to compare well with direct numerical simulation results. The influence of different numerical parameters, such as number of vortices and vortex lifetime, on the accuracy of the SVS predictions is also examined.

Stochastic inversion of cross-borehole radar data from metalliferous vein detection

NASA Astrophysics Data System (ADS)

Zeng, Zhaofa; Huai, Nan; Li, Jing; Zhao, Xueyu; Liu, Cai; Hu, Yingsa; Zhang, Ling; Hu, Zuzhi; Yang, Hui

2017-12-01

In the exploration and evaluation of the metalliferous veins with a cross-borehole radar system, traditional linear inversion methods (least squares inversion, LSQR) only get indirect parameters (permittivity, resistivity, or velocity) to estimate the target structure. They cannot accurately reflect the geological parameters of the metalliferous veins’ media properties. In order to get the intrinsic geological parameters and internal distribution, in this paper, we build a metalliferous veins model based on the stochastic effective medium theory, and carry out stochastic inversion and parameter estimation based on the Monte Carlo sampling algorithm. Compared with conventional LSQR, the stochastic inversion can get higher resolution inversion permittivity and velocity of the target body. We can estimate more accurately the distribution characteristics of abnormality and target internal parameters. It provides a new research idea to evaluate the properties of complex target media.

A non-stochastic iterative computational method to model light propagation in turbid media

NASA Astrophysics Data System (ADS)

McIntyre, Thomas J.; Zemp, Roger J.

2015-03-01

Monte Carlo models are widely used to model light transport in turbid media, however their results implicitly contain stochastic variations. These fluctuations are not ideal, especially for inverse problems where Jacobian matrix errors can lead to large uncertainties upon matrix inversion. Yet Monte Carlo approaches are more computationally favorable than solving the full Radiative Transport Equation. Here, a non-stochastic computational method of estimating fluence distributions in turbid media is proposed, which is called the Non-Stochastic Propagation by Iterative Radiance Evaluation method (NSPIRE). Rather than using stochastic means to determine a random walk for each photon packet, the propagation of light from any element to all other elements in a grid is modelled simultaneously. For locally homogeneous anisotropic turbid media, the matrices used to represent scattering and projection are shown to be block Toeplitz, which leads to computational simplifications via convolution operators. To evaluate the accuracy of the algorithm, 2D simulations were done and compared against Monte Carlo models for the cases of an isotropic point source and a pencil beam incident on a semi-infinite turbid medium. The model was shown to have a mean percent error less than 2%. The algorithm represents a new paradigm in radiative transport modelling and may offer a non-stochastic alternative to modeling light transport in anisotropic scattering media for applications where the diffusion approximation is insufficient.

Seismic stochastic inversion identify river channel sand body

NASA Astrophysics Data System (ADS)

He, Z.

2015-12-01

The technology of seismic inversion is regarded as one of the most important part of geophysics. By using the technology of seismic inversion and the theory of stochastic simulation, the concept of seismic stochastic inversion is proposed.Seismic stochastic inversion can play an significant role in the identifying river channel sand body. Accurate sand body description is a crucial parameter to measure oilfield development and oilfield stimulation during the middle and later periods. Besides, rational well spacing density is an essential condition for efficient production. Based on the geological knowledge of a certain oilfield, in line with the use of seismic stochastic inversion, the river channel sand body in the work area is identified. In this paper, firstly, the single river channel body from the composite river channel body is subdivided. Secondly, the distribution of river channel body is ascertained in order to ascertain the direction of rivers. Morever, the superimposed relationship among the sand body is analyzed, especially among the inter-well sand body. The last but not at the least, via the analysis of inversion results of first vacuating the wells and continuous infilling later, it is meeted the most needs well spacing density that can obtain the optimal inversion result. It would serve effective guidance for oilfield stimulation.

Spatial delineation, fluid-lithology characterization, and petrophysical modeling of deepwater Gulf of Mexico reservoirs though joint AVA deterministic and stochastic inversion of three-dimensional partially-stacked seismic amplitude data and well logs

NASA Astrophysics Data System (ADS)

Contreras, Arturo Javier

This dissertation describes a novel Amplitude-versus-Angle (AVA) inversion methodology to quantitatively integrate pre-stack seismic data, well logs, geologic data, and geostatistical information. Deterministic and stochastic inversion algorithms are used to characterize flow units of deepwater reservoirs located in the central Gulf of Mexico. A detailed fluid/lithology sensitivity analysis was conducted to assess the nature of AVA effects in the study area. Standard AVA analysis indicates that the shale/sand interface represented by the top of the hydrocarbon-bearing turbidite deposits generate typical Class III AVA responses. Layer-dependent Biot-Gassmann analysis shows significant sensitivity of the P-wave velocity and density to fluid substitution, indicating that presence of light saturating fluids clearly affects the elastic response of sands. Accordingly, AVA deterministic and stochastic inversions, which combine the advantages of AVA analysis with those of inversion, have provided quantitative information about the lateral continuity of the turbidite reservoirs based on the interpretation of inverted acoustic properties and fluid-sensitive modulus attributes (P-Impedance, S-Impedance, density, and LambdaRho, in the case of deterministic inversion; and P-velocity, S-velocity, density, and lithotype (sand-shale) distributions, in the case of stochastic inversion). The quantitative use of rock/fluid information through AVA seismic data, coupled with the implementation of co-simulation via lithotype-dependent multidimensional joint probability distributions of acoustic/petrophysical properties, provides accurate 3D models of petrophysical properties such as porosity, permeability, and water saturation. Pre-stack stochastic inversion provides more realistic and higher-resolution results than those obtained from analogous deterministic techniques. Furthermore, 3D petrophysical models can be more accurately co-simulated from AVA stochastic inversion results. By combining AVA sensitivity analysis techniques with pre-stack stochastic inversion, geologic data, and awareness of inversion pitfalls, it is possible to substantially reduce the risk in exploration and development of conventional and non-conventional reservoirs. From the final integration of deterministic and stochastic inversion results with depositional models and analogous examples, the M-series reservoirs have been interpreted as stacked terminal turbidite lobes within an overall fan complex (the Miocene MCAVLU Submarine Fan System); this interpretation is consistent with previous core data interpretations and regional stratigraphic/depositional studies.

A new stochastic algorithm for inversion of dust aerosol size distribution

NASA Astrophysics Data System (ADS)

Wang, Li; Li, Feng; Yang, Ma-ying

2015-08-01

Dust aerosol size distribution is an important source of information about atmospheric aerosols, and it can be determined from multiwavelength extinction measurements. This paper describes a stochastic inverse technique based on artificial bee colony (ABC) algorithm to invert the dust aerosol size distribution by light extinction method. The direct problems for the size distribution of water drop and dust particle, which are the main elements of atmospheric aerosols, are solved by the Mie theory and the Lambert-Beer Law in multispectral region. And then, the parameters of three widely used functions, i.e. the log normal distribution (L-N), the Junge distribution (J-J), and the normal distribution (N-N), which can provide the most useful representation of aerosol size distributions, are inversed by the ABC algorithm in the dependent model. Numerical results show that the ABC algorithm can be successfully applied to recover the aerosol size distribution with high feasibility and reliability even in the presence of random noise.

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.

Discovering network behind infectious disease outbreak

NASA Astrophysics Data System (ADS)

Maeno, Yoshiharu

2010-11-01

Stochasticity and spatial heterogeneity are of great interest recently in studying the spread of an infectious disease. The presented method solves an inverse problem to discover the effectively decisive topology of a heterogeneous network and reveal the transmission parameters which govern the stochastic spreads over the network from a dataset on an infectious disease outbreak in the early growth phase. Populations in a combination of epidemiological compartment models and a meta-population network model are described by stochastic differential equations. Probability density functions are derived from the equations and used for the maximal likelihood estimation of the topology and parameters. The method is tested with computationally synthesized datasets and the WHO dataset on the SARS outbreak.

FAST: a framework for simulation and analysis of large-scale protein-silicon biosensor circuits.

PubMed

Gu, Ming; Chakrabartty, Shantanu

2013-08-01

This paper presents a computer aided design (CAD) framework for verification and reliability analysis of protein-silicon hybrid circuits used in biosensors. It is envisioned that similar to integrated circuit (IC) CAD design tools, the proposed framework will be useful for system level optimization of biosensors and for discovery of new sensing modalities without resorting to laborious fabrication and experimental procedures. The framework referred to as FAST analyzes protein-based circuits by solving inverse problems involving stochastic functional elements that admit non-linear relationships between different circuit variables. In this regard, FAST uses a factor-graph netlist as a user interface and solving the inverse problem entails passing messages/signals between the internal nodes of the netlist. Stochastic analysis techniques like density evolution are used to understand the dynamics of the circuit and estimate the reliability of the solution. As an example, we present a complete design flow using FAST for synthesis, analysis and verification of our previously reported conductometric immunoassay that uses antibody-based circuits to implement forward error-correction (FEC).

Stochastic joint inversion of hydrogeophysical data for salt tracer test monitoring and hydraulic conductivity imaging

NASA Astrophysics Data System (ADS)

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

2013-02-01

The assessment of hydraulic conductivity of heterogeneous aquifers is a difficult task using traditional hydrogeological methods (e.g., steady state or transient pumping tests) due to their low spatial resolution. Geophysical measurements performed at the ground surface and in boreholes provide additional information for increasing the resolution and accuracy of the inverted hydraulic conductivity field. We used a stochastic joint inversion of Direct Current (DC) resistivity and self-potential (SP) data plus in situ measurement of the salinity in a downstream well during a synthetic salt tracer experiment to reconstruct the hydraulic conductivity field between two wells. The pilot point parameterization was used to avoid over-parameterization of the inverse problem. Bounds on the model parameters were used to promote a consistent Markov chain Monte Carlo sampling of the model parameters. To evaluate the effectiveness of the joint inversion process, we compared eight cases in which the geophysical data are coupled or not to the in situ sampling of the salinity to map the hydraulic conductivity. We first tested the effectiveness of the inversion of each type of data alone (concentration sampling, self-potential, and DC resistivity), and then we combined the data two by two. We finally combined all the data together to show the value of each type of geophysical data in the joint inversion process because of their different sensitivity map. We also investigated a case in which the data were contaminated with noise and the variogram unknown and inverted stochastically. The results of the inversion revealed that incorporating the self-potential data improves the estimate of hydraulic conductivity field especially when the self-potential data were combined to the salt concentration measurement in the second well or to the time-lapse cross-well electrical resistivity data. Various tests were also performed to quantify the uncertainty in the inverted hydraulic conductivity field.

Reconstruction of stochastic temporal networks through diffusive arrival times

NASA Astrophysics Data System (ADS)

Li, Xun; Li, Xiang

2017-06-01

Temporal networks have opened a new dimension in defining and quantification of complex interacting systems. Our ability to identify and reproduce time-resolved interaction patterns is, however, limited by the restricted access to empirical individual-level data. Here we propose an inverse modelling method based on first-arrival observations of the diffusion process taking place on temporal networks. We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent interaction sequences at the dyadic level. The results of benchmark tests applied on both synthesized and empirical network data sets confirm the validity of our algorithm, showing the feasibility of statistically accurate inference of temporal networks only from moderate-sized samples of diffusion cascades. Our approach provides an effective and flexible scheme for the temporally augmented inverse problems of network reconstruction and has potential in a broad variety of applications.

Reconstruction of stochastic temporal networks through diffusive arrival times

PubMed Central

Li, Xun; Li, Xiang

2017-01-01

Temporal networks have opened a new dimension in defining and quantification of complex interacting systems. Our ability to identify and reproduce time-resolved interaction patterns is, however, limited by the restricted access to empirical individual-level data. Here we propose an inverse modelling method based on first-arrival observations of the diffusion process taking place on temporal networks. We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent interaction sequences at the dyadic level. The results of benchmark tests applied on both synthesized and empirical network data sets confirm the validity of our algorithm, showing the feasibility of statistically accurate inference of temporal networks only from moderate-sized samples of diffusion cascades. Our approach provides an effective and flexible scheme for the temporally augmented inverse problems of network reconstruction and has potential in a broad variety of applications. PMID:28604687

Statistics of the Kolkata Paise Restaurant problem

NASA Astrophysics Data System (ADS)

Ghosh, Asim; Chatterjee, Arnab; Mitra, Manipushpak; Chakrabarti, Bikas K.

2010-07-01

We study the dynamics of a few stochastic learning strategies for the 'Kolkata Paise Restaurant' problem, where N agents choose among N equally priced but differently ranked restaurants every evening, such that each agent tries to get dinner in the best restaurant (with each restaurant serving only one customer and the rest of the customers arriving there going without dinner that evening). We consider the learning strategies to be similar for all the agents, and assume that each follows the same probabilistic or stochastic strategy dependent on information about past successes in the game. We show that some 'naive' strategies lead to much better utilization of services than some relatively 'smarter' strategies. We also show that a service utilization fraction as high as 0.80 can result for a stochastic strategy, where each agent sticks to his past choice (independent of success achieved or not, with probability decreasing inversely in the past crowd size). The numerical results for the utilization fraction of the services in some limiting cases are analytically examined.

Technical Note: Approximate Bayesian parameterization of a process-based tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2014-02-01

Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to the data. This metric can be expressed by general cost or objective functions, but statistical inversion methods require a particular metric, the probability of observing the data given the model parameters, known as the likelihood. For technical and computational reasons, likelihoods for process-based stochastic models are usually based on general assumptions about variability in the observed data, and not on the stochasticity generated by the model. Only in recent years have new methods become available that allow the generation of 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 Markov chain Monte Carlo (MCMC) sampler, performs well in retrieving known parameter values from virtual inventory data generated by the forest model. We analyze the results of the parameter estimation, examine its sensitivity to the choice and aggregation of model outputs and observed data (summary statistics), and demonstrate the application of this method by fitting the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss how this approach differs from approximate Bayesian computation (ABC), another method commonly used 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 be successfully applied to process-based models of high complexity. The methodology is particularly suitable for 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.

Confidence set interference with a prior quadratic bound. [in geophysics

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

Quantum algorithms for Gibbs sampling and hitting-time estimation

DOE PAGES

Chowdhury, Anirban Narayan; Somma, Rolando D.

2017-02-01

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. Formore » a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.« less

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.

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.

Joint Stochastic Inversion of Pre-Stack 3D Seismic Data and Well Logs for High Resolution Hydrocarbon Reservoir Characterization

NASA Astrophysics Data System (ADS)

Torres-Verdin, C.

2007-05-01

This paper describes the successful implementation of a new 3D AVA stochastic inversion algorithm to quantitatively integrate pre-stack seismic amplitude data and well logs. The stochastic inversion algorithm is used to characterize flow units of a deepwater reservoir located in the central Gulf of Mexico. Conventional fluid/lithology sensitivity analysis indicates that the shale/sand interface represented by the top of the hydrocarbon-bearing turbidite deposits generates typical Class III AVA responses. On the other hand, layer- dependent Biot-Gassmann analysis shows significant sensitivity of the P-wave velocity and density to fluid substitution. Accordingly, AVA stochastic inversion, which combines the advantages of AVA analysis with those of geostatistical inversion, provided quantitative information about the lateral continuity of the turbidite reservoirs based on the interpretation of inverted acoustic properties (P-velocity, S-velocity, density), and lithotype (sand- shale) distributions. The quantitative use of rock/fluid information through AVA seismic amplitude data, coupled with the implementation of co-simulation via lithotype-dependent multidimensional joint probability distributions of acoustic/petrophysical properties, yields accurate 3D models of petrophysical properties such as porosity and permeability. Finally, by fully integrating pre-stack seismic amplitude data and well logs, the vertical resolution of inverted products is higher than that of deterministic inversions methods.

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

Exploring equivalence domain in nonlinear inverse problems using Covariance Matrix Adaption Evolution Strategy (CMAES) and random sampling

NASA Astrophysics Data System (ADS)

Grayver, Alexander V.; Kuvshinov, Alexey V.

2016-05-01

This paper presents a methodology to sample equivalence domain (ED) in nonlinear partial differential equation (PDE)-constrained inverse problems. For this purpose, we first applied state-of-the-art stochastic optimization algorithm called Covariance Matrix Adaptation Evolution Strategy (CMAES) to identify low-misfit regions of the model space. These regions were then randomly sampled to create an ensemble of equivalent models and quantify uncertainty. CMAES is aimed at exploring model space globally and is robust on very ill-conditioned problems. We show that the number of iterations required to converge grows at a moderate rate with respect to number of unknowns and the algorithm is embarrassingly parallel. We formulated the problem by using the generalized Gaussian distribution. This enabled us to seamlessly use arbitrary norms for residual and regularization terms. We show that various regularization norms facilitate studying different classes of equivalent solutions. We further show how performance of the standard Metropolis-Hastings Markov chain Monte Carlo algorithm can be substantially improved by using information CMAES provides. This methodology was tested by using individual and joint inversions of magneotelluric, controlled-source electromagnetic (EM) and global EM induction data.

Probabilistic dual heuristic programming-based adaptive critic

NASA Astrophysics Data System (ADS)

Herzallah, Randa

2010-02-01

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.

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.

Dynamic electrical impedance imaging with the interacting multiple model scheme.

PubMed

Kim, Kyung Youn; Kim, Bong Seok; Kim, Min Chan; Kim, Sin; Isaacson, David; Newell, Jonathan C

2005-04-01

In this paper, an effective dynamical EIT imaging scheme is presented for on-line monitoring of the abruptly changing resistivity distribution inside the object, based on the interacting multiple model (IMM) algorithm. The inverse problem is treated as a stochastic nonlinear state estimation problem with the time-varying resistivity (state) being estimated on-line with the aid of the IMM algorithm. In the design of the IMM algorithm multiple models with different process noise covariance are incorporated to reduce the modeling uncertainty. Simulations and phantom experiments are provided to illustrate the proposed algorithm.

Model-Free Stochastic Localization of CBRN Releases

DTIC Science & Technology

2013-01-01

Ioannis Ch. Paschalidis,‡ Senior Member, IEEE Abstract—We present a novel two-stage methodology for locating a Chemical, Biological, Radiological, or...Nuclear (CBRN) source in an urban area using a network of sensors. In contrast to earlier work, our approach does not solve an inverse dispersion problem...but relies on data obtained from a simulation of the CBRN dispersion to obtain probabilistic descriptors of sensor measurements under a variety of CBRN

3D aquifer characterization using stochastic streamline calibration

NASA Astrophysics Data System (ADS)

Jang, Minchul

2007-03-01

In this study, a new inverse approach, stochastic streamline calibration is proposed. Using both a streamline concept and a stochastic technique, stochastic streamline calibration optimizes an identified field to fit in given observation data in a exceptionally fast and stable fashion. In the stochastic streamline calibration, streamlines are adopted as basic elements not only for describing fluid flow but also for identifying the permeability distribution. Based on the streamline-based inversion by Agarwal et al. [Agarwal B, Blunt MJ. Streamline-based method with full-physics forward simulation for history matching performance data of a North sea field. SPE J 2003;8(2):171-80], Wang and Kovscek [Wang Y, Kovscek AR. Streamline approach for history matching production data. SPE J 2000;5(4):353-62], permeability is modified rather along streamlines than at the individual gridblocks. Permeabilities in the gridblocks which a streamline passes are adjusted by being multiplied by some factor such that we can match flow and transport properties of the streamline. This enables the inverse process to achieve fast convergence. In addition, equipped with a stochastic module, the proposed technique supportively calibrates the identified field in a stochastic manner, while incorporating spatial information into the field. This prevents the inverse process from being stuck in local minima and helps search for a globally optimized solution. Simulation results indicate that stochastic streamline calibration identifies an unknown permeability exceptionally quickly. More notably, the identified permeability distribution reflected realistic geological features, which had not been achieved in the original work by Agarwal et al. with the limitations of the large modifications along streamlines for matching production data only. The constructed model by stochastic streamline calibration forecasted transport of plume which was similar to that of a reference model. By this, we can expect the proposed approach to be applied to the construction of an aquifer model and forecasting of the aquifer performances of interest.

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

The Calderón problem with corrupted data

NASA Astrophysics Data System (ADS)

Caro, Pedro; Garcia, Andoni

2017-08-01

We consider the inverse Calderón problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually assumes the data to be given by such a map. This situation corresponds to having access to infinite-precision measurements, which is totally unrealistic. In this paper, we study the Calderón problem assuming the data to contain measurement errors and provide formulas to reconstruct the conductivity and its normal derivative on the surface. Additionally, we state the rate convergence of the method. Our approach is theoretical and has a stochastic flavour.

Correlation-based regularization and gradient operators for (joint) inversion on unstructured meshes

NASA Astrophysics Data System (ADS)

Jordi, Claudio; Doetsch, Joseph; Günther, Thomas; Schmelzbach, Cedric; Robertsson, Johan

2017-04-01

When working with unstructured meshes for geophysical inversions, special attention should be paid to the design of the operators that are used for regularizing the inverse problem and coupling of different property models in joint inversions. Regularization constraints for inversions on unstructured meshes are often defined in a rather ad-hoc manner and usually only involve the cell to which the operator is applied and its direct neighbours. Similarly, most structural coupling operators for joint inversion, such as the popular cross-gradients operator, are only defined in the direct neighbourhood of a cell. As a result, the regularization and coupling length scales and strength of these operators depend on the discretization as well as cell sizes and shape. Especially for unstructured meshes, where the cell sizes vary throughout the model domain, the dependency of the operator on the discretization may lead to artefacts. Designing operators that are based on a spatial correlation model allows to define correlation length scales over which an operator acts (called footprint), reducing the dependency on the discretization and the effects of variable cell sizes. Moreover, correlation-based operators can accommodate for expected anisotropy by using different length scales in horizontal and vertical directions. Correlation-based regularization operators also known as stochastic regularization operators have already been successfully applied to inversions on regular grids. Here, we formulate stochastic operators for unstructured meshes and apply them in 2D surface and 3D cross-well electrical resistivity tomography data inversion examples of layered media. Especially for the synthetic cross-well example, improved inversion results are achieved when stochastic regularization is used instead of a classical smoothness constraint. For the case of cross-gradients operators for joint inversion, the correlation model is used to define the footprint of the operator and weigh the contributions of the property values that are used to calculate the cross-gradients. In a first series of synthetic-data tests, we examined the mesh dependency of the cross-gradients operators. Compared to operators that are only defined in the direct neighbourhood of a cell, the dependency on the cell size of the cross-gradients calculation is markedly reduced when using operators with larger footprints. A second test with synthetic models focussed on the effect of small-scale variabilities of the parameter value on the cross-gradients calculation. Small-scale variabilities that are superimposed on a global trend of the property value can potentially degrade the cross-gradients calculation and destabilize joint inversion. We observe that the cross-gradients from operators with footprints larger than the length scale of the variabilities are less affected compared to operators with a small footprint. In joint inversions on unstructured meshes, we thus expect the correlation-based coupling operators to ensure robust coupling on a physically meaningful scale.

A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems

NASA Astrophysics Data System (ADS)

Babaee, Hessam; Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em

2017-09-01

We develop a new robust methodology for the stochastic Navier-Stokes equations based on the dynamically-orthogonal (DO) and bi-orthogonal (BO) methods [1-3]. Both approaches are variants of a generalized Karhunen-Loève (KL) expansion in which both the stochastic coefficients and the spatial basis evolve according to system dynamics, hence, capturing the low-dimensional structure of the solution. The DO and BO formulations are mathematically equivalent [3], but they exhibit computationally complimentary properties. Specifically, the BO formulation may fail due to crossing of the eigenvalues of the covariance matrix, while both BO and DO become unstable when there is a high condition number of the covariance matrix or zero eigenvalues. To this end, we combine the two methods into a robust hybrid framework and in addition we employ a pseudo-inverse technique to invert the covariance matrix. The robustness of the proposed method stems from addressing the following issues in the DO/BO formulation: (i) eigenvalue crossing: we resolve the issue of eigenvalue crossing in the BO formulation by switching to the DO near eigenvalue crossing using the equivalence theorem and switching back to BO when the distance between eigenvalues is larger than a threshold value; (ii) ill-conditioned covariance matrix: we utilize a pseudo-inverse strategy to invert the covariance matrix; (iii) adaptivity: we utilize an adaptive strategy to add/remove modes to resolve the covariance matrix up to a threshold value. In particular, we introduce a soft-threshold criterion to allow the system to adapt to the newly added/removed mode and therefore avoid repetitive and unnecessary mode addition/removal. When the total variance approaches zero, we show that the DO/BO formulation becomes equivalent to the evolution equation of the Optimally Time-Dependent modes [4]. We demonstrate the capability of the proposed methodology with several numerical examples, namely (i) stochastic Burgers equation: we analyze the performance of the method in the presence of eigenvalue crossing and zero eigenvalues; (ii) stochastic Kovasznay flow: we examine the method in the presence of a singular covariance matrix; and (iii) we examine the adaptivity of the method for an incompressible flow over a cylinder where for large stochastic forcing thirteen DO/BO modes are active.

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.

Stochastic joint inversion of geoelectrical cross-well data for salt tracer test monitoring to image the hydraulic conductivity field of heterogenous aquifers

NASA Astrophysics Data System (ADS)

Revil, A.; Jardani, A.; Dupont, J.

2012-12-01

The assessment of hydraulic conductivity of heterogeneous aquifers is a difficult task using traditional hydrogeological methods (e.g., steady state or transient pumping tests) due to their low spatial resolution associated with a low density of available piezometers. Geophysical measurements performed at the ground surface and in boreholes provide additional information for increasing the resolution and accuracy of the inverted hydraulic conductivity. We use a stochastic joint inversion of Direct Current (DC) resistivity and Self-Potential (SP) data plus in situ measurement of the salinity in a downstream well during a synthetic salt tracer experiment to reconstruct the hydraulic conductivity field of an heterogeneous aquifer. The pilot point parameterization is used to avoid over-parameterization of the inverse problem. Bounds on the model parameters are used to promote a consistent Markov chain Monte Carlo sampling of the hydrogeological parameters of the model. To evaluate the effectiveness of the inversion process, we compare several scenarios where the geophysical data are coupled or not to the hydrogeological data to map the hydraulic conductivity. We first test the effectiveness of the inversion of each type of data alone, and then we combine the methods two by two. We finally combine all the information together to show the value of each type of geophysical data in the joint inversion process because of their different sensitivity map. The results of the inversion reveal that the self-potential data improve the estimate of hydraulic conductivity especially when the self-potential data are combined to the salt concentration measurement in the second well or to the time-lapse electrical resistivity data. Various tests are also performed to quantify the uncertainty in the inversion when for instance the semi-variogram is not known and its parameters should be inverted as well.

We introduce an algorithm for the simultaneous reconstruction of faults and slip fields. We prove that the minimum of a related regularized functional converges to the unique solution of the fault inverse problem. We consider a Bayesian approach. We use a parallel multi-core platform and we discuss techniques to save on computational time.

NASA Astrophysics Data System (ADS)

Volkov, D.

2017-12-01

We introduce an algorithm for the simultaneous reconstruction of faults and slip fields on those faults. We define a regularized functional to be minimized for the reconstruction. We prove that the minimum of that functional converges to the unique solution of the related fault inverse problem. Due to inherent uncertainties in measurements, rather than seeking a deterministic solution to the fault inverse problem, we consider a Bayesian approach. The advantage of such an approach is that we obtain a way of quantifying uncertainties as part of our final answer. On the downside, this Bayesian approach leads to a very large computation. To contend with the size of this computation we developed an algorithm for the numerical solution to the stochastic minimization problem which can be easily implemented on a parallel multi-core platform and we discuss techniques to save on computational time. After showing how this algorithm performs on simulated data and assessing the effect of noise, we apply it to measured data. The data was recorded during a slow slip event in Guerrero, Mexico.

Integrated seismic stochastic inversion and multi-attributes to delineate reservoir distribution: Case study MZ fields, Central Sumatra Basin

NASA Astrophysics Data System (ADS)

Haris, A.; Novriyani, M.; Suparno, S.; Hidayat, R.; Riyanto, A.

2017-07-01

This study presents the integration of seismic stochastic inversion and multi-attributes for delineating the reservoir distribution in term of lithology and porosity in the formation within depth interval between the Top Sihapas and Top Pematang. The method that has been used is a stochastic inversion, which is integrated with multi-attribute seismic by applying neural network Probabilistic Neural Network (PNN). Stochastic methods are used to predict the probability mapping sandstone as the result of impedance varied with 50 realizations that will produce a good probability. Analysis of Stochastic Seismic Tnversion provides more interpretive because it directly gives the value of the property. Our experiment shows that AT of stochastic inversion provides more diverse uncertainty so that the probability value will be close to the actual values. The produced AT is then used for an input of a multi-attribute analysis, which is used to predict the gamma ray, density and porosity logs. To obtain the number of attributes that are used, stepwise regression algorithm is applied. The results are attributes which are used in the process of PNN. This PNN method is chosen because it has the best correlation of others neural network method. Finally, we interpret the product of the multi-attribute analysis are in the form of pseudo-gamma ray volume, density volume and volume of pseudo-porosity to delineate the reservoir distribution. Our interpretation shows that the structural trap is identified in the southeastern part of study area, which is along the anticline.

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

Kitanidis, Peter

As large-scale, commercial storage projects become operational, the problem of utilizing information from diverse sources becomes more critically important. In this project, we developed, tested, and applied an advanced joint data inversion system for CO 2 storage modeling with large data sets for use in site characterization and real-time monitoring. Emphasis was on the development of advanced and efficient computational algorithms for joint inversion of hydro-geophysical data, coupled with state-of-the-art forward process simulations. The developed system consists of (1) inversion tools using characterization data, such as 3D seismic survey (amplitude images), borehole log and core data, as well as hydraulic,more » tracer and thermal tests before CO 2 injection, (2) joint inversion tools for updating the geologic model with the distribution of rock properties, thus reducing uncertainty, using hydro-geophysical monitoring data, and (3) highly efficient algorithms for directly solving the dense or sparse linear algebra systems derived from the joint inversion. The system combines methods from stochastic analysis, fast linear algebra, and high performance computing. The developed joint inversion tools have been tested through synthetic CO 2 storage examples.« less

Review: Optimization methods for groundwater modeling and management

NASA Astrophysics Data System (ADS)

Yeh, William W.-G.

2015-09-01

Optimization methods have been used in groundwater modeling as well as for the planning and management of groundwater systems. This paper reviews and evaluates the various optimization methods that have been used for solving the inverse problem of parameter identification (estimation), experimental design, and groundwater planning and management. Various model selection criteria are discussed, as well as criteria used for model discrimination. The inverse problem of parameter identification concerns the optimal determination of model parameters using water-level observations. In general, the optimal experimental design seeks to find sampling strategies for the purpose of estimating the unknown model parameters. A typical objective of optimal conjunctive-use planning of surface water and groundwater is to minimize the operational costs of meeting water demand. The optimization methods include mathematical programming techniques such as linear programming, quadratic programming, dynamic programming, stochastic programming, nonlinear programming, and the global search algorithms such as genetic algorithms, simulated annealing, and tabu search. Emphasis is placed on groundwater flow problems as opposed to contaminant transport problems. A typical two-dimensional groundwater flow problem is used to explain the basic formulations and algorithms that have been used to solve the formulated optimization problems.

A Stochastic Seismic Model for the European Arctic

NASA Astrophysics Data System (ADS)

Hauser, J.; Dyer, K.; Pasyanos, M. E.; Bungum, H.; Faleide, J. I.; Clark, S. A.

2009-12-01

The development of three-dimensional seismic models for the crust and upper mantle has traditionally focused on finding one model that provides the best fit to the data, while observing some regularization constraints. Such deterministic models however ignore a fundamental property of many inverse problems in geophysics, non-uniqueness, that is, if a model can be found to satisfy given datasets an infinite number of alternative models will exist that satisfy the datasets equally well. The solution to the inverse problem presented here is therefore a stochastic model, an ensemble of models that satisfy all available data to the same degree, the posterior distribution. It is based on two sources of information, (1) the data, in this work surface-wave group velocities, regional body-wave travel times, gravity data, compiled 1D velocity models, and thickness relationships between sedimentary rocks and underlying crystalline rocks, and (2) prior information, which is independent from the data. A Monte Carlo Markov Chain (MCMC) algorithm allows us to sample models from the prior distribution and test them against the data to generate the posterior distribution. While being computationally much more expensive, such a stochastic inversion provides a more complete picture of solution space and allows to seamlessly combine various datasets. The resulting stochastic model gives an overview of the different structures that can explain the observed datasets while taking the uncertainties in the data into account. Stochastic models are important for improving seismic monitoring capabilities as they allow to not only predict new observables but also their uncertainties. The model introduced here for the crust and upper mantle structure of the European Arctic is parametrized by a series of 8 layers in an equidistant mesh. Within each layer the seismic parameters (Vp, Vs and density) can vary linearly with depth. This allows to model changes of seismic parameters within the sediments and the crystalline crust without introducing artificial discontinuities that would result from parametrizing the structure using layers with constant seismic parameters. The complex geology of the region, encompassing oceanic crust, continental shelf regions, rift basins and old cratonic crust, and the non-uniform coverage of the region by data with varying levels of uncertainty makes the European Arctic a challenging setting for any imaging technique and therefore an ideal environment for demonstrating the practical advantages of a stochastic model. Maps of sediment thickness and thickness of the crystalline crust derived from the posterior distribution are in good agreement with knowledge of the regional tectonic setting. The predicted uncertainties, which are more important than the absolute values, correlate well with the variation in data coverage and data quality in the region. This indicates that the technique behaves as expected, thus we are properly tuning the methodology by allowing the Markov Chain adequate time to fully sample the model space.

Generalised filtering and stochastic DCM for fMRI.

PubMed

Li, Baojuan; Daunizeau, Jean; Stephan, Klaas E; Penny, Will; Hu, Dewen; Friston, Karl

2011-09-15

This paper is about the fitting or inversion of dynamic causal models (DCMs) of fMRI time series. It tries to establish the validity of stochastic DCMs that accommodate random fluctuations in hidden neuronal and physiological states. We compare and contrast deterministic and stochastic DCMs, which do and do not ignore random fluctuations or noise on hidden states. We then compare stochastic DCMs, which do and do not ignore conditional dependence between hidden states and model parameters (generalised filtering and dynamic expectation maximisation, respectively). We first characterise state-noise by comparing the log evidence of models with different a priori assumptions about its amplitude, form and smoothness. Face validity of the inversion scheme is then established using data simulated with and without state-noise to ensure that DCM can identify the parameters and model that generated the data. Finally, we address construct validity using real data from an fMRI study of internet addiction. Our analyses suggest the following. (i) The inversion of stochastic causal models is feasible, given typical fMRI data. (ii) State-noise has nontrivial amplitude and smoothness. (iii) Stochastic DCM has face validity, in the sense that Bayesian model comparison can distinguish between data that have been generated with high and low levels of physiological noise and model inversion provides veridical estimates of effective connectivity. (iv) Relaxing conditional independence assumptions can have greater construct validity, in terms of revealing group differences not disclosed by variational schemes. Finally, we note that the ability to model endogenous or random fluctuations on hidden neuronal (and physiological) states provides a new and possibly more plausible perspective on how regionally specific signals in fMRI are generated. Copyright © 2011. Published by Elsevier Inc.

Dynamic data integration and stochastic inversion of a confined aquifer

NASA Astrophysics Data System (ADS)

Wang, D.; Zhang, Y.; Irsa, J.; Huang, H.; Wang, L.

2013-12-01

Much work has been done in developing and applying inverse methods to aquifer modeling. The scope of this paper is to investigate the applicability of a new direct method for large inversion problems and to incorporate uncertainty measures in the inversion outcomes (Wang et al., 2013). The problem considered is a two-dimensional inverse model (50×50 grid) of steady-state flow for a heterogeneous ground truth model (500×500 grid) with two hydrofacies. From the ground truth model, decreasing number of wells (12, 6, 3) were sampled for facies types, based on which experimental indicator histograms and directional variograms were computed. These parameters and models were used by Sequential Indicator Simulation to generate 100 realizations of hydrofacies patterns in a 100×100 (geostatistical) grid, which were conditioned to the facies measurements at wells. These realizations were smoothed with Simulated Annealing, coarsened to the 50×50 inverse grid, before they were conditioned with the direct method to the dynamic data, i.e., observed heads and groundwater fluxes at the same sampled wells. A set of realizations of estimated hydraulic conductivities (Ks), flow fields, and boundary conditions were created, which centered on the 'true' solutions from solving the ground truth model. Both hydrofacies conductivities were computed with an estimation accuracy of ×10% (12 wells), ×20% (6 wells), ×35% (3 wells) of the true values. For boundary condition estimation, the accuracy was within × 15% (12 wells), 30% (6 wells), and 50% (3 wells) of the true values. The inversion system of equations was solved with LSQR (Paige et al, 1982), for which coordinate transform and matrix scaling preprocessor were used to improve the condition number (CN) of the coefficient matrix. However, when the inverse grid was refined to 100×100, Gaussian Noise Perturbation was used to limit the growth of the CN before the matrix solve. To scale the inverse problem up (i.e., without smoothing and coarsening and therefore reducing the associated estimation uncertainty), a parallel LSQR solver was written and verified. For the 50×50 grid, the parallel solver sped up the serial solution time by 14X using 4 CPUs (research on parallel performance and scaling is ongoing). A sensitivity analysis was conducted to examine the relation between the observed data and the inversion outcomes, where measurement errors of increasing magnitudes (i.e., ×1, 2, 5, 10% of the total head variation and up to ×2% of the total flux variation) were imposed on the observed data. Inversion results were stable but the accuracy of Ks and boundary estimation degraded with increasing errors, as expected. In particular, quality of the observed heads is critical to hydraulic head recovery, while quality of the observed fluxes plays a dominant role in K estimation. References: Wang, D., Y. Zhang, J. Irsa, H. Huang, and L. Wang (2013), Data integration and stochastic inversion of a confined aquifer with high performance computing, Advances in Water Resources, in preparation. Paige, C. C., and M. A. Saunders (1982), LSQR: an algorithm for sparse linear equations and sparse least squares, ACM Transactions on Mathematical Software, 8(1), 43-71.

Stochastic description of geometric phase for polarized waves in random media

NASA Astrophysics Data System (ADS)

Boulanger, Jérémie; Le Bihan, Nicolas; Rossetto, Vincent

2013-01-01

We present a stochastic description of multiple scattering of polarized waves in the regime of forward scattering. In this regime, if the source is polarized, polarization survives along a few transport mean free paths, making it possible to measure an outgoing polarization distribution. We consider thin scattering media illuminated by a polarized source and compute the probability distribution function of the polarization on the exit surface. We solve the direct problem using compound Poisson processes on the rotation group SO(3) and non-commutative harmonic analysis. We obtain an exact expression for the polarization distribution which generalizes previous works and design an algorithm solving the inverse problem of estimating the scattering properties of the medium from the measured polarization distribution. This technique applies to thin disordered layers, spatially fluctuating media and multiple scattering systems and is based on the polarization but not on the signal amplitude. We suggest that it can be used as a non-invasive testing method.

A stochastic asymptotic-preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty

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

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, School of Mathematical Science, MOELSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Shu, Ruiwen, E-mail: rshu2@math.wisc.edu

In this paper we consider a kinetic-fluid model for disperse two-phase flows with uncertainty. We propose a stochastic asymptotic-preserving (s-AP) scheme in the generalized polynomial chaos stochastic Galerkin (gPC-sG) framework, which allows the efficient computation of the problem in both kinetic and hydrodynamic regimes. The s-AP property is proved by deriving the equilibrium of the gPC version of the Fokker–Planck operator. The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions. The computation of the gPC version of a translation operatormore » that arises in the inversion of the Fokker–Planck operator is accelerated by a spectrally accurate splitting method. Numerical examples illustrate the s-AP property and the efficiency of the gPC-sG method in various asymptotic regimes.« less

Combined inverse-forward artificial neural networks for fast and accurate estimation of the diffusion coefficients of cartilage based on multi-physics models.

PubMed

Arbabi, Vahid; Pouran, Behdad; Weinans, Harrie; Zadpoor, Amir A

2016-09-06

Analytical and numerical methods have been used to extract essential engineering parameters such as elastic modulus, Poisson׳s ratio, permeability and diffusion coefficient from experimental data in various types of biological tissues. The major limitation associated with analytical techniques is that they are often only applicable to problems with simplified assumptions. Numerical multi-physics methods, on the other hand, enable minimizing the simplified assumptions but require substantial computational expertise, which is not always available. In this paper, we propose a novel approach that combines inverse and forward artificial neural networks (ANNs) which enables fast and accurate estimation of the diffusion coefficient of cartilage without any need for computational modeling. In this approach, an inverse ANN is trained using our multi-zone biphasic-solute finite-bath computational model of diffusion in cartilage to estimate the diffusion coefficient of the various zones of cartilage given the concentration-time curves. Robust estimation of the diffusion coefficients, however, requires introducing certain levels of stochastic variations during the training process. Determining the required level of stochastic variation is performed by coupling the inverse ANN with a forward ANN that receives the diffusion coefficient as input and returns the concentration-time curve as output. Combined together, forward-inverse ANNs enable computationally inexperienced users to obtain accurate and fast estimation of the diffusion coefficients of cartilage zones. The diffusion coefficients estimated using the proposed approach are compared with those determined using direct scanning of the parameter space as the optimization approach. It has been shown that both approaches yield comparable results. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

Fast model updating coupling Bayesian inference and PGD model reduction

NASA Astrophysics Data System (ADS)

Rubio, Paul-Baptiste; Louf, François; Chamoin, Ludovic

2018-04-01

The paper focuses on a coupled Bayesian-Proper Generalized Decomposition (PGD) approach for the real-time identification and updating of numerical models. The purpose is to use the most general case of Bayesian inference theory in order to address inverse problems and to deal with different sources of uncertainties (measurement and model errors, stochastic parameters). In order to do so with a reasonable CPU cost, the idea is to replace the direct model called for Monte-Carlo sampling by a PGD reduced model, and in some cases directly compute the probability density functions from the obtained analytical formulation. This procedure is first applied to a welding control example with the updating of a deterministic parameter. In the second application, the identification of a stochastic parameter is studied through a glued assembly example.

Stochastic sediment property inversion in Shallow Water 06.

PubMed

Michalopoulou, Zoi-Heleni

2017-11-01

Received time-series at a short distance from the source allow the identification of distinct paths; four of these are direct, surface and bottom reflections, and sediment reflection. In this work, a Gibbs sampling method is used for the estimation of the arrival times of these paths and the corresponding probability density functions. The arrival times for the first three paths are then employed along with linearization for the estimation of source range and depth, water column depth, and sound speed in the water. Propagating densities of arrival times through the linearized inverse problem, densities are also obtained for the above parameters, providing maximum a posteriori estimates. These estimates are employed to calculate densities and point estimates of sediment sound speed and thickness using a non-linear, grid-based model. Density computation is an important aspect of this work, because those densities express the uncertainty in the inversion for sediment properties.

On decoupling of volatility smile and term structure in inverse option pricing

NASA Astrophysics Data System (ADS)

Egger, Herbert; Hein, Torsten; Hofmann, Bernd

2006-08-01

Correct pricing of options and other financial derivatives is of great importance to financial markets and one of the key subjects of mathematical finance. Usually, parameters specifying the underlying stochastic model are not directly observable, but have to be determined indirectly from observable quantities. The identification of local volatility surfaces from market data of European vanilla options is one very important example of this type. As with many other parameter identification problems, the reconstruction of local volatility surfaces is ill-posed, and reasonable results can only be achieved via regularization methods. Moreover, due to the sparsity of data, the local volatility is not uniquely determined, but depends strongly on the kind of regularization norm used and a good a priori guess for the parameter. By assuming a multiplicative structure for the local volatility, which is motivated by the specific data situation, the inverse problem can be decomposed into two separate sub-problems. This removes part of the non-uniqueness and allows us to establish convergence and convergence rates under weak assumptions. Additionally, a numerical solution of the two sub-problems is much cheaper than that of the overall identification problem. The theoretical results are illustrated by numerical tests.

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.

Aerosol properties from spectral extinction and backscatter estimated by an inverse Monte Carlo method.

PubMed

Ligon, D A; Gillespie, J B; Pellegrino, P

2000-08-20

The feasibility of using a generalized stochastic inversion methodology to estimate aerosol size distributions accurately by use of spectral extinction, backscatter data, or both is examined. The stochastic method used, inverse Monte Carlo (IMC), is verified with both simulated and experimental data from aerosols composed of spherical dielectrics with a known refractive index. Various levels of noise are superimposed on the data such that the effect of noise on the stability and results of inversion can be determined. Computational results show that the application of the IMC technique to inversion of spectral extinction or backscatter data or both can produce good estimates of aerosol size distributions. Specifically, for inversions for which both spectral extinction and backscatter data are used, the IMC technique was extremely accurate in determining particle size distributions well outside the wavelength range. Also, the IMC inversion results proved to be stable and accurate even when the data had significant noise, with a signal-to-noise ratio of 3.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

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

Thimmisetty, Charanraj A.; Zhao, Wenju; Chen, Xiao

2017-10-18

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). Thismore » approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.« less

Stochastic simulation of spatially correlated geo-processes

USGS Publications Warehouse

Christakos, G.

1987-01-01

In this study, developments in the theory of stochastic simulation are discussed. The unifying element is the notion of Radon projection in Euclidean spaces. This notion provides a natural way of reconstructing the real process from a corresponding process observable on a reduced dimensionality space, where analysis is theoretically easier and computationally tractable. Within this framework, the concept of space transformation is defined and several of its properties, which are of significant importance within the context of spatially correlated processes, are explored. The turning bands operator is shown to follow from this. This strengthens considerably the theoretical background of the geostatistical method of simulation, and some new results are obtained in both the space and frequency domains. The inverse problem is solved generally and the applicability of the method is extended to anisotropic as well as integrated processes. Some ill-posed problems of the inverse operator are discussed. Effects of the measurement error and impulses at origin are examined. Important features of the simulated process as described by geomechanical laws, the morphology of the deposit, etc., may be incorporated in the analysis. The simulation may become a model-dependent procedure and this, in turn, may provide numerical solutions to spatial-temporal geologic models. Because the spatial simu??lation may be technically reduced to unidimensional simulations, various techniques of generating one-dimensional realizations are reviewed. To link theory and practice, an example is computed in detail. ?? 1987 International Association for Mathematical Geology.

Inverse problems in complex material design: Applications to non-crystalline solids

NASA Astrophysics Data System (ADS)

Biswas, Parthapratim; Drabold, David; Elliott, Stephen

The design of complex amorphous materials is one of the fundamental problems in disordered condensed-matter science. While impressive developments of ab-initio simulation methods during the past several decades have brought tremendous success in understanding materials property from micro- to mesoscopic length scales, a major drawback is that they fail to incorporate existing knowledge of the materials in simulation methodologies. Since an essential feature of materials design is the synergy between experiment and theory, a properly developed approach to design materials should be able to exploit all available knowledge of the materials from measured experimental data. In this talk, we will address the design of complex disordered materials as an inverse problem involving experimental data and available empirical information. We show that the problem can be posed as a multi-objective non-convex optimization program, which can be addressed using a number of recently-developed bio-inspired global optimization techniques. In particular, we will discuss how a population-based stochastic search procedure can be used to determine the structure of non-crystalline solids (e.g. a-SiH, a-SiO2, amorphous graphene, and Fe and Ni clusters). The work is partially supported by NSF under Grant Nos. DMR 1507166 and 1507670.

The inverse problem of estimating the gravitational time dilation

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

Gusev, A. V., E-mail: avg@sai.msu.ru; Litvinov, D. A.; Rudenko, V. N.

2016-11-15

Precise testing of the gravitational time dilation effect suggests comparing the clocks at points with different gravitational potentials. Such a configuration arises when radio frequency standards are installed at orbital and ground stations. The ground-based standard is accessible directly, while the spaceborne one is accessible only via the electromagnetic signal exchange. Reconstructing the current frequency of the spaceborne standard is an ill-posed inverse problem whose solution depends significantly on the characteristics of the stochastic electromagnetic background. The solution for Gaussian noise is known, but the nature of the standards themselves is associated with nonstationary fluctuations of a wide class ofmore » distributions. A solution is proposed for a background of flicker fluctuations with a spectrum (1/f){sup γ}, where 1 < γ < 3, and stationary increments. The results include formulas for the error in reconstructing the frequency of the spaceborne standard and numerical estimates for the accuracy of measuring the relativistic redshift effect.« less

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.

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

Fast Geostatistical Inversion using Randomized Matrix Decompositions and Sketchings for Heterogeneous Aquifer Characterization

NASA Astrophysics Data System (ADS)

O'Malley, D.; Le, E. B.; Vesselinov, V. V.

2015-12-01

We present a fast, scalable, and highly-implementable stochastic inverse method for characterization of aquifer heterogeneity. The method utilizes recent advances in randomized matrix algebra and exploits the structure of the Quasi-Linear Geostatistical Approach (QLGA), without requiring a structured grid like Fast-Fourier Transform (FFT) methods. The QLGA framework is a more stable version of Gauss-Newton iterates for a large number of unknown model parameters, but provides unbiased estimates. The methods are matrix-free and do not require derivatives or adjoints, and are thus ideal for complex models and black-box implementation. We also incorporate randomized least-square solvers and data-reduction methods, which speed up computation and simulate missing data points. The new inverse methodology is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). Julia is an advanced high-level scientific programing language that allows for efficient memory management and utilization of high-performance computational resources. Inversion results based on series of synthetic problems with steady-state and transient calibration data are presented.

Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian

NASA Astrophysics Data System (ADS)

Teneng, Dean

2013-09-01

We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.

A stochastic framework for spot-scanning particle therapy.

PubMed

Robini, Marc; Yuemin Zhu; Wanyu Liu; Magnin, Isabelle

2016-08-01

In spot-scanning particle therapy, inverse treatment planning is usually limited to finding the optimal beam fluences given the beam trajectories and energies. We address the much more challenging problem of jointly optimizing the beam fluences, trajectories and energies. For this purpose, we design a simulated annealing algorithm with an exploration mechanism that balances the conflicting demands of a small mixing time at high temperatures and a reasonable acceptance rate at low temperatures. Numerical experiments substantiate the relevance of our approach and open new horizons to spot-scanning particle therapy.

Use of LANDSAT images of vegetation cover to estimate effective hydraulic properties of soils

NASA Technical Reports Server (NTRS)

Eagleson, Peter S.; Jasinski, Michael F.

1988-01-01

This work focuses on the characterization of natural, spatially variable, semivegetated landscapes using a linear, stochastic, canopy-soil reflectance model. A first application of the model was the investigation of the effects of subpixel and regional variability of scenes on the shape and structure of red-infrared scattergrams. Additionally, the model was used to investigate the inverse problem, the estimation of subpixel vegetation cover, given only the scattergrams of simulated satellite scale multispectral scenes. The major aspects of that work, including recent field investigations, are summarized.

Stochastic static fault slip inversion from geodetic data with non-negativity and bound constraints

NASA Astrophysics Data System (ADS)

Nocquet, J.-M.

2018-07-01

Despite surface displacements observed by geodesy are linear combinations of slip at faults in an elastic medium, determining the spatial distribution of fault slip remains a ill-posed inverse problem. A widely used approach to circumvent the illness of the inversion is to add regularization constraints in terms of smoothing and/or damping so that the linear system becomes invertible. However, the choice of regularization parameters is often arbitrary, and sometimes leads to significantly different results. Furthermore, the resolution analysis is usually empirical and cannot be made independently of the regularization. The stochastic approach of inverse problems provides a rigorous framework where the a priori information about the searched parameters is combined with the observations in order to derive posterior probabilities of the unkown parameters. Here, I investigate an approach where the prior probability density function (pdf) is a multivariate Gaussian function, with single truncation to impose positivity of slip or double truncation to impose positivity and upper bounds on slip for interseismic modelling. I show that the joint posterior pdf is similar to the linear untruncated Gaussian case and can be expressed as a truncated multivariate normal (TMVN) distribution. The TMVN form can then be used to obtain semi-analytical formulae for the single, 2-D or n-D marginal pdf. The semi-analytical formula involves the product of a Gaussian by an integral term that can be evaluated using recent developments in TMVN probabilities calculations. Posterior mean and covariance can also be efficiently derived. I show that the maximum posterior (MAP) can be obtained using a non-negative least-squares algorithm for the single truncated case or using the bounded-variable least-squares algorithm for the double truncated case. I show that the case of independent uniform priors can be approximated using TMVN. The numerical equivalence to Bayesian inversions using Monte Carlo Markov chain (MCMC) sampling is shown for a synthetic example and a real case for interseismic modelling in Central Peru. The TMVN method overcomes several limitations of the Bayesian approach using MCMC sampling. First, the need of computer power is largely reduced. Second, unlike Bayesian MCMC-based approach, marginal pdf, mean, variance or covariance are obtained independently one from each other. Third, the probability and cumulative density functions can be obtained with any density of points. Finally, determining the MAP is extremely fast.

Field dynamics inference via spectral density estimation

NASA Astrophysics Data System (ADS)

Frank, Philipp; Steininger, Theo; Enßlin, Torsten A.

2017-11-01

Stochastic differential equations are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to solve, e.g., when modeling Brownian motion. In some cases, the equations governing the dynamics of a physical system on macroscopic scales occur to be unknown since they typically cannot be deduced from general principles. In this work, we describe how the underlying laws of a stochastic process can be approximated by the spectral density of the corresponding process. Furthermore, we show how the density can be inferred from possibly very noisy and incomplete measurements of the dynamical field. Generally, inverse problems like these can be tackled with the help of Information Field Theory. For now, we restrict to linear and autonomous processes. To demonstrate its applicability, we employ our reconstruction algorithm on a time-series and spatiotemporal processes.

Field dynamics inference via spectral density estimation.

PubMed

Frank, Philipp; Steininger, Theo; Enßlin, Torsten A

2017-11-01

Stochastic differential equations are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to solve, e.g., when modeling Brownian motion. In some cases, the equations governing the dynamics of a physical system on macroscopic scales occur to be unknown since they typically cannot be deduced from general principles. In this work, we describe how the underlying laws of a stochastic process can be approximated by the spectral density of the corresponding process. Furthermore, we show how the density can be inferred from possibly very noisy and incomplete measurements of the dynamical field. Generally, inverse problems like these can be tackled with the help of Information Field Theory. For now, we restrict to linear and autonomous processes. To demonstrate its applicability, we employ our reconstruction algorithm on a time-series and spatiotemporal processes.

Optimal Control for Stochastic Delay Evolution Equations

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

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

Nonlinear Inference in Partially Observed Physical Systems and Deep Neural Networks

NASA Astrophysics Data System (ADS)

Rozdeba, Paul J.

The problem of model state and parameter estimation is a significant challenge in nonlinear systems. Due to practical considerations of experimental design, it is often the case that physical systems are partially observed, meaning that data is only available for a subset of the degrees of freedom required to fully model the observed system's behaviors and, ultimately, predict future observations. Estimation in this context is highly complicated by the presence of chaos, stochasticity, and measurement noise in dynamical systems. One of the aims of this dissertation is to simultaneously analyze state and parameter estimation in as a regularized inverse problem, where the introduction of a model makes it possible to reverse the forward problem of partial, noisy observation; and as a statistical inference problem using data assimilation to transfer information from measurements to the model states and parameters. Ultimately these two formulations achieve the same goal. Similar aspects that appear in both are highlighted as a means for better understanding the structure of the nonlinear inference problem. An alternative approach to data assimilation that uses model reduction is then examined as a way to eliminate unresolved nonlinear gating variables from neuron models. In this formulation, only measured variables enter into the model, and the resulting errors are themselves modeled by nonlinear stochastic processes with memory. Finally, variational annealing, a data assimilation method previously applied to dynamical systems, is introduced as a potentially useful tool for understanding deep neural network training in machine learning by exploiting similarities between the two problems.

Cellular Automata

NASA Astrophysics Data System (ADS)

Gutowitz, Howard

1991-08-01

Cellular automata, dynamic systems in which space and time are discrete, are yielding interesting applications in both the physical and natural sciences. The thirty four contributions in this book cover many aspects of contemporary studies on cellular automata and include reviews, research reports, and guides to recent literature and available software. Chapters cover mathematical analysis, the structure of the space of cellular automata, learning rules with specified properties: cellular automata in biology, physics, chemistry, and computation theory; and generalizations of cellular automata in neural nets, Boolean nets, and coupled map lattices. Current work on cellular automata may be viewed as revolving around two central and closely related problems: the forward problem and the inverse problem. The forward problem concerns the description of properties of given cellular automata. Properties considered include reversibility, invariants, criticality, fractal dimension, and computational power. The role of cellular automata in computation theory is seen as a particularly exciting venue for exploring parallel computers as theoretical and practical tools in mathematical physics. The inverse problem, an area of study gaining prominence particularly in the natural sciences, involves designing rules that possess specified properties or perform specified task. A long-term goal is to develop a set of techniques that can find a rule or set of rules that can reproduce quantitative observations of a physical system. Studies of the inverse problem take up the organization and structure of the set of automata, in particular the parameterization of the space of cellular automata. Optimization and learning techniques, like the genetic algorithm and adaptive stochastic cellular automata are applied to find cellular automaton rules that model such physical phenomena as crystal growth or perform such adaptive-learning tasks as balancing an inverted pole. Howard Gutowitz is Collaborateur in the Service de Physique du Solide et Résonance Magnetique, Commissariat a I'Energie Atomique, Saclay, France.

Simulation studies of phase inversion in agitated vessels using a Monte Carlo technique.

PubMed

Yeo, Leslie Y; Matar, Omar K; Perez de Ortiz, E Susana; Hewitt, Geoffrey F

2002-04-15

A speculative study on the conditions under which phase inversion occurs in agitated liquid-liquid dispersions is conducted using a Monte Carlo technique. The simulation is based on a stochastic model, which accounts for fundamental physical processes such as drop deformation, breakup, and coalescence, and utilizes the minimization of interfacial energy as a criterion for phase inversion. Profiles of the interfacial energy indicate that a steady-state equilibrium is reached after a sufficiently large number of random moves and that predictions are insensitive to initial drop conditions. The calculated phase inversion holdup is observed to increase with increasing density and viscosity ratio, and to decrease with increasing agitation speed for a fixed viscosity ratio. It is also observed that, for a fixed viscosity ratio, the phase inversion holdup remains constant for large enough agitation speeds. The proposed model is therefore capable of achieving reasonable qualitative agreement with general experimental trends and of reproducing key features observed experimentally. The results of this investigation indicate that this simple stochastic method could be the basis upon which more advanced models for predicting phase inversion behavior can be developed.

An interval model updating strategy using interval response surface models

NASA Astrophysics Data System (ADS)

Fang, Sheng-En; Zhang, Qiu-Hu; Ren, Wei-Xin

2015-08-01

Stochastic model updating provides an effective way of handling uncertainties existing in real-world structures. In general, probabilistic theories, fuzzy mathematics or interval analyses are involved in the solution of inverse problems. However in practice, probability distributions or membership functions of structural parameters are often unavailable due to insufficient information of a structure. At this moment an interval model updating procedure shows its superiority in the aspect of problem simplification since only the upper and lower bounds of parameters and responses are sought. To this end, this study develops a new concept of interval response surface models for the purpose of efficiently implementing the interval model updating procedure. The frequent interval overestimation due to the use of interval arithmetic can be maximally avoided leading to accurate estimation of parameter intervals. Meanwhile, the establishment of an interval inverse problem is highly simplified, accompanied by a saving of computational costs. By this means a relatively simple and cost-efficient interval updating process can be achieved. Lastly, the feasibility and reliability of the developed method have been verified against a numerical mass-spring system and also against a set of experimentally tested steel plates.

Dimension-independent likelihood-informed MCMC

DOE PAGES

Cui, Tiangang; Law, Kody J. H.; Marzouk, Youssef M.

2015-10-08

Many Bayesian inference problems require exploring the posterior distribution of highdimensional parameters that represent the discretization of an underlying function. Our work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. There are two distinct lines of research that intersect in the methods we develop here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian informationmore » and any associated lowdimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Finally, we use two nonlinear inverse problems in order to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.« less

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.

Tomographic reconstruction of atmospheric turbulence with the use of time-dependent stochastic inversion.

PubMed

Vecherin, Sergey N; Ostashev, Vladimir E; Ziemann, A; Wilson, D Keith; Arnold, K; Barth, M

2007-09-01

Acoustic travel-time tomography allows one to reconstruct temperature and wind velocity fields in the atmosphere. In a recently published paper [S. Vecherin et al., J. Acoust. Soc. Am. 119, 2579 (2006)], a time-dependent stochastic inversion (TDSI) was developed for the reconstruction of these fields from travel times of sound propagation between sources and receivers in a tomography array. TDSI accounts for the correlation of temperature and wind velocity fluctuations both in space and time and therefore yields more accurate reconstruction of these fields in comparison with algebraic techniques and regular stochastic inversion. To use TDSI, one needs to estimate spatial-temporal covariance functions of temperature and wind velocity fluctuations. In this paper, these spatial-temporal covariance functions are derived for locally frozen turbulence which is a more general concept than a widely used hypothesis of frozen turbulence. The developed theory is applied to reconstruction of temperature and wind velocity fields in the acoustic tomography experiment carried out by University of Leipzig, Germany. The reconstructed temperature and velocity fields are presented and errors in reconstruction of these fields are studied.

A stochastic approach for model reduction and memory function design in hydrogeophysical inversion

NASA Astrophysics Data System (ADS)

Hou, Z.; Kellogg, A.; Terry, N.

2009-12-01

Geophysical (e.g., seismic, electromagnetic, radar) techniques and statistical methods are essential for research related to subsurface characterization, including monitoring subsurface flow and transport processes, oil/gas reservoir identification, etc. For deep subsurface characterization such as reservoir petroleum exploration, seismic methods have been widely used. Recently, electromagnetic (EM) methods have drawn great attention in the area of reservoir characterization. However, considering the enormous computational demand corresponding to seismic and EM forward modeling, it is usually a big problem to have too many unknown parameters in the modeling domain. For shallow subsurface applications, the characterization can be very complicated considering the complexity and nonlinearity of flow and transport processes in the unsaturated zone. It is warranted to reduce the dimension of parameter space to a reasonable level. Another common concern is how to make the best use of time-lapse data with spatial-temporal correlations. This is even more critical when we try to monitor subsurface processes using geophysical data collected at different times. The normal practice is to get the inverse images individually. These images are not necessarily continuous or even reasonably related, because of the non-uniqueness of hydrogeophysical inversion. We propose to use a stochastic framework by integrating minimum-relative-entropy concept, quasi Monto Carlo sampling techniques, and statistical tests. The approach allows efficient and sufficient exploration of all possibilities of model parameters and evaluation of their significances to geophysical responses. The analyses enable us to reduce the parameter space significantly. The approach can be combined with Bayesian updating, allowing us to treat the updated ‘posterior’ pdf as a memory function, which stores all the information up to date about the distributions of soil/field attributes/properties, then consider the memory function as a new prior and generate samples from it for further updating when more geophysical data is available. We applied this approach for deep oil reservoir characterization and for shallow subsurface flow monitoring. The model reduction approach reliably helps reduce the joint seismic/EM/radar inversion computational time to reasonable levels. Continuous inversion images are obtained using time-lapse data with the “memory function” applied in the Bayesian inversion.

Control of stochastic sensitivity in a stabilization problem for gas discharge system

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

Bashkirtseva, Irina

2015-11-30

We consider a nonlinear dynamic stochastic system with control. A problem of stochastic sensitivity synthesis of the equilibrium is studied. A mathematical technique of the solution of this problem is discussed. This technique is applied to the problem of the stabilization of the operating mode for the stochastic gas discharge system. We construct a feedback regulator that reduces the stochastic sensitivity of the equilibrium, suppresses large-amplitude oscillations, and provides a proper operation of this engineering device.

Optimal sensor locations for the backward Lagrangian stochastic technique in measuring lagoon gas emission

USDA-ARS?s Scientific Manuscript database

This study evaluated the impact of gas concentration and wind sensor locations on the accuracy of the backward Lagrangian stochastic inverse-dispersion technique (bLS) for measuring gas emission rates from a typical lagoon environment. Path-integrated concentrations (PICs) and 3-dimensional (3D) wi...

On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems

DOE PAGES

Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan

2015-05-19

The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less

Time-Dependent Stochastic Inversion in Acoustic Tomography of the Atmosphere with Reciprocal Sound Transmission

DTIC Science & Technology

2008-10-17

R E 1960 A new approach to linear filtering and prediction problems Trans. ASME D 82 35–45 [23] Brown R G and Hwang Y C 1992 Introduction to Random...vector Wiener filter [21]. TDSI is also somewhat similar to the Kalman filter [22, 23] which is applied in many areas including tomography [24–27]. The...453–76 [21] Links J M, Prince J L and Gupta S N 1996 A vector Wiener filter for dual-radionuclide imaging IEEE Trans. Med. Imaging 15 700–9 [22] Kalman

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.

The Sharma-Parthasarathy stochastic two-body problem

NASA Astrophysics Data System (ADS)

Cresson, J.; Pierret, F.; Puig, B.

2015-03-01

We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in ["Dynamics of a stochastically perturbed two-body problem," Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss's equations in the planar case.

Algebraic, geometric, and stochastic aspects of genetic operators

NASA Technical Reports Server (NTRS)

Foo, N. Y.; Bosworth, J. L.

1972-01-01

Genetic algorithms for function optimization employ genetic operators patterned after those observed in search strategies employed in natural adaptation. Two of these operators, crossover and inversion, are interpreted in terms of their algebraic and geometric properties. Stochastic models of the operators are developed which are employed in Monte Carlo simulations of their behavior.

Computation of direct and inverse mutations with the SEGM web server (Stochastic Evolution of Genetic Motifs): an application to splice sites of human genome introns.

PubMed

Benard, Emmanuel; Michel, Christian J

2009-08-01

We present here the SEGM web server (Stochastic Evolution of Genetic Motifs) in order to study the evolution of genetic motifs both in the direct evolutionary sense (past-present) and in the inverse evolutionary sense (present-past). The genetic motifs studied can be nucleotides, dinucleotides and trinucleotides. As an example of an application of SEGM and to understand its functionalities, we give an analysis of inverse mutations of splice sites of human genome introns. SEGM is freely accessible at http://lsiit-bioinfo.u-strasbg.fr:8080/webMathematica/SEGM/SEGM.html directly or by the web site http://dpt-info.u-strasbg.fr/~michel/. To our knowledge, this SEGM web server is to date the only computational biology software in this evolutionary approach.

[Research on the measurement range of particle size with total light scattering method in vis-IR region].

PubMed

Sun, Xiao-gang; Tang, Hong; Dai, Jing-min

2008-12-01

The problem of determining the particle size range in the visible-infrared region was studied using the independent model algorithm in the total scattering technique. By the analysis and comparison of the accuracy of the inversion results for different R-R distributions, the measurement range of particle size was determined. Meanwhile, the corrected extinction coefficient was used instead of the original extinction coefficient, which could determine the measurement range of particle size with higher accuracy. Simulation experiments illustrate that the particle size distribution can be retrieved very well in the range from 0. 05 to 18 microm at relative refractive index m=1.235 in the visible-infrared spectral region, and the measurement range of particle size will vary with the varied wavelength range and relative refractive index. It is feasible to use the constrained least squares inversion method in the independent model to overcome the influence of the measurement error, and the inverse results are all still satisfactory when 1% stochastic noise is added to the value of the light extinction.

Uncertainty quantification of CO₂ saturation estimated from electrical resistance tomography data at the Cranfield site

DOE PAGES

Yang, Xianjin; Chen, Xiao; Carrigan, Charles R.; ...

2014-06-03

A parametric bootstrap approach is presented for uncertainty quantification (UQ) of CO₂ saturation derived from electrical resistance tomography (ERT) data collected at the Cranfield, Mississippi (USA) carbon sequestration site. There are many sources of uncertainty in ERT-derived CO₂ saturation, but we focus on how the ERT observation errors propagate to the estimated CO₂ saturation in a nonlinear inversion process. Our UQ approach consists of three steps. We first estimated the observational errors from a large number of reciprocal ERT measurements. The second step was to invert the pre-injection baseline data and the resulting resistivity tomograph was used as the priormore » information for nonlinear inversion of time-lapse data. We assigned a 3% random noise to the baseline model. Finally, we used a parametric bootstrap method to obtain bootstrap CO₂ saturation samples by deterministically solving a nonlinear inverse problem many times with resampled data and resampled baseline models. Then the mean and standard deviation of CO₂ saturation were calculated from the bootstrap samples. We found that the maximum standard deviation of CO₂ saturation was around 6% with a corresponding maximum saturation of 30% for a data set collected 100 days after injection began. There was no apparent spatial correlation between the mean and standard deviation of CO₂ saturation but the standard deviation values increased with time as the saturation increased. The uncertainty in CO₂ saturation also depends on the ERT reciprocal error threshold used to identify and remove noisy data and inversion constraints such as temporal roughness. Five hundred realizations requiring 3.5 h on a single 12-core node were needed for the nonlinear Monte Carlo inversion to arrive at stationary variances while the Markov Chain Monte Carlo (MCMC) stochastic inverse approach may expend days for a global search. This indicates that UQ of 2D or 3D ERT inverse problems can be performed on a laptop or desktop PC.« less

The Sharma-Parthasarathy stochastic two-body problem

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

Cresson, J.; SYRTE/Observatoire de Paris, 75014 Paris; Pierret, F.

2015-03-15

We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed two-body problem,” Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss’s equations in the planar case.

Stochastic static fault slip inversion from geodetic data with non-negativity and bounds constraints

NASA Astrophysics Data System (ADS)

Nocquet, J.-M.

2018-04-01

Despite surface displacements observed by geodesy are linear combinations of slip at faults in an elastic medium, determining the spatial distribution of fault slip remains a ill-posed inverse problem. A widely used approach to circumvent the illness of the inversion is to add regularization constraints in terms of smoothing and/or damping so that the linear system becomes invertible. However, the choice of regularization parameters is often arbitrary, and sometimes leads to significantly different results. Furthermore, the resolution analysis is usually empirical and cannot be made independently of the regularization. The stochastic approach of inverse problems (Tarantola & Valette 1982; Tarantola 2005) provides a rigorous framework where the a priori information about the searched parameters is combined with the observations in order to derive posterior probabilities of the unkown parameters. Here, I investigate an approach where the prior probability density function (pdf) is a multivariate Gaussian function, with single truncation to impose positivity of slip or double truncation to impose positivity and upper bounds on slip for interseismic modeling. I show that the joint posterior pdf is similar to the linear untruncated Gaussian case and can be expressed as a Truncated Multi-Variate Normal (TMVN) distribution. The TMVN form can then be used to obtain semi-analytical formulas for the single, two-dimensional or n-dimensional marginal pdf. The semi-analytical formula involves the product of a Gaussian by an integral term that can be evaluated using recent developments in TMVN probabilities calculations (e.g. Genz & Bretz 2009). Posterior mean and covariance can also be efficiently derived. I show that the Maximum Posterior (MAP) can be obtained using a Non-Negative Least-Squares algorithm (Lawson & Hanson 1974) for the single truncated case or using the Bounded-Variable Least-Squares algorithm (Stark & Parker 1995) for the double truncated case. I show that the case of independent uniform priors can be approximated using TMVN. The numerical equivalence to Bayesian inversions using Monte Carlo Markov Chain (MCMC) sampling is shown for a synthetic example and a real case for interseismic modeling in Central Peru. The TMVN method overcomes several limitations of the Bayesian approach using MCMC sampling. First, the need of computer power is largely reduced. Second, unlike Bayesian MCMC based approach, marginal pdf, mean, variance or covariance are obtained independently one from each other. Third, the probability and cumulative density functions can be obtained with any density of points. Finally, determining the Maximum Posterior (MAP) is extremely fast.

Application of stochastic particle swarm optimization algorithm to determine the graded refractive index distribution in participating media

NASA Astrophysics Data System (ADS)

Wei, Lin-Yang; Qi, Hong; Ren, Ya-Tao; Ruan, Li-Ming

2016-11-01

Inverse estimation of the refractive index distribution in one-dimensional participating media with graded refractive index (GRI) is investigated. The forward radiative transfer problem is solved by the Chebyshev collocation spectral method. The stochastic particle swarm optimization (SPSO) algorithm is employed to retrieve three kinds of GRI distribution, i.e. the linear, sinusoidal and quadratic GRI distribution. The retrieval accuracy of GRI distribution with different wall emissivity, optical thickness, absorption coefficients and scattering coefficients are discussed thoroughly. To improve the retrieval accuracy of quadratic GRI distribution, a double-layer model is proposed to supply more measurement information. The influence of measurement errors upon the precision of estimated results is also investigated. Considering the GRI distribution is unknown beforehand in practice, a quadratic function is employed to retrieve the linear GRI by SPSO algorithm. All the results show that the SPSO algorithm is applicable to retrieve different GRI distributions in participating media accurately even with noisy data.

Stochastic Inversion of InSAR Data to Assess the Probability of Pressure Penetration into the Lower Caprock at In Salah

DOE PAGES

Ramirez, Abelardo; Foxall, William

2014-05-28

Stochastic inversions of InSAR data were carried out to assess the probability that pressure perturbations resulting from CO 2 injection into well KB-502 at In Salah penetrated into the lower caprock seal above the reservoir. Inversions of synthetic data were employed to evaluate the factors that affect the vertical resolution of overpressure distributions, and to assess the impact of various sources of uncertainty in prior constraints on inverse solutions. These include alternative pressure-driven deformation modes within reservoir and caprock, the geometry of a sub-vertical fracture zone in the caprock identified in previous studies, and imperfect estimates of the rock mechanicalmore » properties. Inversions of field data indicate that there is a high probability that a pressure perturbation during the first phase of injection extended upwards along the fracture zone ~ 150 m above the reservoir, and less than 50% probability that it reached the Hot Shale unit at 1500 m depth. Within the uncertainty bounds considered, it was concluded that it is very unlikely that the pressure perturbation approached within 150 m of the top of the lower caprock at the Hercynian Unconformity. The results are consistent with previous deterministic inversion and forward modeling studies.« less

Modeling of long-range memory processes with inverse cubic distributions by the nonlinear stochastic differential equations

NASA Astrophysics Data System (ADS)

Kaulakys, B.; Alaburda, M.; Ruseckas, J.

2016-05-01

A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.

Active and Passive Hydrologic Tomographic Surveys:A Revolution in Hydrology (Invited)

NASA Astrophysics Data System (ADS)

Yeh, T. J.

2013-12-01

Mathematical forward or inverse problems of flow through geological media always have unique solutions if necessary conditions are givens. Unique mathematical solutions to forward or inverse modeling of field problems are however always uncertain (an infinite number of possibilities) due to many reasons. They include non-representativeness of the governing equations, inaccurate necessary conditions, multi-scale heterogeneity, scale discrepancies between observation and model, noise and others. Conditional stochastic approaches, which derives the unbiased solution and quantifies the solution uncertainty, are therefore most appropriate for forward and inverse modeling of hydrological processes. Conditioning using non-redundant data sets reduces uncertainty. In this presentation, we explain non-redundant data sets in cross-hole aquifer tests, and demonstrate that active hydraulic tomographic survey (using man-made excitations) is a cost-effective approach to collect the same type but non-redundant data sets for reducing uncertainty in the inverse modeling. We subsequently show that including flux measurements (a piece of non-redundant data set) collected in the same well setup as in hydraulic tomography improves the estimated hydraulic conductivity field. We finally conclude with examples and propositions regarding how to collect and analyze data intelligently by exploiting natural recurrent events (river stage fluctuations, earthquakes, lightning, etc.) as energy sources for basin-scale passive tomographic surveys. The development of information fusion technologies that integrate traditional point measurements and active/passive hydrogeophysical tomographic surveys, as well as advances in sensor, computing, and information technologies may ultimately advance our capability of characterizing groundwater basins to achieve resolution far beyond the feat of current science and technology.

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

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

Regularized two-step brain activity reconstruction from spatiotemporal EEG data

NASA Astrophysics Data System (ADS)

Alecu, Teodor I.; Voloshynovskiy, Sviatoslav; Pun, Thierry

2004-10-01

We are aiming at using EEG source localization in the framework of a Brain Computer Interface project. We propose here a new reconstruction procedure, targeting source (or equivalently mental task) differentiation. EEG data can be thought of as a collection of time continuous streams from sparse locations. The measured electric potential on one electrode is the result of the superposition of synchronized synaptic activity from sources in all the brain volume. Consequently, the EEG inverse problem is a highly underdetermined (and ill-posed) problem. Moreover, each source contribution is linear with respect to its amplitude but non-linear with respect to its localization and orientation. In order to overcome these drawbacks we propose a novel two-step inversion procedure. The solution is based on a double scale division of the solution space. The first step uses a coarse discretization and has the sole purpose of globally identifying the active regions, via a sparse approximation algorithm. The second step is applied only on the retained regions and makes use of a fine discretization of the space, aiming at detailing the brain activity. The local configuration of sources is recovered using an iterative stochastic estimator with adaptive joint minimum energy and directional consistency constraints.

Lidar inversion of atmospheric backscatter and extinction-to-backscatter ratios by use of a Kalman filter.

PubMed

Rocadenbosch, F; Soriano, C; Comerón, A; Baldasano, J M

1999-05-20

A first inversion of the backscatter profile and extinction-to-backscatter ratio from pulsed elastic-backscatter lidar returns is treated by means of an extended Kalman filter (EKF). The EKF approach enables one to overcome the intrinsic limitations of standard straightforward nonmemory procedures such as the slope method, exponential curve fitting, and the backward inversion algorithm. Whereas those procedures are inherently not adaptable because independent inversions are performed for each return signal and neither the statistics of the signals nor a priori uncertainties (e.g., boundary calibrations) are taken into account, in the case of the Kalman filter the filter updates itself because it is weighted by the imbalance between the a priori estimates of the optical parameters (i.e., past inversions) and the new estimates based on a minimum-variance criterion, as long as there are different lidar returns. Calibration errors and initialization uncertainties can be assimilated also. The study begins with the formulation of the inversion problem and an appropriate atmospheric stochastic model. Based on extensive simulation and realistic conditions, it is shown that the EKF approach enables one to retrieve the optical parameters as time-range-dependent functions and hence to track the atmospheric evolution; the performance of this approach is limited only by the quality and availability of the a priori information and the accuracy of the atmospheric model used. The study ends with an encouraging practical inversion of a live scene measured at the Nd:YAG elastic-backscatter lidar station at our premises at the Polytechnic University of Catalonia, Barcelona.

CMOS-based Stochastically Spiking Neural Network for Optimization under Uncertainties

DTIC Science & Technology

2017-03-01

inverse tangent characteristics at varying input voltage (VIN) [Fig. 3], thereby it is suitable for Kernel function implementation. By varying bias...cost function/constraint variables are generated based on inverse transform on CDF. In Fig. 5, F-1(u) for uniformly distributed random number u [0, 1...extracts random samples of x varying with CDF of F(x). In Fig. 6, we present a successive approximation (SA) circuit to evaluate inverse

Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

ERIC Educational Resources Information Center

Varga, Katherine Yvonne

2015-01-01

We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

Towards sub-optimal stochastic control of partially observable stochastic systems

NASA Technical Reports Server (NTRS)

Ruzicka, G. J.

1980-01-01

A class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design is examined. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in dimensions is proven.

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

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

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Errormore » analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.« less

Problems of Mathematical Finance by Stochastic Control Methods

NASA Astrophysics Data System (ADS)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

Including geological information in the inverse problem of palaeothermal reconstruction

NASA Astrophysics Data System (ADS)

Trautner, S.; Nielsen, S. B.

2003-04-01

A reliable reconstruction of sediment thermal history is of central importance to the assessment of hydrocarbon potential and the understanding of basin evolution. However, only rarely do sedimentation history and borehole data in the form of present day temperatures and vitrinite reflectance constrain the past thermal evolution to a useful level of accuracy (Gallagher and Sambridge,1992; Nielsen,1998; Trautner and Nielsen,2003). This is reflected in the inverse solutions to the problem of determining heat flow history from borehole data: The recent heat flow is constrained by data while older values are governed by the chosen a prior heat flow. In this paper we reduce this problem by including geological information in the inverse problem. Through a careful analysis of geological and geophysical data the timing of the tectonic processes, which may influence heat flow, can be inferred. The heat flow history is then parameterised to allow for the temporal variations characteristic of the different tectonic events. The inversion scheme applies a Markov chain Monte Carlo (MCMC) approach (Nielsen and Gallagher, 1999; Ferrero and Gallagher,2002), which efficiently explores the model space and futhermore samples the posterior probability distribution of the model. The technique is demonstrated on wells in the northern North Sea with emphasis on the stretching event in Late Jurassic. The wells are characterised by maximum sediment temperature at the present day, which is the worst case for resolution of the past thermal history because vitrinite reflectance is determined mainly by the maximum temperature. Including geological information significantly improves the thermal resolution. Ferrero, C. and Gallagher,K.,2002. Stochastic thermal history modelling.1. Constraining heat flow histories and their uncertainty. Marine and Petroleum Geology, 19, 633-648. Gallagher,K. and Sambridge, M., 1992. The resolution of past heat flow in sedimentary basins from non-linear inversion of geochemical data: the smoothest model approach, with synthetic examples. Geophysical Journal International, 109, 78-95. Nielsen, S.B, 1998. Inversion and sensitivity analysis in basin modelling. Geoscience 98. Keele University, UK, Abstract Volume, 56. Nielsen, S.B. and Gallagher, K., 1999. Efficient sampling of 3-D basin modelling scenarios. Extended Abstracts Volume, 1999 AAPG International Conference &Exhibition, Birmingham, England, September 12-15, 1999, p. 369 - 372. Trautner S. and Nielsen, S.B., 2003. 2-D inverse thermal modelling in the Norwegian shelf using Fast Approximate Forward (FAF) solutions. In R. Marzi and Duppenbecker, S. (Ed.), Multi-Dimensional Basin Modeling, AAPG, in press.

Stochastic mechanical model of vocal folds for producing jitter and for identifying pathologies through real voices.

PubMed

Cataldo, E; Soize, C

2018-06-06

Jitter, in voice production applications, is a random phenomenon characterized by the deviation of the glottal cycle length with respect to a mean value. Its study can help in identifying pathologies related to the vocal folds according to the values obtained through the different ways to measure it. This paper aims to propose a stochastic model, considering three control parameters, to generate jitter based on a deterministic one-mass model for the dynamics of the vocal folds and to identify parameters from the stochastic model taking into account real voice signals experimentally obtained. To solve the corresponding stochastic inverse problem, the cost function used is based on the distance between probability density functions of the random variables associated with the fundamental frequencies obtained by the experimental voices and the simulated ones, and also on the distance between features extracted from the voice signals, simulated and experimental, to calculate jitter. The results obtained show that the model proposed is valid and some samples of voices are synthesized considering the identified parameters for normal and pathological cases. The strategy adopted is also a novelty and mainly because a solution was obtained. In addition to the use of three parameters to construct the model of jitter, it is the discussion of a parameter related to the bandwidth of the power spectral density function of the stochastic process to measure the quality of the signal generated. A study about the influence of all the main parameters is also performed. The identification of the parameters of the model considering pathological cases is maybe of all novelties introduced by the paper the most interesting. Copyright © 2018 Elsevier Ltd. All rights reserved.

A Stochastic Employment Problem

ERIC Educational Resources Information Center

Wu, Teng

2013-01-01

The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…

Nonholonomic relativistic diffusion and exact solutions for stochastic Einstein spaces

NASA Astrophysics Data System (ADS)

Vacaru, S. I.

2012-03-01

We develop an approach to the theory of nonholonomic relativistic stochastic processes in curved spaces. The Itô and Stratonovich calculus are formulated for spaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting defined by nonlinear connection structures. Geometric models of the relativistic diffusion theory are elaborated for nonholonomic (pseudo) Riemannian manifolds and phase velocity spaces. Applying the anholonomic deformation method, the field equations in Einstein's gravity and various modifications are formally integrated in general forms, with generic off-diagonal metrics depending on some classes of generating and integration functions. Choosing random generating functions we can construct various classes of stochastic Einstein manifolds. We show how stochastic gravitational interactions with mixed holonomic/nonholonomic and random variables can be modelled in explicit form and study their main geometric and stochastic properties. Finally, the conditions when non-random classical gravitational processes transform into stochastic ones and inversely are analyzed.

Maximum principle for a stochastic delayed system involving terminal state constraints.

PubMed

Wen, Jiaqiang; Shi, Yufeng

2017-01-01

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.

Monte Carlo uncertainty analyses of a bLS inverse-dispersion technique for measuring gas emissions from livestock operations

USDA-ARS?s Scientific Manuscript database

The backward Lagrangian stochastic (bLS) inverse-dispersion technique has been used to measure fugitive gas emissions from livestock operations. The accuracy of the bLS technique, as indicated by the percentages of gas recovery in various tracer-release experiments, has generally been within ± 10% o...

Jump-and-return sandwiches: A new family of binomial-like selective inversion sequences with improved performance

NASA Astrophysics Data System (ADS)

Brenner, Tom; Chen, Johnny; Stait-Gardner, Tim; Zheng, Gang; Matsukawa, Shingo; Price, William S.

2018-03-01

A new family of binomial-like inversion sequences, named jump-and-return sandwiches (JRS), has been developed by inserting a binomial-like sequence into a standard jump-and-return sequence, discovered through use of a stochastic Genetic Algorithm optimisation. Compared to currently used binomial-like inversion sequences (e.g., 3-9-19 and W5), the new sequences afford wider inversion bands and narrower non-inversion bands with an equal number of pulses. As an example, two jump-and-return sandwich 10-pulse sequences achieved 95% inversion at offsets corresponding to 9.4% and 10.3% of the non-inversion band spacing, compared to 14.7% for the binomial-like W5 inversion sequence, i.e., they afforded non-inversion bands about two thirds the width of the W5 non-inversion band.

Perspective: Stochastic magnetic devices for cognitive computing

NASA Astrophysics Data System (ADS)

Roy, Kaushik; Sengupta, Abhronil; Shim, Yong

2018-06-01

Stochastic switching of nanomagnets can potentially enable probabilistic cognitive hardware consisting of noisy neural and synaptic components. Furthermore, computational paradigms inspired from the Ising computing model require stochasticity for achieving near-optimality in solutions to various types of combinatorial optimization problems such as the Graph Coloring Problem or the Travelling Salesman Problem. Achieving optimal solutions in such problems are computationally exhaustive and requires natural annealing to arrive at the near-optimal solutions. Stochastic switching of devices also finds use in applications involving Deep Belief Networks and Bayesian Inference. In this article, we provide a multi-disciplinary perspective across the stack of devices, circuits, and algorithms to illustrate how the stochastic switching dynamics of spintronic devices in the presence of thermal noise can provide a direct mapping to the computational units of such probabilistic intelligent systems.

Stochastic seismic inversion based on an improved local gradual deformation method

NASA Astrophysics Data System (ADS)

Yang, Xiuwei; Zhu, Peimin

2017-12-01

A new stochastic seismic inversion method based on the local gradual deformation method is proposed, which can incorporate seismic data, well data, geology and their spatial correlations into the inversion process. Geological information, such as sedimentary facies and structures, could provide significant a priori information to constrain an inversion and arrive at reasonable solutions. The local a priori conditional cumulative distributions at each node of model to be inverted are first established by indicator cokriging, which integrates well data as hard data and geological information as soft data. Probability field simulation is used to simulate different realizations consistent with the spatial correlations and local conditional cumulative distributions. The corresponding probability field is generated by the fast Fourier transform moving average method. Then, optimization is performed to match the seismic data via an improved local gradual deformation method. Two improved strategies are proposed to be suitable for seismic inversion. The first strategy is that we select and update local areas of bad fitting between synthetic seismic data and real seismic data. The second one is that we divide each seismic trace into several parts and obtain the optimal parameters for each part individually. The applications to a synthetic example and a real case study demonstrate that our approach can effectively find fine-scale acoustic impedance models and provide uncertainty estimations.

Generation of Look-Up Tables for Dynamic Job Shop Scheduling Decision Support Tool

NASA Astrophysics Data System (ADS)

Oktaviandri, Muchamad; Hassan, Adnan; Mohd Shaharoun, Awaluddin

2016-02-01

Majority of existing scheduling techniques are based on static demand and deterministic processing time, while most job shop scheduling problem are concerned with dynamic demand and stochastic processing time. As a consequence, the solutions obtained from the traditional scheduling technique are ineffective wherever changes occur to the system. Therefore, this research intends to develop a decision support tool (DST) based on promising artificial intelligent that is able to accommodate the dynamics that regularly occur in job shop scheduling problem. The DST was designed through three phases, i.e. (i) the look-up table generation, (ii) inverse model development and (iii) integration of DST components. This paper reports the generation of look-up tables for various scenarios as a part in development of the DST. A discrete event simulation model was used to compare the performance among SPT, EDD, FCFS, S/OPN and Slack rules; the best performances measures (mean flow time, mean tardiness and mean lateness) and the job order requirement (inter-arrival time, due dates tightness and setup time ratio) which were compiled into look-up tables. The well-known 6/6/J/Cmax Problem from Muth and Thompson (1963) was used as a case study. In the future, the performance measure of various scheduling scenarios and the job order requirement will be mapped using ANN inverse model.

Inverse Modeling Using Markov Chain Monte Carlo Aided by Adaptive Stochastic Collocation Method with Transformation

NASA Astrophysics Data System (ADS)

Zhang, D.; Liao, Q.

2016-12-01

The Bayesian inference provides a convenient framework to solve statistical inverse problems. In this method, the parameters to be identified are treated as random variables. The prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated in the posterior probability density function (PDF) of the parameters. The Markov chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior PDF. However, since the MCMC usually requires thousands or even millions of forward simulations, it can be a computationally intensive endeavor, particularly when faced with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model responses in the form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and takes into account the different importance of the parameters, under the condition of high random dimensions in the stochastic space. Furthermore, in case of low regularity such as discontinuous or unsmooth relation between the input parameters and the output responses, we introduce an additional transform process to improve the accuracy of the surrogate model. Once we build the surrogate system, we may evaluate the likelihood with very little computational cost. We analyzed the convergence rate of the forward solution and the surrogate posterior by Kullback-Leibler divergence, which quantifies the difference between probability distributions. The fast convergence of the forward solution implies fast convergence of the surrogate posterior to the true posterior. We also tested the proposed algorithm on water-flooding two-phase flow reservoir examples. The posterior PDF calculated from a very long chain with direct forward simulation is assumed to be accurate. The posterior PDF calculated using the surrogate model is in reasonable agreement with the reference, revealing a great improvement in terms of computational efficiency.

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.

On some stochastic formulations and related statistical moments of pharmacokinetic models.

PubMed

Matis, J H; Wehrly, T E; Metzler, C M

1983-02-01

This paper presents the deterministic and stochastic model for a linear compartment system with constant coefficients, and it develops expressions for the mean residence times (MRT) and the variances of the residence times (VRT) for the stochastic model. The expressions are relatively simple computationally, involving primarily matrix inversion, and they are elegant mathematically, in avoiding eigenvalue analysis and the complex domain. The MRT and VRT provide a set of new meaningful response measures for pharmacokinetic analysis and they give added insight into the system kinetics. The new analysis is illustrated with an example involving the cholesterol turnover in rats.

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

A chance-constrained stochastic approach to intermodal container routing problems.

PubMed

Zhao, Yi; Liu, Ronghui; Zhang, Xi; Whiteing, Anthony

2018-01-01

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost.

A chance-constrained stochastic approach to intermodal container routing problems

PubMed Central

Zhao, Yi; Zhang, Xi; Whiteing, Anthony

2018-01-01

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost. PMID:29438389

Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle Using Stochastic Methods

NASA Technical Reports Server (NTRS)

Zang, Thomas A.; Mathelin, Lionel; Hussaini, M. Yousuff; Bataille, Francoise

2003-01-01

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.

Final Technical Report: Quantification of Uncertainty in Extreme Scale Computations (QUEST)

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

Knio, Omar M.

QUEST is a SciDAC Institute comprising Sandia National Laboratories, Los Alamos National Laboratory, University of Southern California, Massachusetts Institute of Technology, University of Texas at Austin, and Duke University. The mission of QUEST is to: (1) develop a broad class of uncertainty quantification (UQ) methods/tools, and (2) provide UQ expertise and software to other SciDAC projects, thereby enabling/guiding their UQ activities. The Duke effort focused on the development of algorithms and utility software for non-intrusive sparse UQ representations, and on participation in the organization of annual workshops and tutorials to disseminate UQ tools to the community, and to gather inputmore » in order to adapt approaches to the needs of SciDAC customers. In particular, fundamental developments were made in (a) multiscale stochastic preconditioners, (b) gradient-based approaches to inverse problems, (c) adaptive pseudo-spectral approximations, (d) stochastic limit cycles, and (e) sensitivity analysis tools for noisy systems. In addition, large-scale demonstrations were performed, namely in the context of ocean general circulation models.« less

Minimum mean squared error (MSE) adjustment and the optimal Tykhonov-Phillips regularization parameter via reproducing best invariant quadratic uniformly unbiased estimates (repro-BIQUUE)

NASA Astrophysics Data System (ADS)

Schaffrin, Burkhard

2008-02-01

In a linear Gauss-Markov model, the parameter estimates from BLUUE (Best Linear Uniformly Unbiased Estimate) are not robust against possible outliers in the observations. Moreover, by giving up the unbiasedness constraint, the mean squared error (MSE) risk may be further reduced, in particular when the problem is ill-posed. In this paper, the α-weighted S-homBLE (Best homogeneously Linear Estimate) is derived via formulas originally used for variance component estimation on the basis of the repro-BIQUUE (reproducing Best Invariant Quadratic Uniformly Unbiased Estimate) principle in a model with stochastic prior information. In the present model, however, such prior information is not included, which allows the comparison of the stochastic approach (α-weighted S-homBLE) with the well-established algebraic approach of Tykhonov-Phillips regularization, also known as R-HAPS (Hybrid APproximation Solution), whenever the inverse of the “substitute matrix” S exists and is chosen as the R matrix that defines the relative impact of the regularizing term on the final result.

SU-E-J-161: Inverse Problems for Optical Parameters in Laser Induced Thermal Therapy

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

Fahrenholtz, SJ; Stafford, RJ; Fuentes, DT

Purpose: Magnetic resonance-guided laser-induced thermal therapy (MRgLITT) is investigated as a neurosurgical intervention for oncological applications throughout the body by active post market studies. Real-time MR temperature imaging is used to monitor ablative thermal delivery in the clinic. Additionally, brain MRgLITT could improve through effective planning for laser fiber's placement. Mathematical bioheat models have been extensively investigated but require reliable patient specific physical parameter data, e.g. optical parameters. This abstract applies an inverse problem algorithm to characterize optical parameter data obtained from previous MRgLITT interventions. Methods: The implemented inverse problem has three primary components: a parameter-space search algorithm, a physicsmore » model, and training data. First, the parameter-space search algorithm uses a gradient-based quasi-Newton method to optimize the effective optical attenuation coefficient, μ-eff. A parameter reduction reduces the amount of optical parameter-space the algorithm must search. Second, the physics model is a simplified bioheat model for homogeneous tissue where closed-form Green's functions represent the exact solution. Third, the training data was temperature imaging data from 23 MRgLITT oncological brain ablations (980 nm wavelength) from seven different patients. Results: To three significant figures, the descriptive statistics for μ-eff were 1470 m{sup −1} mean, 1360 m{sup −1} median, 369 m{sup −1} standard deviation, 933 m{sup −1} minimum and 2260 m{sup −1} maximum. The standard deviation normalized by the mean was 25.0%. The inverse problem took <30 minutes to optimize all 23 datasets. Conclusion: As expected, the inferred average is biased by underlying physics model. However, the standard deviation normalized by the mean is smaller than literature values and indicates an increased precision in the characterization of the optical parameters needed to plan MRgLITT procedures. This investigation demonstrates the potential for the optimization and validation of more sophisticated bioheat models that incorporate the uncertainty of the data into the predictions, e.g. stochastic finite element methods.« less

Alternatives to the stochastic "noise vector" approach

NASA Astrophysics Data System (ADS)

de Forcrand, Philippe; Jäger, Benjamin

2018-03-01

Several important observables, like the quark condensate and the Taylor coefficients of the expansion of the QCD pressure with respect to the chemical potential, are based on the trace of the inverse Dirac operator and of its powers. Such traces are traditionally estimated with "noise vectors" sandwiching the operator. We explore alternative approaches based on polynomial approximations of the inverse Dirac operator.

The quasi-optimality criterion in the linear functional strategy

NASA Astrophysics Data System (ADS)

Kindermann, Stefan; Pereverzyev, Sergiy, Jr.; Pilipenko, Andrey

2018-07-01

The linear functional strategy for the regularization of inverse problems is considered. For selecting the regularization parameter therein, we propose the heuristic quasi-optimality principle and some modifications including the smoothness of the linear functionals. We prove convergence rates for the linear functional strategy with these heuristic rules taking into account the smoothness of the solution and the functionals and imposing a structural condition on the noise. Furthermore, we study these noise conditions in both a deterministic and stochastic setup and verify that for mildly-ill-posed problems and Gaussian noise, these conditions are satisfied almost surely, where on the contrary, in the severely-ill-posed case and in a similar setup, the corresponding noise condition fails to hold. Moreover, we propose an aggregation method for adaptively optimizing the parameter choice rule by making use of improved rates for linear functionals. Numerical results indicate that this method yields better results than the standard heuristic rule.

Jump-and-return sandwiches: A new family of binomial-like selective inversion sequences with improved performance.

PubMed

Brenner, Tom; Chen, Johnny; Stait-Gardner, Tim; Zheng, Gang; Matsukawa, Shingo; Price, William S

2018-03-01

A new family of binomial-like inversion sequences, named jump-and-return sandwiches (JRS), has been developed by inserting a binomial-like sequence into a standard jump-and-return sequence, discovered through use of a stochastic Genetic Algorithm optimisation. Compared to currently used binomial-like inversion sequences (e.g., 3-9-19 and W5), the new sequences afford wider inversion bands and narrower non-inversion bands with an equal number of pulses. As an example, two jump-and-return sandwich 10-pulse sequences achieved 95% inversion at offsets corresponding to 9.4% and 10.3% of the non-inversion band spacing, compared to 14.7% for the binomial-like W5 inversion sequence, i.e., they afforded non-inversion bands about two thirds the width of the W5 non-inversion band. Copyright © 2018 Elsevier Inc. All rights reserved.

Hydrogeophysical Assessment of Aquifer Uncertainty Using Simulated Annealing driven MRF-Based Stochastic Joint Inversion

NASA Astrophysics Data System (ADS)

Oware, E. K.

2017-12-01

Geophysical quantification of hydrogeological parameters typically involve limited noisy measurements coupled with inadequate understanding of the target phenomenon. Hence, a deterministic solution is unrealistic in light of the largely uncertain inputs. Stochastic imaging (SI), in contrast, provides multiple equiprobable realizations that enable probabilistic assessment of aquifer properties in a realistic manner. Generation of geologically realistic prior models is central to SI frameworks. Higher-order statistics for representing prior geological features in SI are, however, usually borrowed from training images (TIs), which may produce undesirable outcomes if the TIs are unpresentatitve of the target structures. The Markov random field (MRF)-based SI strategy provides a data-driven alternative to TI-based SI algorithms. In the MRF-based method, the simulation of spatial features is guided by Gibbs energy (GE) minimization. Local configurations with smaller GEs have higher likelihood of occurrence and vice versa. The parameters of the Gibbs distribution for computing the GE are estimated from the hydrogeophysical data, thereby enabling the generation of site-specific structures in the absence of reliable TIs. In Metropolis-like SI methods, the variance of the transition probability controls the jump-size. The procedure is a standard Markov chain Monte Carlo (McMC) method when a constant variance is assumed, and becomes simulated annealing (SA) when the variance (cooling temperature) is allowed to decrease gradually with time. We observe that in certain problems, the large variance typically employed at the beginning to hasten burn-in may be unideal for sampling at the equilibrium state. The powerfulness of SA stems from its flexibility to adaptively scale the variance at different stages of the sampling. Degeneration of results were reported in a previous implementation of the MRF-based SI strategy based on a constant variance. Here, we present an updated version of the algorithm based on SA that appears to resolve the degeneration problem with seemingly improved results. We illustrate the performance of the SA version with a joint inversion of time-lapse concentration and electrical resistivity measurements in a hypothetical trinary hydrofacies aquifer characterization problem.

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

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

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

On two mathematical problems of canonical quantization. IV

NASA Astrophysics Data System (ADS)

Kirillov, A. I.

1992-11-01

A method for solving the problem of reconstructing a measure beginning with its logarithmic derivative is presented. The method completes that of solving the stochastic differential equation via Dirichlet forms proposed by S. Albeverio and M. Rockner. As a result one obtains the mathematical apparatus for the stochastic quantization. The apparatus is applied to prove the existence of the Feynman-Kac measure of the sine-Gordon and λφ2n/(1 + K2φ2n)-models. A synthesis of both mathematical problems of canonical quantization is obtained in the form of a second-order martingale problem for vacuum noise. It is shown that in stochastic mechanics the martingale problem is an analog of Newton's second law and enables us to find the Nelson's stochastic trajectories without determining the wave functions.

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem.

PubMed

Schilde, M; Doerner, K F; Hartl, R F

2014-10-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches.

Price sensitive demand with random sales price - a newsboy problem

NASA Astrophysics Data System (ADS)

Sankar Sana, Shib

2012-03-01

Up to now, many newsboy problems have been considered in the stochastic inventory literature. Some assume that stochastic demand is independent of selling price (p) and others consider the demand as a function of stochastic shock factor and deterministic sales price. This article introduces a price-dependent demand with stochastic selling price into the classical Newsboy problem. The proposed model analyses the expected average profit for a general distribution function of p and obtains an optimal order size. Finally, the model is discussed for various appropriate distribution functions of p and illustrated with numerical examples.

Boosting Stochastic Problem Solvers Through Online Self-Analysis of Performance

DTIC Science & Technology

2003-07-21

Boosting Stochastic Problem Solvers Through Online Self-Analysis of Performance Vincent A. Cicirello CMU-RI-TR-03-27 Submitted in partial fulfillment...AND SUBTITLE Boosting Stochastic Problem Solvers Through Online Self-Analysis of Performance 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM...lead to the development of a search control framework, called QD-BEACON that uses online -generated statistical models of search performance to

Enhanced algorithms for stochastic programming

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

Krishna, Alamuru S.

1993-09-01

In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean ofmore » a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.« less

Identification and stochastic control of helicopter dynamic modes

NASA Technical Reports Server (NTRS)

Molusis, J. A.; Bar-Shalom, Y.

1983-01-01

A general treatment of parameter identification and stochastic control for use on helicopter dynamic systems is presented. Rotor dynamic models, including specific applications to rotor blade flapping and the helicopter ground resonance problem are emphasized. Dynamic systems which are governed by periodic coefficients as well as constant coefficient models are addressed. The dynamic systems are modeled by linear state variable equations which are used in the identification and stochastic control formulation. The pure identification problem as well as the stochastic control problem which includes combined identification and control for dynamic systems is addressed. The stochastic control problem includes the effect of parameter uncertainty on the solution and the concept of learning and how this is affected by the control's duel effect. The identification formulation requires algorithms suitable for on line use and thus recursive identification algorithms are considered. The applications presented use the recursive extended kalman filter for parameter identification which has excellent convergence for systems without process noise.

Large-Scale CTRW Analysis of Push-Pull Tracer Tests and Other Transport in Heterogeneous Porous Media

NASA Astrophysics Data System (ADS)

Hansen, S. K.; Berkowitz, B.

2014-12-01

Recently, we developed an alternative CTRW formulation which uses a "latching" upscaling scheme to rigorously map continuous or fine-scale stochastic solute motion onto discrete transitions on an arbitrarily coarse lattice (with spacing potentially on the meter scale or more). This approach enables model simplification, among many other things. Under advection, for example, we see that many relevant anomalous transport problems may be mapped into 1D, with latching to a sequence of successive, uniformly spaced planes. On this formulation (which we term RP-CTRW), the spatial transition vector may generally be made deterministic, with CTRW waiting time distributions encapsulating all the stochastic behavior. We demonstrate the excellent performance of this technique alongside Pareto-distributed waiting times in explaining experiments across a variety of scales using only two degrees of freedom. An interesting new application of the RP-CTRW technique is the analysis of radial (push-pull) tracer tests. Given modern computational power, random walk simulations are a natural fit for the inverse problem of inferring subsurface parameters from push-pull test data, and we propose them as an alternative to the classical type curve approach. In particular, we explore the visibility of heterogeneity through non-Fickian behavior in push-pull tests, and illustrate the ability of a radial RP-CTRW technique to encapsulate this behavior using a sparse parameterization which has predictive value.

K-Minimax Stochastic Programming Problems

NASA Astrophysics Data System (ADS)

Nedeva, C.

2007-10-01

The purpose of this paper is a discussion of a numerical procedure based on the simplex method for stochastic optimization problems with partially known distribution functions. The convergence of this procedure is proved by the condition on dual problems.

Refractory pulse counting processes in stochastic neural computers.

PubMed

McNeill, Dean K; Card, Howard C

2005-03-01

This letter quantitiatively investigates the effect of a temporary refractory period or dead time in the ability of a stochastic Bernoulli processor to record subsequent pulse events, following the arrival of a pulse. These effects can arise in either the input detectors of a stochastic neural network or in subsequent processing. A transient period is observed, which increases with both the dead time and the Bernoulli probability of the dead-time free system, during which the system reaches equilibrium. Unless the Bernoulli probability is small compared to the inverse of the dead time, the mean and variance of the pulse count distributions are both appreciably reduced.

Point-source stochastic-method simulations of ground motions for the PEER NGA-East Project

USGS Publications Warehouse

Boore, David

2015-01-01

Ground-motions for the PEER NGA-East project were simulated using a point-source stochastic method. The simulated motions are provided for distances between of 0 and 1200 km, M from 4 to 8, and 25 ground-motion intensity measures: peak ground velocity (PGV), peak ground acceleration (PGA), and 5%-damped pseudoabsolute response spectral acceleration (PSA) for 23 periods ranging from 0.01 s to 10.0 s. Tables of motions are provided for each of six attenuation models. The attenuation-model-dependent stress parameters used in the stochastic-method simulations were derived from inversion of PSA data from eight earthquakes in eastern North America.

Variational formulation for Black-Scholes equations in stochastic volatility models

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Valkov, Radoslav L.

2012-11-01

In this note we prove existence and uniqueness of weak solutions to a boundary value problem arising from stochastic volatility models in financial mathematics. Our settings are variational in weighted Sobolev spaces. Nevertheless, as it will become apparent our variational formulation agrees well with the stochastic part of the problem.

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

Control of Finite-State, Finite Memory Stochastic Systems

NASA Technical Reports Server (NTRS)

Sandell, Nils R.

1974-01-01

A generalized problem of stochastic control is discussed in which multiple controllers with different data bases are present. The vehicle for the investigation is the finite state, finite memory (FSFM) stochastic control problem. Optimality conditions are obtained by deriving an equivalent deterministic optimal control problem. A FSFM minimum principle is obtained via the equivalent deterministic problem. The minimum principle suggests the development of a numerical optimization algorithm, the min-H algorithm. The relationship between the sufficiency of the minimum principle and the informational properties of the problem are investigated. A problem of hypothesis testing with 1-bit memory is investigated to illustrate the application of control theoretic techniques to information processing problems.

Pilot Study on the Applicability of Variance Reduction Techniques to the Simulation of a Stochastic Combat Model

DTIC Science & Technology

1987-09-01

inverse transform method to obtain unit-mean exponential random variables, where Vi is the jth random number in the sequence of a stream of uniform random...numbers. The inverse transform method is discussed in the simulation textbooks listed in the reference section of this thesis. X(b,c,d) = - P(b,c,d...Defender ,C * P(b,c,d) We again use the inverse transform method to obtain the conditions for an interim event to occur and to induce the change in

Approximate methods for the fast computation of EPR and ST-EPR spectra. V. Application of the perturbation approach to the problem of anisotropic motion

NASA Astrophysics Data System (ADS)

Robinson, B. H.; Dalton, L. R.

1981-01-01

The modulation perturbation treatment of Galloway and Dalton is applied to the solution of the stochastic Liouville equation for the spin density matrix which incorporates an anisotropic rotational diffusion operator. Pseudosecular and saturation terms of the spin hamiltonian are explicitly considered as is the interaction of the electron spins with the applied Zeeman modulation field. The modulation perturbation treatment results in a factor of four improvement in computational speed relative to inversion of the full supermatrix with little or no loss of computational accuracy. The theoretical simulations of EPR and ST-EPR spectra are in nearly quantitative agreement with experimental spectra taken under high resolution conditions.

Unification theory of optimal life histories and linear demographic models in internal stochasticity.

PubMed

Oizumi, Ryo

2014-01-01

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of "Stochastic Control Theory" in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path-integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models.

Unification Theory of Optimal Life Histories and Linear Demographic Models in Internal Stochasticity

PubMed Central

Oizumi, Ryo

2014-01-01

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of “Stochastic Control Theory” in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path–integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models. PMID:24945258

Inversion of oceanic constituents in case I and II waters with genetic programming algorithms.

PubMed

Chami, Malik; Robilliard, Denis

2002-10-20

A stochastic inverse technique based on agenetic programming (GP) algorithm was developed toinvert oceanic constituents from simulated data for case I and case II water applications. The simulations were carried out with the Ordre Successifs Ocean Atmosphere (OSOA) radiative transfer model. They include the effects of oceanic substances such as algal-related chlorophyll, nonchlorophyllous suspended matter, and dissolved organic matter. The synthetic data set also takes into account the directional effects of particles through a variation of their phase function that makes the simulated data realistic. It is shown that GP can be successfully applied to the inverse problem with acceptable stability in the presence of realistic noise in the data. GP is compared with neural network methodology for case I waters; GP exhibits similar retrieval accuracy, which is greater than for traditional techniques such as band ratio algorithms. The application of GP to real satellite data [a Sea-viewing Wide Field-of-view Sensor (SeaWiFS)] was also carried out for case I waters as a validation. Good agreement was obtained when GP results were compared with the SeaWiFS empirical algorithm. For case II waters the accuracy of GP is less than 33%, which remains satisfactory, at the present time, for remote-sensing purposes.

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem

PubMed Central

Schilde, M.; Doerner, K.F.; Hartl, R.F.

2014-01-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches. PMID:25844013

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

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

Hamadameen, Abdulqader Othman; Zainuddin, Zaitul Marlizawati

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

Optimal estimation of parameters and states in stochastic time-varying systems with time delay

NASA Astrophysics Data System (ADS)

Torkamani, Shahab; Butcher, Eric A.

2013-08-01

In this study estimation of parameters and states in stochastic linear and nonlinear delay differential systems with time-varying coefficients and constant delay is explored. The approach consists of first employing a continuous time approximation to approximate the stochastic delay differential equation with a set of stochastic ordinary differential equations. Then the problem of parameter estimation in the resulting stochastic differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the resulting system, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states.

Isotropic probability measures in infinite-dimensional spaces

NASA Technical Reports Server (NTRS)

Backus, George

1987-01-01

Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub in :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity) (P sub n to the -1 (B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond.

PubMed

Perdikaris, Paris; Karniadakis, George Em

2016-05-01

We present a computational framework for model inversion based on multi-fidelity information fusion and Bayesian optimization. The proposed methodology targets the accurate construction of response surfaces in parameter space, and the efficient pursuit to identify global optima while keeping the number of expensive function evaluations at a minimum. We train families of correlated surrogates on available data using Gaussian processes and auto-regressive stochastic schemes, and exploit the resulting predictive posterior distributions within a Bayesian optimization setting. This enables a smart adaptive sampling procedure that uses the predictive posterior variance to balance the exploration versus exploitation trade-off, and is a key enabler for practical computations under limited budgets. The effectiveness of the proposed framework is tested on three parameter estimation problems. The first two involve the calibration of outflow boundary conditions of blood flow simulations in arterial bifurcations using multi-fidelity realizations of one- and three-dimensional models, whereas the last one aims to identify the forcing term that generated a particular solution to an elliptic partial differential equation. © 2016 The Author(s).

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond

PubMed Central

Perdikaris, Paris; Karniadakis, George Em

2016-01-01

We present a computational framework for model inversion based on multi-fidelity information fusion and Bayesian optimization. The proposed methodology targets the accurate construction of response surfaces in parameter space, and the efficient pursuit to identify global optima while keeping the number of expensive function evaluations at a minimum. We train families of correlated surrogates on available data using Gaussian processes and auto-regressive stochastic schemes, and exploit the resulting predictive posterior distributions within a Bayesian optimization setting. This enables a smart adaptive sampling procedure that uses the predictive posterior variance to balance the exploration versus exploitation trade-off, and is a key enabler for practical computations under limited budgets. The effectiveness of the proposed framework is tested on three parameter estimation problems. The first two involve the calibration of outflow boundary conditions of blood flow simulations in arterial bifurcations using multi-fidelity realizations of one- and three-dimensional models, whereas the last one aims to identify the forcing term that generated a particular solution to an elliptic partial differential equation. PMID:27194481

Partial ASL extensions for stochastic programming.

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

Gay, David

2010-03-31

partially completed extensions for stochastic programming to the AMPL/solver interface library (ASL).modeling and experimenting with stochastic recourse problems. This software is not primarily for military applications

Inversion of atmospheric optical parameters from elastic-backscatter lidar returns using a Kalman filter

NASA Astrophysics Data System (ADS)

Rocadenbosch, Francesc; Comeron, Adolfo; Vazquez, Gregori; Rodriguez-Gomez, Alejandro; Soriano, Cecilia; Baldasano, Jose M.

1998-12-01

Up to now, retrieval of the atmospheric extinction and backscatter has mainly relied on standard straightforward non-memory procedures such as slope-method, exponential- curve fitting and Klett's method. Yet, their performance becomes ultimately limited by the inherent lack of adaptability as they only work with present returns and neither past estimations, nor the statistics of the signals or a prior uncertainties are taken into account. In this work, a first inversion of the backscatter and extinction- to-backscatter ratio from pulsed elastic-backscatter lidar returns is tackled by means of an extended Kalman filter (EKF), which overcomes these limitations. Thus, as long as different return signals income,the filter updates itself weighted by the unbalance between the a priori estimates of the optical parameters and the new ones based on a minimum variance criterion. Calibration errors or initialization uncertainties can be assimilated also. The study begins with the formulation of the inversion problem and an appropriate stochastic model. Based on extensive simulation and realistic conditions, it is shown that the EKF approach enables to retrieve the sought-after optical parameters as time-range-dependent functions and hence, to track the atmospheric evolution, its performance being only limited by the quality and availability of the 'a priori' information and the accuracy of the atmospheric model assumed. The study ends with an encouraging practical inversion of a live-scene measured with the Nd:YAG elastic-backscatter lidar station at our premises in Barcelona.

Optimization of contrast resolution by genetic algorithm in ultrasound tissue harmonic imaging.

PubMed

Ménigot, Sébastien; Girault, Jean-Marc

2016-09-01

The development of ultrasound imaging techniques such as pulse inversion has improved tissue harmonic imaging. Nevertheless, no recommendation has been made to date for the design of the waveform transmitted through the medium being explored. Our aim was therefore to find automatically the optimal "imaging" wave which maximized the contrast resolution without a priori information. To overcome assumption regarding the waveform, a genetic algorithm investigated the medium thanks to the transmission of stochastic "explorer" waves. Moreover, these stochastic signals could be constrained by the type of generator available (bipolar or arbitrary). To implement it, we changed the current pulse inversion imaging system by including feedback. Thus the method optimized the contrast resolution by adaptively selecting the samples of the excitation. In simulation, we benchmarked the contrast effectiveness of the best found transmitted stochastic commands and the usual fixed-frequency command. The optimization method converged quickly after around 300 iterations in the same optimal area. These results were confirmed experimentally. In the experimental case, the contrast resolution measured on a radiofrequency line could be improved by 6% with a bipolar generator and it could still increase by 15% with an arbitrary waveform generator. Copyright © 2016 Elsevier B.V. All rights reserved.

Solution of the finite Milne problem in stochastic media with RVT Technique

NASA Astrophysics Data System (ADS)

Slama, Howida; El-Bedwhey, Nabila A.; El-Depsy, Alia; Selim, Mustafa M.

2017-12-01

This paper presents the solution to the Milne problem in the steady state with isotropic scattering phase function. The properties of the medium are considered as stochastic ones with Gaussian or exponential distributions and hence the problem treated as a stochastic integro-differential equation. To get an explicit form for the radiant energy density, the linear extrapolation distance, reflectivity and transmissivity in the deterministic case the problem is solved using the Pomraning-Eddington method. The obtained solution is found to be dependent on the optical space variable and thickness of the medium which are considered as random variables. The random variable transformation (RVT) technique is used to find the first probability density function (1-PDF) of the solution process. Then the stochastic linear extrapolation distance, reflectivity and transmissivity are calculated. For illustration, numerical results with conclusions are provided.

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

Foxall, W; Cunningham, C; Mellors, R

Many clandestine development and production activities can be conducted underground to evade surveillance. The purpose of the study reported here was to develop a technique to detect underground facilities by broad-area search and then to characterize the facilities by inversion of the collected data. This would enable constraints to be placed on the types of activities that would be feasible at each underground site, providing a basis the design of targeted surveillance and analysis for more complete characterization. Excavation of underground cavities causes deformation in the host material and overburden that produces displacements at the ground surface. Such displacements aremore » often measurable by a variety of surveying or geodetic techniques. One measurement technique, Interferometric Synthetic Aperture Radar (InSAR), uses data from satellite-borne (or airborne) synthetic aperture radars (SARs) and so is ideal for detecting and measuring surface displacements in denied access regions. Depending on the radar frequency and the acquisition mode and the surface conditions, displacement maps derived from SAR interferograms can provide millimeter- to centimeter-level measurement accuracy on regional and local scales at spatial resolution of {approx}1-10 m. Relatively low-resolution ({approx}20 m, say) maps covering large regions can be used for broad-area detection, while finer resolutions ({approx}1 m) can be used to image details of displacement fields over targeted small areas. Surface displacements are generally expected to be largest during or a relatively short time after active excavation, but, depending on the material properties, measurable displacement may continue at a decreasing rate for a considerable time after completion. For a given excavated volume in a given geological setting, the amplitude of the surface displacements decreases as the depth of excavation increases, while the area of the discernable displacement pattern increases. Therefore, the ability to detect evidence for an underground facility using InSAR depends on the displacement sensitivity and spatial resolution of the interferogram, as well as on the size and depth of the facility and the time since its completion. The methodology development described in this report focuses on the exploitation of synthetic aperture radar data that are available commercially from a number of satellite missions. Development of the method involves three components: (1) Evaluation of the capability of InSAR to detect and characterize underground facilities ; (2) inversion of InSAR data to infer the location, depth, shape and volume of a subsurface facility; and (3) evaluation and selection of suitable geomechanical forward models to use in the inversion. We adapted LLNL's general-purpose Bayesian Markov Chain-Monte Carlo procedure, the 'Stochastic Engine' (SE), to carry out inversions to characterize subsurface void geometries. The SE performs forward simulations for a large number of trial source models to identify the set of models that are consistent with the observations and prior constraints. The inverse solution produced by this kind of stochastic method is a posterior probability density function (pdf) over alternative models, which forms an appropriate input to risk-based decision analyses to evaluate subsequent response strategies. One major advantage of a stochastic inversion approach is its ability to deal with complex, non-linear forward models employing empirical, analytical or numerical methods. However, while a geomechanical model must incorporate adequate physics to enable sufficiently accurate prediction of surface displacements, it must also be computationally fast enough to render the large number of forward realizations needed in stochastic inversion feasible. This latter requirement prompted us first to investigate computationally efficient empirical relations and closed-form analytical solutions. However, our evaluation revealed severe limitations in the ability of existing empirical and analytical forms to predict deformations from underground cavities with an accuracy consistent with the potential resolution and precision of InSAR data. We followed two approaches to overcoming these limitations. The first was to develop a new analytical solution for a 3D cavity excavated in an elastic half-space. The second was to adapt a fast parallelized finite element method to the SE and evaluate the feasibility of using in the stochastic inversion. To date we have demonstrated the ability of InSAR to detect underground facilities and measure the associated surface displacements by mapping surface deformations that track the excavation of the Los Angeles Metro system. The Stochastic Engine implementation has been completed and undergone functional testing.« less

Using Stochastic Approximation Techniques to Efficiently Construct Confidence Intervals for Heritability.

PubMed

Schweiger, Regev; Fisher, Eyal; Rahmani, Elior; Shenhav, Liat; Rosset, Saharon; Halperin, Eran

2018-06-22

Estimation of heritability is an important task in genetics. The use of linear mixed models (LMMs) to determine narrow-sense single-nucleotide polymorphism (SNP)-heritability and related quantities has received much recent attention, due of its ability to account for variants with small effect sizes. Typically, heritability estimation under LMMs uses the restricted maximum likelihood (REML) approach. The common way to report the uncertainty in REML estimation uses standard errors (SEs), which rely on asymptotic properties. However, these assumptions are often violated because of the bounded parameter space, statistical dependencies, and limited sample size, leading to biased estimates and inflated or deflated confidence intervals (CIs). In addition, for larger data sets (e.g., tens of thousands of individuals), the construction of SEs itself may require considerable time, as it requires expensive matrix inversions and multiplications. Here, we present FIESTA (Fast confidence IntErvals using STochastic Approximation), a method for constructing accurate CIs. FIESTA is based on parametric bootstrap sampling, and, therefore, avoids unjustified assumptions on the distribution of the heritability estimator. FIESTA uses stochastic approximation techniques, which accelerate the construction of CIs by several orders of magnitude, compared with previous approaches as well as to the analytical approximation used by SEs. FIESTA builds accurate CIs rapidly, for example, requiring only several seconds for data sets of tens of thousands of individuals, making FIESTA a very fast solution to the problem of building accurate CIs for heritability for all data set sizes.

Methods for High-Order Multi-Scale and Stochastic Problems Analysis, Algorithms, and Applications

DTIC Science & Technology

2016-10-17

finite volume schemes, discontinuous Galerkin finite element method, and related methods, for solving computational fluid dynamics (CFD) problems and...approximation for finite element methods. (3) The development of methods of simulation and analysis for the study of large scale stochastic systems of...laws, finite element method, Bernstein-Bezier finite elements , weakly interacting particle systems, accelerated Monte Carlo, stochastic networks 16

Reconstruction From Multiple Particles for 3D Isotropic Resolution in Fluorescence Microscopy.

PubMed

Fortun, Denis; Guichard, Paul; Hamel, Virginie; Sorzano, Carlos Oscar S; Banterle, Niccolo; Gonczy, Pierre; Unser, Michael

2018-05-01

The imaging of proteins within macromolecular complexes has been limited by the low axial resolution of optical microscopes. To overcome this problem, we propose a novel computational reconstruction method that yields isotropic resolution in fluorescence imaging. The guiding principle is to reconstruct a single volume from the observations of multiple rotated particles. Our new operational framework detects particles, estimates their orientation, and reconstructs the final volume. The main challenge comes from the absence of initial template and a priori knowledge about the orientations. We formulate the estimation as a blind inverse problem, and propose a block-coordinate stochastic approach to solve the associated non-convex optimization problem. The reconstruction is performed jointly in multiple channels. We demonstrate that our method is able to reconstruct volumes with 3D isotropic resolution on simulated data. We also perform isotropic reconstructions from real experimental data of doubly labeled purified human centrioles. Our approach revealed the precise localization of the centriolar protein Cep63 around the centriole microtubule barrel. Overall, our method offers new perspectives for applications in biology that require the isotropic mapping of proteins within macromolecular assemblies.

A Monte Carlo simulation based inverse propagation method for stochastic model updating

NASA Astrophysics Data System (ADS)

Bao, Nuo; Wang, Chunjie

2015-08-01

This paper presents an efficient stochastic model updating method based on statistical theory. Significant parameters have been selected implementing the F-test evaluation and design of experiments, and then the incomplete fourth-order polynomial response surface model (RSM) has been developed. Exploiting of the RSM combined with Monte Carlo simulation (MCS), reduces the calculation amount and the rapid random sampling becomes possible. The inverse uncertainty propagation is given by the equally weighted sum of mean and covariance matrix objective functions. The mean and covariance of parameters are estimated synchronously by minimizing the weighted objective function through hybrid of particle-swarm and Nelder-Mead simplex optimization method, thus the better correlation between simulation and test is achieved. Numerical examples of a three degree-of-freedom mass-spring system under different conditions and GARTEUR assembly structure validated the feasibility and effectiveness of the proposed method.

Simultaneous stochastic inversion for geomagnetic main field and secular variation. II - 1820-1980

NASA Technical Reports Server (NTRS)

Bloxham, Jeremy; Jackson, Andrew

1989-01-01

With the aim of producing readable time-dependent maps of the geomagnetic field at the core-mantle boundary, the method of simultaneous stochastic inversion for the geomagnetic main field and secular variation, described by Bloxham (1987), was applied to survey data from the period 1820-1980 to yield two time-dependent geomagnetic-field models, one for the period 1900-1980 and the other for 1820-1900. Particular consideration was given to the effect of crustal fields on observations. It was found that the existing methods of accounting for these fields as sources of random noise are inadequate in two circumstances: (1) when sequences of measurements are made at one particular site, and (2) for measurements made at satellite altitude. The present model shows many of the features in the earth's magnetic field at the core-mantle boundary described by Bloxham and Gubbins (1985) and supports many of their earlier conclusions.

Discreteness-induced concentration inversion in mesoscopic chemical systems.

PubMed

Ramaswamy, Rajesh; González-Segredo, Nélido; Sbalzarini, Ivo F; Grima, Ramon

2012-04-10

Molecular discreteness is apparent in small-volume chemical systems, such as biological cells, leading to stochastic kinetics. Here we present a theoretical framework to understand the effects of discreteness on the steady state of a monostable chemical reaction network. We consider independent realizations of the same chemical system in compartments of different volumes. Rate equations ignore molecular discreteness and predict the same average steady-state concentrations in all compartments. However, our theory predicts that the average steady state of the system varies with volume: if a species is more abundant than another for large volumes, then the reverse occurs for volumes below a critical value, leading to a concentration inversion effect. The addition of extrinsic noise increases the size of the critical volume. We theoretically predict the critical volumes and verify, by exact stochastic simulations, that rate equations are qualitatively incorrect in sub-critical volumes.

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.

Essays on variational approximation techniques for stochastic optimization problems

NASA Astrophysics Data System (ADS)

Deride Silva, Julio A.

This dissertation presents five essays on approximation and modeling techniques, based on variational analysis, applied to stochastic optimization problems. It is divided into two parts, where the first is devoted to equilibrium problems and maxinf optimization, and the second corresponds to two essays in statistics and uncertainty modeling. Stochastic optimization lies at the core of this research as we were interested in relevant equilibrium applications that contain an uncertain component, and the design of a solution strategy. In addition, every stochastic optimization problem relies heavily on the underlying probability distribution that models the uncertainty. We studied these distributions, in particular, their design process and theoretical properties such as their convergence. Finally, the last aspect of stochastic optimization that we covered is the scenario creation problem, in which we described a procedure based on a probabilistic model to create scenarios for the applied problem of power estimation of renewable energies. In the first part, Equilibrium problems and maxinf optimization, we considered three Walrasian equilibrium problems: from economics, we studied a stochastic general equilibrium problem in a pure exchange economy, described in Chapter 3, and a stochastic general equilibrium with financial contracts, in Chapter 4; finally from engineering, we studied an infrastructure planning problem in Chapter 5. We stated these problems as belonging to the maxinf optimization class and, in each instance, we provided an approximation scheme based on the notion of lopsided convergence and non-concave duality. This strategy is the foundation of the augmented Walrasian algorithm, whose convergence is guaranteed by lopsided convergence, that was implemented computationally, obtaining numerical results for relevant examples. The second part, Essays about statistics and uncertainty modeling, contains two essays covering a convergence problem for a sequence of estimators, and a problem for creating probabilistic scenarios on renewable energies estimation. In Chapter 7 we re-visited one of the "folk theorems" in statistics, where a family of Bayes estimators under 0-1 loss functions is claimed to converge to the maximum a posteriori estimator. This assertion is studied under the scope of the hypo-convergence theory, and the density functions are included in the class of upper semicontinuous functions. We conclude this chapter with an example in which the convergence does not hold true, and we provided sufficient conditions that guarantee convergence. The last chapter, Chapter 8, addresses the important topic of creating probabilistic scenarios for solar power generation. Scenarios are a fundamental input for the stochastic optimization problem of energy dispatch, especially when incorporating renewables. We proposed a model designed to capture the constraints induced by physical characteristics of the variables based on the application of an epi-spline density estimation along with a copula estimation, in order to account for partial correlations between variables.

Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

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

Chen, Yi; Jakeman, John; Gittelson, Claude

2015-01-08

In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. Furthermore, the local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained frommore » the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In our paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.« less

Stochastic approach for radionuclides quantification

NASA Astrophysics Data System (ADS)

Clement, A.; Saurel, N.; Perrin, G.

2018-01-01

Gamma spectrometry is a passive non-destructive assay used to quantify radionuclides present in more or less complex objects. Basic methods using empirical calibration with a standard in order to quantify the activity of nuclear materials by determining the calibration coefficient are useless on non-reproducible, complex and single nuclear objects such as waste packages. Package specifications as composition or geometry change from one package to another and involve a high variability of objects. Current quantification process uses numerical modelling of the measured scene with few available data such as geometry or composition. These data are density, material, screen, geometric shape, matrix composition, matrix and source distribution. Some of them are strongly dependent on package data knowledge and operator backgrounds. The French Commissariat à l'Energie Atomique (CEA) is developing a new methodology to quantify nuclear materials in waste packages and waste drums without operator adjustment and internal package configuration knowledge. This method suggests combining a global stochastic approach which uses, among others, surrogate models available to simulate the gamma attenuation behaviour, a Bayesian approach which considers conditional probability densities of problem inputs, and Markov Chains Monte Carlo algorithms (MCMC) which solve inverse problems, with gamma ray emission radionuclide spectrum, and outside dimensions of interest objects. The methodology is testing to quantify actinide activity in different kind of matrix, composition, and configuration of sources standard in terms of actinide masses, locations and distributions. Activity uncertainties are taken into account by this adjustment methodology.

Regional source identification using Lagrangian stochastic particle dispersion and HYSPLIT backward-trajectory models.

PubMed

Koracin, Darko; Vellore, Ramesh; Lowenthal, Douglas H; Watson, John G; Koracin, Julide; McCord, Travis; DuBois, David W; Chen, L W Antony; Kumar, Naresh; Knipping, Eladio M; Wheeler, Neil J M; Craig, Kenneth; Reid, Stephen

2011-06-01

The main objective of this study was to investigate the capabilities of the receptor-oriented inverse mode Lagrangian Stochastic Particle Dispersion Model (LSPDM) with the 12-km resolution Mesoscale Model 5 (MM5) wind field input for the assessment of source identification from seven regions impacting two receptors located in the eastern United States. The LSPDM analysis was compared with a standard version of the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) single-particle backward-trajectory analysis using inputs from MM5 and the Eta Data Assimilation System (EDAS) with horizontal grid resolutions of 12 and 80 km, respectively. The analysis included four 7-day summertime events in 2002; residence times in the modeling domain were computed from the inverse LSPDM runs and HYPSLIT-simulated backward trajectories started from receptor-source heights of 100, 500, 1000, 1500, and 3000 m. Statistics were derived using normalized values of LSPDM- and HYSPLIT-predicted residence times versus Community Multiscale Air Quality model-predicted sulfate concentrations used as baseline information. From 40 cases considered, the LSPDM identified first- and second-ranked emission region influences in 37 cases, whereas HYSPLIT-MM5 (HYSPLIT-EDAS) identified the sources in 21 (16) cases. The LSPDM produced a higher overall correlation coefficient (0.89) compared with HYSPLIT (0.55-0.62). The improvement of using the LSPDM is also seen in the overall normalized root mean square error values of 0.17 for LSPDM compared with 0.30-0.32 for HYSPLIT. The HYSPLIT backward trajectories generally tend to underestimate near-receptor sources because of a lack of stochastic dispersion of the backward trajectories and to overestimate distant sources because of a lack of treatment of dispersion. Additionally, the HYSPLIT backward trajectories showed a lack of consistency in the results obtained from different single vertical levels for starting the backward trajectories. To alleviate problems due to selection of a backward-trajectory starting level within a large complex set of 3-dimensional winds, turbulence, and dispersion, results were averaged from all heights, which yielded uniform improvement against all individual cases.

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports.

PubMed

Schilde, M; Doerner, K F; Hartl, R F

2011-12-01

The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15%. Moreover, improvements of up to 41% can be achieved for some test instances.

Inverse Modeling of Hydrologic Parameters Using Surface Flux and Runoff Observations in the Community Land Model

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

Sun, Yu; Hou, Zhangshuan; Huang, Maoyi

2013-12-10

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Two inversion strategies, the deterministic least-square fitting and stochastic Markov-Chain Monte-Carlo (MCMC) - Bayesian inversion approaches, are evaluated by applying them to CLM4 at selected sites. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find thatmore » using model parameters calibrated by the least-square fitting provides little improvements in the model simulations but the sampling-based stochastic inversion approaches are consistent - as more information comes in, the predictive intervals of the calibrated parameters become narrower and the misfits between the calculated and observed responses decrease. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to the different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.« less

Structural factoring approach for analyzing stochastic networks

NASA Technical Reports Server (NTRS)

Hayhurst, Kelly J.; Shier, Douglas R.

1991-01-01

The problem of finding the distribution of the shortest path length through a stochastic network is investigated. A general algorithm for determining the exact distribution of the shortest path length is developed based on the concept of conditional factoring, in which a directed, stochastic network is decomposed into an equivalent set of smaller, generally less complex subnetworks. Several network constructs are identified and exploited to reduce significantly the computational effort required to solve a network problem relative to complete enumeration. This algorithm can be applied to two important classes of stochastic path problems: determining the critical path distribution for acyclic networks and the exact two-terminal reliability for probabilistic networks. Computational experience with the algorithm was encouraging and allowed the exact solution of networks that have been previously analyzed only by approximation techniques.

Initialization and Restart in Stochastic Local Search: Computing a Most Probable Explanation in Bayesian Networks

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.; Wilkins, David C.; Roth, Dan

2010-01-01

For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary topologies. We also give a novel formalization of stochastic local search, with focus on initialization and restart, using probability theory and mixture models. Experimentally, we apply our methods to the problem of MPE computation, using a stochastic local search algorithm known as Stochastic Greedy Search. By carefully optimizing both initialization and restart, we reduce the MPE search time for application BNs by several orders of magnitude compared to using uniform at random initialization without restart. On several BNs from applications, the performance of Stochastic Greedy Search is competitive with clique tree clustering, a state-of-the-art exact algorithm used for MPE computation in BNs.

Stochastic density waves of granular flows: strong-intermittent dissipation fields with self-organization

NASA Astrophysics Data System (ADS)

Bershadskii, A.

1994-10-01

The quantitative (scaling) results of a recent lattice-gas simulation of granular flows [1] are interpreted in terms of Kolmogorov-Obukhov approach revised for strong space-intermittent systems. Renormalised power spectrum with exponent '-4/3' seems to be an universal spectrum of scalar fluctuations convected by stochastic velocity fields in dissipative systems with inverse energy transfer (some other laboratory and geophysic turbulent flows with this power spectrum as well as an analogy between this phenomenon and turbulent percolation on elastic backbone are pointed out).

Stochastic ontogenetic growth model

NASA Astrophysics Data System (ADS)

West, B. J.; West, D.

2012-02-01

An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.

Delay-distribution-dependent H∞ state estimation for delayed neural networks with (x,v)-dependent noises and fading channels.

PubMed

Sheng, Li; Wang, Zidong; Tian, Engang; Alsaadi, Fuad E

2016-12-01

This paper deals with the H ∞ state estimation problem for a class of discrete-time neural networks with stochastic delays subject to state- and disturbance-dependent noises (also called (x,v)-dependent noises) and fading channels. The time-varying stochastic delay takes values on certain intervals with known probability distributions. The system measurement is transmitted through fading channels described by the Rice fading model. The aim of the addressed problem is to design a state estimator such that the estimation performance is guaranteed in the mean-square sense against admissible stochastic time-delays, stochastic noises as well as stochastic fading signals. By employing the stochastic analysis approach combined with the Kronecker product, several delay-distribution-dependent conditions are derived to ensure that the error dynamics of the neuron states is stochastically stable with prescribed H ∞ performance. Finally, a numerical example is provided to illustrate the effectiveness of the obtained results. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

Deriving Link Travel-Time Distributions via Stochastic Speed Processes

DTIC Science & Technology

2004-02-01

general, an exact expression for the inverse transform is available when Equation (9) is a vector of rational functions in both of the complex variables...Otherwise, recovery of the original function is accom- plished through the inverse transform f t= 1 2(j ∫ c+j c−j estf ∗s ds (13) which is usually...given by f x t = f ∗s1 s2 = ∫ 0 ∫ 0 e−s1x+s2tf x t dx dt (14) with inverse transform f x t = 1 4(2 ∫ c1+j c1−j ∫ c2+j c2−j e

Bayesian probabilistic approach for inverse source determination from limited and noisy chemical or biological sensor concentration measurements

NASA Astrophysics Data System (ADS)

Yee, Eugene

2007-04-01

Although a great deal of research effort has been focused on the forward prediction of the dispersion of contaminants (e.g., chemical and biological warfare agents) released into the turbulent atmosphere, much less work has been directed toward the inverse prediction of agent source location and strength from the measured concentration, even though the importance of this problem for a number of practical applications is obvious. In general, the inverse problem of source reconstruction is ill-posed and unsolvable without additional information. It is demonstrated that a Bayesian probabilistic inferential framework provides a natural and logically consistent method for source reconstruction from a limited number of noisy concentration data. In particular, the Bayesian approach permits one to incorporate prior knowledge about the source as well as additional information regarding both model and data errors. The latter enables a rigorous determination of the uncertainty in the inference of the source parameters (e.g., spatial location, emission rate, release time, etc.), hence extending the potential of the methodology as a tool for quantitative source reconstruction. A model (or, source-receptor relationship) that relates the source distribution to the concentration data measured by a number of sensors is formulated, and Bayesian probability theory is used to derive the posterior probability density function of the source parameters. A computationally efficient methodology for determination of the likelihood function for the problem, based on an adjoint representation of the source-receptor relationship, is described. Furthermore, we describe the application of efficient stochastic algorithms based on Markov chain Monte Carlo (MCMC) for sampling from the posterior distribution of the source parameters, the latter of which is required to undertake the Bayesian computation. The Bayesian inferential methodology for source reconstruction is validated against real dispersion data for two cases involving contaminant dispersion in highly disturbed flows over urban and complex environments where the idealizations of horizontal homogeneity and/or temporal stationarity in the flow cannot be applied to simplify the problem. Furthermore, the methodology is applied to the case of reconstruction of multiple sources.

Continuous-Time Public Good Contribution Under Uncertainty: A Stochastic Control Approach

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

Ferrari, Giorgio, E-mail: giorgio.ferrari@uni-bielefeld.de; Riedel, Frank, E-mail: frank.riedel@uni-bielefeld.de; Steg, Jan-Henrik, E-mail: jsteg@uni-bielefeld.de

In this paper we study continuous-time stochastic control problems with both monotone and classical controls motivated by the so-called public good contribution problem. That is the problem of n economic agents aiming to maximize their expected utility allocating initial wealth over a given time period between private consumption and irreversible contributions to increase the level of some public good. We investigate the corresponding social planner problem and the case of strategic interaction between the agents, i.e. the public good contribution game. We show existence and uniqueness of the social planner’s optimal policy, we characterize it by necessary and sufficient stochasticmore » Kuhn–Tucker conditions and we provide its expression in terms of the unique optional solution of a stochastic backward equation. Similar stochastic first order conditions prove to be very useful for studying any Nash equilibria of the public good contribution game. In the symmetric case they allow us to prove (qualitative) uniqueness of the Nash equilibrium, which we again construct as the unique optional solution of a stochastic backward equation. We finally also provide a detailed analysis of the so-called free rider effect.« less

Towards a new technique to construct a 3D shear-wave velocity model based on converted waves

NASA Astrophysics Data System (ADS)

Hetényi, G.; Colavitti, L.

2017-12-01

A 3D model is essential in all branches of solid Earth sciences because geological structures can be heterogeneous and change significantly in their lateral dimension. The main target of this research is to build a crustal S-wave velocity structure in 3D. The currently popular methodologies to construct 3D shear-wave velocity models are Ambient Noise Tomography (ANT) and Local Earthquake Tomography (LET). Here we propose a new technique to map Earth discontinuities and velocities at depth based on the analysis of receiver functions. The 3D model is obtained by simultaneously inverting P-to-S converted waveforms recorded at a dense array. The individual velocity models corresponding to each trace are extracted from the 3D initial model along ray paths that are calculated using the shooting method, and the velocity model is updated during the inversion. We consider a spherical approximation of ray propagation using a global velocity model (iasp91, Kennett and Engdahl, 1991) for the teleseismic part, while we adopt Cartesian coordinates and a local velocity model for the crust. During the inversion process we work with a multi-layer crustal model for shear-wave velocity, with a flexible mesh for the depth of the interfaces. The RFs inversion represents a complex problem because the amplitude and the arrival time of different phases depend in a non-linear way on the depth of interfaces and the characteristics of the velocity structure. The solution we envisage to manage the inversion problem is the stochastic Neighbourhood Algorithm (NA, Sambridge, 1999), whose goal is to find an ensemble of models that sample the good data-fitting regions of a multidimensional parameter space. Depending on the studied area, this method can accommodate possible independent and complementary geophysical data (gravity, active seismics, LET, ANT, etc.), helping to reduce the non-linearity of the inversion. Our first focus of application is the Central Alps, where a 20-year long dataset of high-quality teleseismic events recorded at 81 stations is available, and we have high-resolution P-wave velocity model available (Diehl et al., 2009). We plan to extend the 3D shear-wave velocity inversion method to the entire Alpine domain in frame of the AlpArray project, and apply it to other areas with a dense network of broadband seismometers.

A New Methodology for Open Pit Slope Design in Karst-Prone Ground Conditions Based on Integrated Stochastic-Limit Equilibrium Analysis

NASA Astrophysics Data System (ADS)

Zhang, Ke; Cao, Ping; Ma, Guowei; Fan, Wenchen; Meng, Jingjing; Li, Kaihui

2016-07-01

Using the Chengmenshan Copper Mine as a case study, a new methodology for open pit slope design in karst-prone ground conditions is presented based on integrated stochastic-limit equilibrium analysis. The numerical modeling and optimization design procedure contain a collection of drill core data, karst cave stochastic model generation, SLIDE simulation and bisection method optimization. Borehole investigations are performed, and the statistical result shows that the length of the karst cave fits a negative exponential distribution model, but the length of carbonatite does not exactly follow any standard distribution. The inverse transform method and acceptance-rejection method are used to reproduce the length of the karst cave and carbonatite, respectively. A code for karst cave stochastic model generation, named KCSMG, is developed. The stability of the rock slope with the karst cave stochastic model is analyzed by combining the KCSMG code and the SLIDE program. This approach is then applied to study the effect of the karst cave on the stability of the open pit slope, and a procedure to optimize the open pit slope angle is presented.

On stochastic control and optimal measurement strategies. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kramer, L. C.

1971-01-01

The control of stochastic dynamic systems is studied with particular emphasis on those which influence the quality or nature of the measurements which are made to effect control. Four main areas are discussed: (1) the meaning of stochastic optimality and the means by which dynamic programming may be applied to solve a combined control/measurement problem; (2) a technique by which it is possible to apply deterministic methods, specifically the minimum principle, to the study of stochastic problems; (3) the methods described are applied to linear systems with Gaussian disturbances to study the structure of the resulting control system; and (4) several applications are considered.

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

NASA Technical Reports Server (NTRS)

Aguilo, Miguel A.; Warner, James E.

2017-01-01

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

A stochastic maximum principle for backward control systems with random default time

NASA Astrophysics Data System (ADS)

Shen, Yang; Kuen Siu, Tak

2013-05-01

This paper establishes a necessary and sufficient stochastic maximum principle for backward systems, where the state processes are governed by jump-diffusion backward stochastic differential equations with random default time. An application of the sufficient stochastic maximum principle to an optimal investment and capital injection problem in the presence of default risk is discussed.

Stochastic parameter estimation in nonlinear time-delayed vibratory systems with distributed delay

NASA Astrophysics Data System (ADS)

Torkamani, Shahab; Butcher, Eric A.

2013-07-01

The stochastic estimation of parameters and states in linear and nonlinear time-delayed vibratory systems with distributed delay is explored. The approach consists of first employing a continuous time approximation to approximate the delayed integro-differential system with a large set of ordinary differential equations having stochastic excitations. Then the problem of state and parameter estimation in the resulting stochastic ordinary differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the augmented filtering problem, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states. Similarly, the upper bound of the distributed delay can also be estimated by the proposed technique. As an illustrative example to a practical problem in vibrations, the parameter, delay upper bound, and state estimation from noise-corrupted measurements in a distributed force model widely used for modeling machine tool vibrations in the turning operation is investigated.

Stochastic Modeling of Sediment Connectivity for Reconstructing Sand Fluxes and Origins in the Unmonitored Se Kong, Se San, and Sre Pok Tributaries of the Mekong River

NASA Astrophysics Data System (ADS)

Schmitt, R. J. P.; Bizzi, S.; Castelletti, A. F.; Kondolf, G. M.

2018-01-01

Sediment supply to rivers, subsequent fluvial transport, and the resulting sediment connectivity on network scales are often sparsely monitored and subject to major uncertainty. We propose to approach that uncertainty by adopting a stochastic method for modeling network sediment connectivity, which we present for the Se Kong, Se San, and Sre Pok (3S) tributaries of the Mekong. We quantify how unknown properties of sand sources translate into uncertainty regarding network connectivity by running the CASCADE (CAtchment Sediment Connectivity And DElivery) modeling framework in a Monte Carlo approach for 7,500 random realizations. Only a small ensemble of realizations reproduces downstream observations of sand transport. This ensemble presents an inverse stochastic approximation of the magnitude and variability of transport capacity, sediment flux, and grain size distribution of the sediment transported in the network (i.e., upscaling point observations to the entire network). The approximated magnitude of sand delivered from each tributary to the Mekong is controlled by reaches of low transport capacity ("bottlenecks"). These bottlenecks limit the ability to predict transport in the upper parts of the catchment through inverse stochastic approximation, a limitation that could be addressed by targeted monitoring upstream of identified bottlenecks. Nonetheless, bottlenecks also allow a clear partitioning of natural sand deliveries from the 3S to the Mekong, with the Se Kong delivering less (1.9 Mt/yr) and coarser (median grain size: 0.4 mm) sand than the Se San (5.3 Mt/yr, 0.22 mm) and Sre Pok (11 Mt/yr, 0.19 mm).

Adaptive optimal stochastic state feedback control of resistive wall modes in tokamaks

NASA Astrophysics Data System (ADS)

Sun, Z.; Sen, A. K.; Longman, R. W.

2006-01-01

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least-square method with exponential forgetting factor and covariance resetting is used to identify (experimentally determine) the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time-dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used.

Adaptive Optimal Stochastic State Feedback Control of Resistive Wall Modes in Tokamaks

NASA Astrophysics Data System (ADS)

Sun, Z.; Sen, A. K.; Longman, R. W.

2007-06-01

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended least square method with exponential forgetting factor and covariance resetting is used to identify the time-varying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the time dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly four times the inverse of the growth rate for the time-invariant model used.

Stochastic kinetic mean field model

NASA Astrophysics Data System (ADS)

Erdélyi, Zoltán; Pasichnyy, Mykola; Bezpalchuk, Volodymyr; Tomán, János J.; Gajdics, Bence; Gusak, Andriy M.

2016-07-01

This paper introduces a new model for calculating the change in time of three-dimensional atomic configurations. The model is based on the kinetic mean field (KMF) approach, however we have transformed that model into a stochastic approach by introducing dynamic Langevin noise. The result is a stochastic kinetic mean field model (SKMF) which produces results similar to the lattice kinetic Monte Carlo (KMC). SKMF is, however, far more cost-effective and easier to implement the algorithm (open source program code is provided on http://skmf.eu website). We will show that the result of one SKMF run may correspond to the average of several KMC runs. The number of KMC runs is inversely proportional to the amplitude square of the noise in SKMF. This makes SKMF an ideal tool also for statistical purposes.

Compensating for estimation smoothing in kriging

USGS Publications Warehouse

Olea, R.A.; Pawlowsky, Vera

1996-01-01

Smoothing is a characteristic inherent to all minimum mean-square-error spatial estimators such as kriging. Cross-validation can be used to detect and model such smoothing. Inversion of the model produces a new estimator-compensated kriging. A numerical comparison based on an exhaustive permeability sampling of a 4-fr2 slab of Berea Sandstone shows that the estimation surface generated by compensated kriging has properties intermediate between those generated by ordinary kriging and stochastic realizations resulting from simulated annealing and sequential Gaussian simulation. The frequency distribution is well reproduced by the compensated kriging surface, which also approximates the experimental semivariogram well - better than ordinary kriging, but not as well as stochastic realizations. Compensated kriging produces surfaces that are more accurate than stochastic realizations, but not as accurate as ordinary kriging. ?? 1996 International Association for Mathematical Geology.

A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing.

PubMed

Wang, Lipo; Li, Sa; Tian, Fuyu; Fu, Xiuju

2004-10-01

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.

Selected inversion as key to a stable Langevin evolution across the QCD phase boundary

NASA Astrophysics Data System (ADS)

Bloch, Jacques; Schenk, Olaf

2018-03-01

We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the complex Langevin method was shown to break down when the inverse coupling decreases and enters the transition region from the deconfined to the confined phase. We found that the stochastic technique used to estimate the drift term can be very unstable for indefinite matrices. This may be avoided by using the full inverse of the Dirac operator, which is, however, too costly for four-dimensional lattices. The major breakthrough in this work was achieved by realizing that the inverse elements necessary for the drift term can be computed efficiently using the selected inversion technique provided by the parallel sparse direct solver package PARDISO. In our new study we show that no breakdown of the complex Langevin method is encountered and that simulations can be performed across the phase boundary.

[Study of inversion and classification of particle size distribution under dependent model algorithm].

PubMed

Sun, Xiao-Gang; Tang, Hong; Yuan, Gui-Bin

2008-05-01

For the total light scattering particle sizing technique, an inversion and classification method was proposed with the dependent model algorithm. The measured particle system was inversed simultaneously by different particle distribution functions whose mathematic model was known in advance, and then classified according to the inversion errors. The simulation experiments illustrated that it is feasible to use the inversion errors to determine the particle size distribution. The particle size distribution function was obtained accurately at only three wavelengths in the visible light range with the genetic algorithm, and the inversion results were steady and reliable, which decreased the number of multi wavelengths to the greatest extent and increased the selectivity of light source. The single peak distribution inversion error was less than 5% and the bimodal distribution inversion error was less than 10% when 5% stochastic noise was put in the transmission extinction measurement values at two wavelengths. The running time of this method was less than 2 s. The method has advantages of simplicity, rapidity, and suitability for on-line particle size measurement.

Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports

PubMed Central

Schilde, M.; Doerner, K.F.; Hartl, R.F.

2011-01-01

The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15%. Moreover, improvements of up to 41% can be achieved for some test instances. PMID:23543641

Inverse stochastic-dynamic models for high-resolution Greenland ice core records

NASA Astrophysics Data System (ADS)

Boers, Niklas; Chekroun, Mickael D.; Liu, Honghu; Kondrashov, Dmitri; Rousseau, Denis-Didier; Svensson, Anders; Bigler, Matthias; Ghil, Michael

2017-12-01

Proxy records from Greenland ice cores have been studied for several decades, yet many open questions remain regarding the climate variability encoded therein. Here, we use a Bayesian framework for inferring inverse, stochastic-dynamic models from δ18O and dust records of unprecedented, subdecadal temporal resolution. The records stem from the North Greenland Ice Core Project (NGRIP), and we focus on the time interval 59-22 ka b2k. Our model reproduces the dynamical characteristics of both the δ18O and dust proxy records, including the millennial-scale Dansgaard-Oeschger variability, as well as statistical properties such as probability density functions, waiting times and power spectra, with no need for any external forcing. The crucial ingredients for capturing these properties are (i) high-resolution training data, (ii) cubic drift terms, (iii) nonlinear coupling terms between the δ18O and dust time series, and (iv) non-Markovian contributions that represent short-term memory effects.

A single promoter inversion switches Photorhabdus between pathogenic and mutualistic states.

PubMed

Somvanshi, Vishal S; Sloup, Rudolph E; Crawford, Jason M; Martin, Alexander R; Heidt, Anthony J; Kim, Kwi-suk; Clardy, Jon; Ciche, Todd A

2012-07-06

Microbial populations stochastically generate variants with strikingly different properties, such as virulence or avirulence and antibiotic tolerance or sensitivity. Photorhabdus luminescens bacteria have a variable life history in which they alternate between pathogens to a wide variety of insects and mutualists to their specific host nematodes. Here, we show that the P. luminescens pathogenic variant (P form) switches to a smaller-cell variant (M form) to initiate mutualism in host nematode intestines. A stochastic promoter inversion causes the switch between the two distinct forms. M-form cells are much smaller (one-seventh the volume), slower growing, and less bioluminescent than P-form cells; they are also avirulent and produce fewer secondary metabolites. Observations of form switching by individual cells in nematodes revealed that the M form persisted in maternal nematode intestines, were the first cells to colonize infective juvenile (IJ) offspring, and then switched to P form in the IJ intestine, which armed these nematodes for the next cycle of insect infection.

Stochastic inversion of ocean color data using the cross-entropy method.

PubMed

Salama, Mhd Suhyb; Shen, Fang

2010-01-18

Improving the inversion of ocean color data is an ever continuing effort to increase the accuracy of derived inherent optical properties. In this paper we present a stochastic inversion algorithm to derive inherent optical properties from ocean color, ship and space borne data. The inversion algorithm is based on the cross-entropy method where sets of inherent optical properties are generated and converged to the optimal set using iterative process. The algorithm is validated against four data sets: simulated, noisy simulated in-situ measured and satellite match-up data sets. Statistical analysis of validation results is based on model-II regression using five goodness-of-fit indicators; only R2 and root mean square of error (RMSE) are mentioned hereafter. Accurate values of total absorption coefficient are derived with R2 > 0.91 and RMSE, of log transformed data, less than 0.55. Reliable values of the total backscattering coefficient are also obtained with R2 > 0.7 (after removing outliers) and RMSE < 0.37. The developed algorithm has the ability to derive reliable results from noisy data with R2 above 0.96 for the total absorption and above 0.84 for the backscattering coefficients. The algorithm is self contained and easy to implement and modify to derive the variability of chlorophyll-a absorption that may correspond to different phytoplankton species. It gives consistently accurate results and is therefore worth considering for ocean color global products.

Intrinsic optimization using stochastic nanomagnets

PubMed Central

Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo

2017-01-01

This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets. PMID:28295053

Intrinsic optimization using stochastic nanomagnets

NASA Astrophysics Data System (ADS)

Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo

2017-03-01

This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets.

Stochastic DT-MRI connectivity mapping on the GPU.

PubMed

McGraw, Tim; Nadar, Mariappan

2007-01-01

We present a method for stochastic fiber tract mapping from diffusion tensor MRI (DT-MRI) implemented on graphics hardware. From the simulated fibers we compute a connectivity map that gives an indication of the probability that two points in the dataset are connected by a neuronal fiber path. A Bayesian formulation of the fiber model is given and it is shown that the inversion method can be used to construct plausible connectivity. An implementation of this fiber model on the graphics processing unit (GPU) is presented. Since the fiber paths can be stochastically generated independently of one another, the algorithm is highly parallelizable. This allows us to exploit the data-parallel nature of the GPU fragment processors. We also present a framework for the connectivity computation on the GPU. Our implementation allows the user to interactively select regions of interest and observe the evolving connectivity results during computation. Results are presented from the stochastic generation of over 250,000 fiber steps per iteration at interactive frame rates on consumer-grade graphics hardware.

On the role of dimensionality and sample size for unstructured and structured covariance matrix estimation

NASA Technical Reports Server (NTRS)

Morgera, S. D.; Cooper, D. B.

1976-01-01

The experimental observation that a surprisingly small sample size vis-a-vis dimension is needed to achieve good signal-to-interference ratio (SIR) performance with an adaptive predetection filter is explained. The adaptive filter requires estimates as obtained by a recursive stochastic algorithm of the inverse of the filter input data covariance matrix. The SIR performance with sample size is compared for the situations where the covariance matrix estimates are of unstructured (generalized) form and of structured (finite Toeplitz) form; the latter case is consistent with weak stationarity of the input data stochastic process.

Stochastic series expansion simulation of the t -V model

NASA Astrophysics Data System (ADS)

Wang, Lei; Liu, Ye-Hua; Troyer, Matthias

2016-04-01

We present an algorithm for the efficient simulation of the half-filled spinless t -V model on bipartite lattices, which combines the stochastic series expansion method with determinantal quantum Monte Carlo techniques widely used in fermionic simulations. The algorithm scales linearly in the inverse temperature, cubically with the system size, and is free from the time-discretization error. We use it to map out the finite-temperature phase diagram of the spinless t -V model on the honeycomb lattice and observe a suppression of the critical temperature of the charge-density-wave phase in the vicinity of a fermionic quantum critical point.

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

NASA Astrophysics Data System (ADS)

Novák, Pavel; Šprlák, Michal

2018-03-01

The static Earth's gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth's surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet's boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green's kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.

The Approximate Bayesian Computation methods in the localization of the atmospheric contamination source

NASA Astrophysics Data System (ADS)

Kopka, P.; Wawrzynczak, A.; Borysiewicz, M.

2015-09-01

In many areas of application, a central problem is a solution to the inverse problem, especially estimation of the unknown model parameters to model the underlying dynamics of a physical system precisely. In this situation, the Bayesian inference is a powerful tool to combine observed data with prior knowledge to gain the probability distribution of searched parameters. We have applied the modern methodology named Sequential Approximate Bayesian Computation (S-ABC) to the problem of tracing the atmospheric contaminant source. The ABC is technique commonly used in the Bayesian analysis of complex models and dynamic system. Sequential methods can significantly increase the efficiency of the ABC. In the presented algorithm, the input data are the on-line arriving concentrations of released substance registered by distributed sensor network from OVER-LAND ATMOSPHERIC DISPERSION (OLAD) experiment. The algorithm output are the probability distributions of a contamination source parameters i.e. its particular location, release rate, speed and direction of the movement, start time and duration. The stochastic approach presented in this paper is completely general and can be used in other fields where the parameters of the model bet fitted to the observable data should be found.

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

Distributed parallel computing in stochastic modeling of groundwater systems.

PubMed

Dong, Yanhui; Li, Guomin; Xu, Haizhen

2013-03-01

Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519

Exact solution of a model DNA-inversion genetic switch with orientational control.

PubMed

Visco, Paolo; Allen, Rosalind J; Evans, Martin R

2008-09-12

DNA inversion is an important mechanism by which bacteria and bacteriophage switch reversibly between phenotypic states. In such switches, the orientation of a short DNA element is flipped by a site-specific recombinase enzyme. We propose a simple model for a DNA-inversion switch in which recombinase production is dependent on the switch state (orientational control). Our model is inspired by the fim switch in E. coli. We present an exact analytical solution of the chemical master equation for the model switch, as well as stochastic simulations. Orientational control causes the switch to deviate from Poissonian behavior: the distribution of times in the on state shows a peak and successive flip times are correlated.

Uncertainties in the 2004 Sumatra–Andaman source through nonlinear stochastic inversion of tsunami waves

PubMed Central

Venugopal, M.; Roy, D.; Rajendran, K.; Guillas, S.; Dias, F.

2017-01-01

Numerical inversions for earthquake source parameters from tsunami wave data usually incorporate subjective elements to stabilize the search. In addition, noisy and possibly insufficient data result in instability and non-uniqueness in most deterministic inversions, which are barely acknowledged. Here, we employ the satellite altimetry data for the 2004 Sumatra–Andaman tsunami event to invert the source parameters. We also include kinematic parameters that improve the description of tsunami generation and propagation, especially near the source. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a new type of nonlinear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large uncertainties in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest that objective inversion strategies should incorporate more sophisticated physical models of seabed deformation in order to significantly improve the performance of early warning systems. PMID:28989311

Uncertainties in the 2004 Sumatra-Andaman source through nonlinear stochastic inversion of tsunami waves.

PubMed

Gopinathan, D; Venugopal, M; Roy, D; Rajendran, K; Guillas, S; Dias, F

2017-09-01

Numerical inversions for earthquake source parameters from tsunami wave data usually incorporate subjective elements to stabilize the search. In addition, noisy and possibly insufficient data result in instability and non-uniqueness in most deterministic inversions, which are barely acknowledged. Here, we employ the satellite altimetry data for the 2004 Sumatra-Andaman tsunami event to invert the source parameters. We also include kinematic parameters that improve the description of tsunami generation and propagation, especially near the source. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a new type of nonlinear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large uncertainties in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest that objective inversion strategies should incorporate more sophisticated physical models of seabed deformation in order to significantly improve the performance of early warning systems.

Application of stochastic inversion in auroral tomography

NASA Astrophysics Data System (ADS)

Nygrén, T.; Markkanen, M.; Lehtinen, M.; Kaila, K.

1996-11-01

A software package originally developed for satellite radio tomography is briefly introduced and its use in two-dimensional auroral tomography is described. The method is based on stochastic inversion, i.e. finding the most probable values of the unknown volume emission rates once the optical measurements are made using either a scanning photometer or an auroral camera. A set of simulation results is shown for a different number and separations of optical instruments at ground level. It is observed that arcs with a thickness of a few kilometers and separated by a few tens of kilometers are easily reconstructed. The maximum values of the inversion results, however, are often weaker than in the model. The most obvious reason for this is the grid size, which cannot be much smaller than the arc thickness. The grid necessarily generates a spatial averaging effect broadening the arc cross-sections and reducing the peak values. Finally, results from TV-camera observations at Tromsø and Esrange are shown. Although these sites are separated by more than 200 km, arcs close to Tromsø have been successfully reconstructed. Acknowledgements. The work done by P. Henelius and E. Vilenius in programme development is gratefully acknowledged. Topical Editor D. Alcayde thanks I. Pryse and A. Vallance-Jones for their help in evaluating this paper.--> Correspondence to: T. Nygrén-->

Inverse modeling of hydrologic parameters using surface flux and runoff observations in the Community Land Model

NASA Astrophysics Data System (ADS)

Sun, Y.; Hou, Z.; Huang, M.; Tian, F.; Leung, L. Ruby

2013-12-01

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Both deterministic least-square fitting and stochastic Markov-chain Monte Carlo (MCMC)-Bayesian inversion approaches are evaluated by applying them to CLM4 at selected sites with different climate and soil conditions. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the sampling-based stochastic inversion approaches provides significant improvements in the model simulations compared to using default CLM4 parameter values, and that as more information comes in, the predictive intervals (ranges of posterior distributions) of the calibrated parameters become narrower. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.

Numerical methods for the inverse problem of density functional theory

DOE PAGES

Jensen, Daniel S.; Wasserman, Adam

2017-07-17

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Numerical methods for the inverse problem of density functional theory

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

Jensen, Daniel S.; Wasserman, Adam

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Application of an Evolution Strategy in Planetary Ephemeris Optimization

NASA Astrophysics Data System (ADS)

Mai, E.

2016-12-01

Classical planetary ephemeris construction comprises three major steps, which are performed iteratively: simultaneous numerical integration of coupled equations of motion of a multi-body system (propagator step), reduction of thousands of observations (reduction step), and optimization of various selected model parameters (adjustment step). This traditional approach is challenged by ongoing refinements in force modeling, e.g. inclusion of much more significant minor bodies, an ever-growing number of planetary observations, e.g. vast amount of spacecraft tracking data, etc. To master the high computational burden and in order to circumvent the need for inversion of huge normal equation matrices, we propose an alternative ephemeris construction method. The main idea is to solve the overall optimization problem by a straightforward direct evaluation of the whole set of mathematical formulas involved, rather than to solve it as an inverse problem with all its tacit mathematical assumptions and numerical difficulties. We replace the usual gradient search by a stochastic search, namely an evolution strategy, the latter of which is also perfect for the exploitation of parallel computing capabilities. Furthermore, this new approach enables multi-criteria optimization and time-varying optima. This issue will become important in future once ephemeris construction is just one part of even larger optimization problems, e.g. the combined and consistent determination of the physical state (orbit, size, shape, rotation, gravity,…) of celestial bodies (planets, satellites, asteroids, or comets), and if one seeks near real-time solutions. Here we outline the general idea and discuss first results. As an example, we present a simultaneous optimization of high-correlated asteroidal ring model parameters (total mass and heliocentric radius), based on simulations.

Robust Consumption-Investment Problem on Infinite Horizon

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

Zawisza, Dariusz, E-mail: dariusz.zawisza@im.uj.edu.pl

In our paper we consider an infinite horizon consumption-investment problem under a model misspecification in a general stochastic factor model. We formulate the problem as a stochastic game and finally characterize the saddle point and the value function of that game using an ODE of semilinear type, for which we provide a proof of an existence and uniqueness theorem for its solution. Such equation is interested on its own right, since it generalizes many other equations arising in various infinite horizon optimization problems.

Using Probabilistic Information in Solving Resource Allocation Problems for a Decentralized Firm

DTIC Science & Technology

1978-09-01

deterministic equivalent form of HIQ’s problem (5) by an approach similar to the one used in stochastic programming with simple recourse. See Ziemba [38) or, in...1964). 38. Ziemba , W.T., "Stochastic Programs with Simple Recourse," Technical Report 72-15, Stanford University, Department of Operations Research

General stochastic variational formulation for the oligopolistic market equilibrium problem with excesses

NASA Astrophysics Data System (ADS)

Barbagallo, Annamaria; Di Meglio, Guglielmo; Mauro, Paolo

2017-07-01

The aim of the paper is to study, in a Hilbert space setting, a general random oligopolistic market equilibrium problem in presence of both production and demand excesses and to characterize the random Cournot-Nash equilibrium principle by means of a stochastic variational inequality. Some existence results are presented.

H∞ state estimation of stochastic memristor-based neural networks with time-varying delays.

PubMed

Bao, Haibo; Cao, Jinde; Kurths, Jürgen; Alsaedi, Ahmed; Ahmad, Bashir

2018-03-01

This paper addresses the problem of H ∞ state estimation for a class of stochastic memristor-based neural networks with time-varying delays. Under the framework of Filippov solution, the stochastic memristor-based neural networks are transformed into systems with interval parameters. The present paper is the first to investigate the H ∞ state estimation problem for continuous-time Itô-type stochastic memristor-based neural networks. By means of Lyapunov functionals and some stochastic technique, sufficient conditions are derived to ensure that the estimation error system is asymptotically stable in the mean square with a prescribed H ∞ performance. An explicit expression of the state estimator gain is given in terms of linear matrix inequalities (LMIs). Compared with other results, our results reduce control gain and control cost effectively. Finally, numerical simulations are provided to demonstrate the efficiency of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

Stochastic differential equations

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

Sobczyk, K.

1990-01-01

This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshoremore » structures.« less

Emulation: A fast stochastic Bayesian method to eliminate model space

NASA Astrophysics Data System (ADS)

Roberts, Alan; Hobbs, Richard; Goldstein, Michael

2010-05-01

Joint inversion of large 3D datasets has been the goal of geophysicists ever since the datasets first started to be produced. There are two broad approaches to this kind of problem, traditional deterministic inversion schemes and more recently developed Bayesian search methods, such as MCMC (Markov Chain Monte Carlo). However, using both these kinds of schemes has proved prohibitively expensive, both in computing power and time cost, due to the normally very large model space which needs to be searched using forward model simulators which take considerable time to run. At the heart of strategies aimed at accomplishing this kind of inversion is the question of how to reliably and practicably reduce the size of the model space in which the inversion is to be carried out. Here we present a practical Bayesian method, known as emulation, which can address this issue. Emulation is a Bayesian technique used with considerable success in a number of technical fields, such as in astronomy, where the evolution of the universe has been modelled using this technique, and in the petroleum industry where history matching is carried out of hydrocarbon reservoirs. The method of emulation involves building a fast-to-compute uncertainty-calibrated approximation to a forward model simulator. We do this by modelling the output data from a number of forward simulator runs by a computationally cheap function, and then fitting the coefficients defining this function to the model parameters. By calibrating the error of the emulator output with respect to the full simulator output, we can use this to screen out large areas of model space which contain only implausible models. For example, starting with what may be considered a geologically reasonable prior model space of 10000 models, using the emulator we can quickly show that only models which lie within 10% of that model space actually produce output data which is plausibly similar in character to an observed dataset. We can thus much more tightly constrain the input model space for a deterministic inversion or MCMC method. By using this technique jointly on several datasets (specifically seismic, gravity, and magnetotelluric (MT) describing the same region), we can include in our modelling uncertainties in the data measurements, the relationships between the various physical parameters involved, as well as the model representation uncertainty, and at the same time further reduce the range of plausible models to several percent of the original model space. Being stochastic in nature, the output posterior parameter distributions also allow our understanding of/beliefs about a geological region can be objectively updated, with full assessment of uncertainties, and so the emulator is also an inversion-type tool in it's own right, with the advantage (as with any Bayesian method) that our uncertainties from all sources (both data and model) can be fully evaluated.

Energy diffusion controlled reaction rate of reacting particle driven by broad-band noise

NASA Astrophysics Data System (ADS)

Deng, M. L.; Zhu, W. Q.

2007-10-01

The energy diffusion controlled reaction rate of a reacting particle with linear weak damping and broad-band noise excitation is studied by using the stochastic averaging method. First, the stochastic averaging method for strongly nonlinear oscillators under broad-band noise excitation using generalized harmonic functions is briefly introduced. Then, the reaction rate of the classical Kramers' reacting model with linear weak damping and broad-band noise excitation is investigated by using the stochastic averaging method. The averaged Itô stochastic differential equation describing the energy diffusion and the Pontryagin equation governing the mean first-passage time (MFPT) are established. The energy diffusion controlled reaction rate is obtained as the inverse of the MFPT by solving the Pontryagin equation. The results of two special cases of broad-band noises, i.e. the harmonic noise and the exponentially corrected noise, are discussed in details. It is demonstrated that the general expression of reaction rate derived by the authors can be reduced to the classical ones via linear approximation and high potential barrier approximation. The good agreement with the results of the Monte Carlo simulation verifies that the reaction rate can be well predicted using the stochastic averaging method.

Optimal Control Inventory Stochastic With Production Deteriorating

NASA Astrophysics Data System (ADS)

Affandi, Pardi

2018-01-01

In this paper, we are using optimal control approach to determine the optimal rate in production. Most of the inventory production models deal with a single item. First build the mathematical models inventory stochastic, in this model we also assume that the items are in the same store. The mathematical model of the problem inventory can be deterministic and stochastic models. In this research will be discussed how to model the stochastic as well as how to solve the inventory model using optimal control techniques. The main tool in the study problems for the necessary optimality conditions in the form of the Pontryagin maximum principle involves the Hamilton function. So we can have the optimal production rate in a production inventory system where items are subject deterioration.

Optimal Control of Hybrid Systems in Air Traffic Applications

NASA Astrophysics Data System (ADS)

Kamgarpour, Maryam

Growing concerns over the scalability of air traffic operations, air transportation fuel emissions and prices, as well as the advent of communication and sensing technologies motivate improvements to the air traffic management system. To address such improvements, in this thesis a hybrid dynamical model as an abstraction of the air traffic system is considered. Wind and hazardous weather impacts are included using a stochastic model. This thesis focuses on the design of algorithms for verification and control of hybrid and stochastic dynamical systems and the application of these algorithms to air traffic management problems. In the deterministic setting, a numerically efficient algorithm for optimal control of hybrid systems is proposed based on extensions of classical optimal control techniques. This algorithm is applied to optimize the trajectory of an Airbus 320 aircraft in the presence of wind and storms. In the stochastic setting, the verification problem of reaching a target set while avoiding obstacles (reach-avoid) is formulated as a two-player game to account for external agents' influence on system dynamics. The solution approach is applied to air traffic conflict prediction in the presence of stochastic wind. Due to the uncertainty in forecasts of the hazardous weather, and hence the unsafe regions of airspace for aircraft flight, the reach-avoid framework is extended to account for stochastic target and safe sets. This methodology is used to maximize the probability of the safety of aircraft paths through hazardous weather. Finally, the problem of modeling and optimization of arrival air traffic and runway configuration in dense airspace subject to stochastic weather data is addressed. This problem is formulated as a hybrid optimal control problem and is solved with a hierarchical approach that decouples safety and performance. As illustrated with this problem, the large scale of air traffic operations motivates future work on the efficient implementation of the proposed algorithms.

Comparing hard and soft prior bounds in geophysical inverse problems

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describes the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect.

Comparing hard and soft prior bounds in geophysical inverse problems

NASA Technical Reports Server (NTRS)

Backus, George E.

1987-01-01

In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describeds the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect.

Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions

DTIC Science & Technology

2014-10-09

problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...linear systems with Brownian motion or a discrete time linear system with a white Gaussian noise and costs 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 stochastic optimal control, fractional Brownian motion , stochastic

Advanced Covariance-Based Stochastic Inversion and Neuro-Genetic Optimization for Rosetta CONSERT Radar Data to Improve Spatial Resolution of Multi-Fractal Depth Profiles for Cometary Nucleus

NASA Astrophysics Data System (ADS)

Edenhofer, Peter; Ulamec, Stephan

2015-04-01

The paper is devoted to results of doctoral research work at University of Bochum as applied to the radar transmission experiment CONSERT of the ESA cometary mission Rosetta. This research aims at achieving the limits of optimum spatial (and temporal) resolution for radar remote sensing by implementation of covariance informations concerned with error-balanced control as well as coherence of wave propagation effects through random composite media involved (based on Joel Franklin's approach of extended stochastic inversion). As a consequence the well-known inherent numerical instabilities of remote sensing are significantly reduced in a robust way by increasing the weight of main diagonal elements of the resulting composite matrix to be inverted with respect to off-diagonal elements following synergy relations as to the principle of correlation receiver in wireless telecommunications. It is shown that the enhancement of resolution for remote sensing holds for an integral and differential equation approach of inversion as well. In addition to that the paper presents a discussion on how the efficiency of inversion for radar data gets achieved by an overall optimization of inversion due to a novel neuro-genetic approach. Such kind of approach is in synergy with the priority research program "Organic Computing" of DFG / German Research Organization. This Neuro-Genetic Optimization (NGO) turns out, firstly, to take into account more detailed physical informations supporting further improved resolution such as the process of accretion for cometary nucleus, wave propagation effects from rough surfaces, ground clutter, nonlinear focusing, etc. as well as, secondly, to accelerate the computing process of inversion in a really significantly enhanced and fast way, e.g., enabling online-control of autonomous processes such as detection of unknown objects, navigation, etc. The paper describes in some detail how this neuro-genetic approach of optimization is incorporated into the procedure of data inversion by combining inverted artificial neural networks of adequately chosen topology and learning routines for short access times with the concept of genetic algorithms enabling to achieve a multi-dimensional global optimum subject to a properly constructed and problem-oriented target function, ensemble selection rules, etc. Finally the paper discusses how the power of realistic simulation of the structures of the interior of a cometary nucleus can be improved by applying Benoit Mandelbrot's concept of fractal structures. It is shown how the fractal volumetric modelling of the nucleus of a comet can be accomplished by finite 3D elements of flexibility (serving topography and morphology as well) such as of tetrahedron shape with specific scaling factors of self similarity and a Maxwellian type of distribution function. By applying the widely accepted fBm-concept of fractal Brownian motion basically each of the corresponding Hurst exponents 0 (rough) < H < 1 (smooth) can be derived for the multi-fractal depth (and terrain) profiles of the equivalent dielectric constant per tomographic angular orbital segment of intersection by transmissive radar ray paths with the nucleus of the comet. Cooperative efforts and work are in progress to achieve numerical results of depth profiles for the nucleus of comet 67P/Churyumov-Gerasimenko.

Final Technical Report for "Applied Mathematics Research: Simulation Based Optimization and Application to Electromagnetic Inverse Problems"

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

Haber, Eldad

2014-03-17

The focus of research was: Developing adaptive mesh for the solution of Maxwell's equations; Developing a parallel framework for time dependent inverse Maxwell's equations; Developing multilevel methods for optimization problems with inequality constraints; A new inversion code for inverse Maxwell's equations in the 0th frequency (DC resistivity); A new inversion code for inverse Maxwell's equations in low frequency regime. Although the research concentrated on electromagnetic forward and in- verse problems the results of the research was applied to the problem of image registration.

Easy way to determine quantitative spatial resolution distribution for a general inverse problem

NASA Astrophysics Data System (ADS)

An, M.; Feng, M.

2013-12-01

The spatial resolution computation of a solution was nontrivial and more difficult than solving an inverse problem. Most geophysical studies, except for tomographic studies, almost uniformly neglect the calculation of a practical spatial resolution. In seismic tomography studies, a qualitative resolution length can be indicatively given via visual inspection of the restoration of a synthetic structure (e.g., checkerboard tests). An effective strategy for obtaining quantitative resolution length is to calculate Backus-Gilbert resolution kernels (also referred to as a resolution matrix) by matrix operation. However, not all resolution matrices can provide resolution length information, and the computation of resolution matrix is often a difficult problem for very large inverse problems. A new class of resolution matrices, called the statistical resolution matrices (An, 2012, GJI), can be directly determined via a simple one-parameter nonlinear inversion performed based on limited pairs of random synthetic models and their inverse solutions. The total procedure were restricted to forward/inversion processes used in the real inverse problem and were independent of the degree of inverse skill used in the solution inversion. Spatial resolution lengths can be directly given during the inversion. Tests on 1D/2D/3D model inversion demonstrated that this simple method can be at least valid for a general linear inverse problem.

Some variance reduction methods for numerical stochastic homogenization

PubMed Central

Blanc, X.; Le Bris, C.; Legoll, F.

2016-01-01

We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here. PMID:27002065

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.

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.

Stochastic volatility models and Kelvin waves

NASA Astrophysics Data System (ADS)

Lipton, Alex; Sepp, Artur

2008-08-01

We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.

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.

A Novel Weighted Kernel PCA-Based Method for Optimization and Uncertainty Quantification

NASA Astrophysics Data System (ADS)

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

2016-12-01

It has been demonstrated that machine learning methods can be successfully applied to uncertainty quantification for geophysical systems through the use of the adjoint method coupled with kernel PCA-based optimization. In addition, it has been shown through weighted linear PCA how optimization with respect to both observation weights and feature space control variables can accelerate convergence of such methods. Linear machine learning methods, however, are inherently limited in their ability to represent features of non-Gaussian stochastic random fields, as they are based on only the first two statistical moments of the original data. Nonlinear spatial relationships and multipoint statistics leading to the tortuosity characteristic of channelized media, for example, are captured only to a limited extent by linear PCA. With the aim of coupling the kernel-based and weighted methods discussed, we present a novel mathematical formulation of kernel PCA, Weighted Kernel Principal Component Analysis (WKPCA), that both captures nonlinear relationships and incorporates the attribution of significance levels to different realizations of the stochastic random field of interest. We also demonstrate how new instantiations retaining defining characteristics of the random field can be generated using Bayesian methods. In particular, we present a novel WKPCA-based optimization method that minimizes a given objective function with respect to both feature space random variables and observation weights through which optimal snapshot significance levels and optimal features are learned. We showcase how WKPCA can be applied to nonlinear optimal control problems involving channelized media, and in particular demonstrate an application of the method to learning the spatial distribution of material parameter values in the context of linear elasticity, and discuss further extensions of the method to stochastic inversion.

High-resolution mapping of bifurcations in nonlinear biochemical circuits

NASA Astrophysics Data System (ADS)

Genot, A. J.; Baccouche, A.; Sieskind, R.; Aubert-Kato, N.; Bredeche, N.; Bartolo, J. F.; Taly, V.; Fujii, T.; Rondelez, Y.

2016-08-01

Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.

Some Applications Of Semigroups And Computer Algebra In Discrete Structures

NASA Astrophysics Data System (ADS)

Bijev, G.

2009-11-01

An algebraic approach to the pseudoinverse generalization problem in Boolean vector spaces is used. A map (p) is defined, which is similar to an orthogonal projection in linear vector spaces. Some other important maps with properties similar to those of the generalized inverses (pseudoinverses) of linear transformations and matrices corresponding to them are also defined and investigated. Let Ax = b be an equation with matrix A and vectors x and b Boolean. Stochastic experiments for solving the equation, which involves the maps defined and use computer algebra methods, have been made. As a result, the Hamming distance between vectors Ax = p(b) and b is equal or close to the least possible. We also share our experience in using computer algebra systems for teaching discrete mathematics and linear algebra and research. Some examples for computations with binary relations using Maple are given.

Estimation of road profile variability from measured vehicle responses

NASA Astrophysics Data System (ADS)

Fauriat, W.; Mattrand, C.; Gayton, N.; Beakou, A.; Cembrzynski, T.

2016-05-01

When assessing the statistical variability of fatigue loads acting throughout the life of a vehicle, the question of the variability of road roughness naturally arises, as both quantities are strongly related. For car manufacturers, gathering information on the environment in which vehicles evolve is a long and costly but necessary process to adapt their products to durability requirements. In the present paper, a data processing algorithm is proposed in order to estimate the road profiles covered by a given vehicle, from the dynamic responses measured on this vehicle. The algorithm based on Kalman filtering theory aims at solving a so-called inverse problem, in a stochastic framework. It is validated using experimental data obtained from simulations and real measurements. The proposed method is subsequently applied to extract valuable statistical information on road roughness from an existing load characterisation campaign carried out by Renault within one of its markets.

Simulation of dilute polymeric fluids in a three-dimensional contraction using a multiscale FENE model

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

Griebel, M., E-mail: griebel@ins.uni-bonn.de, E-mail: ruettgers@ins.uni-bonn.de; Rüttgers, A., E-mail: griebel@ins.uni-bonn.de, E-mail: ruettgers@ins.uni-bonn.de

The multiscale FENE model is applied to a 3D square-square contraction flow problem. For this purpose, the stochastic Brownian configuration field method (BCF) has been coupled with our fully parallelized three-dimensional Navier-Stokes solver NaSt3DGPF. The robustness of the BCF method enables the numerical simulation of high Deborah number flows for which most macroscopic methods suffer from stability issues. The results of our simulations are compared with that of experimental measurements from literature and show a very good agreement. In particular, flow phenomena such as a strong vortex enhancement, streamline divergence and a flow inversion for highly elastic flows are reproduced.more » Due to their computational complexity, our simulations require massively parallel computations. Using a domain decomposition approach with MPI, the implementation achieves excellent scale-up results for up to 128 processors.« less

Multivariate space - time analysis of PRE-STORM precipitation

NASA Technical Reports Server (NTRS)

Polyak, Ilya; North, Gerald R.; Valdes, Juan B.

1994-01-01

This paper presents the methodologies and results of the multivariate modeling and two-dimensional spectral and correlation analysis of PRE-STORM rainfall gauge data. Estimated parameters of the models for the specific spatial averages clearly indicate the eastward and southeastward wave propagation of rainfall fluctuations. A relationship between the coefficients of the diffusion equation and the parameters of the stochastic model of rainfall fluctuations is derived that leads directly to the exclusive use of rainfall data to estimate advection speed (about 12 m/s) as well as other coefficients of the diffusion equation of the corresponding fields. The statistical methodology developed here can be used for confirmation of physical models by comparison of the corresponding second-moment statistics of the observed and simulated data, for generating multiple samples of any size, for solving the inverse problem of the hydrodynamic equations, and for application in some other areas of meteorological and climatological data analysis and modeling.

Decimetric-resolution stochastic inversion of shallow marine seismic reflection data; dedicated strategy and application to a geohazard case study

NASA Astrophysics Data System (ADS)

Provenzano, Giuseppe; Vardy, Mark E.; Henstock, Timothy J.

2018-06-01

Characterisation of the top 10-50 m of the subseabed is key for landslide hazard assessment, offshore structure engineering design and underground gas-storage monitoring. In this paper, we present a methodology for the stochastic inversion of ultra-high-frequency (UHF, 0.2-4.0 kHz) pre-stack seismic reflection waveforms, designed to obtain a decimetric-resolution remote elastic characterisation of the shallow sediments with minimal pre-processing and little a-priori information. We use a genetic algorithm in which the space of possible solutions is sampled by explicitly decoupling the short and long wavelengths of the P-wave velocity model. This approach, combined with an objective function robust to cycle skipping, outperforms a conventional model parametrisation when the ground-truth is offset from the centre of the search domain. The robust P-wave velocity model is used to precondition the width of the search range of the multi-parameter elastic inversion, thereby improving the efficiency in high dimensional parametrizations. Multiple independent runs provide a set of independent results from which the reproducibility of the solution can be estimated. In a real dataset acquired in Finneidfjord, Norway, we also demonstrate the sensitivity of UHF seismic inversion to shallow subseabed anomalies that play a role in submarine slope stability. Thus, the methodology has the potential to become an important practical tool for marine ground model building in spatially heterogeneous areas, reducing the reliance on expensive and time-consuming coring campaigns for geohazard mitigation in marine areas.

Kolkata Paise Restaurant Problem: An Introduction

NASA Astrophysics Data System (ADS)

Ghosh, Asim; Biswas, Soumyajyoti; Chatterjee, Arnab; Chakrabarti, Anindya Sundar; Naskar, Tapan; Mitra, Manipushpak; Chakrabarti, Bikas K.

We discuss several stochastic optimization strategies in games with many players having large number of choices (Kolkata Paise Restaurant Problem) and two choices (minority game problem). It is seen that a stochastic crowd avoiding strategy gives very efficient utilization in KPR problem. A slightly modified strategy in the minority game problem gives full utilization but the dynamics stops after reaching full efficiency, thereby making the utilization helpful for only about half of the population (those in minority). We further discuss the ways in which the dynamics may be continued and the utilization becomes effective for all the agents keeping fluctuation arbitrarily small.

Theoretical consideration of the energy resolution in planar HPGe detectors for low energy X-rays

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

Samedov, Victor V.

In this work, theoretical consideration of the processes in planar High Purity Ge (HPGe) detectors for low energy X-rays using the random stochastic processes formalism was carried out. Using the random stochastic processes formalism, the generating function of the processes of X-rays registration in a planar HPGe detector was derived. The power serial expansions of the detector amplitude and the variance in terms of the inverse bias voltage were derived. The coefficients of these expansions allow determining the Fano factor, electron mobility lifetime product, nonuniformity of the trap density, and other characteristics of the semiconductor material. (authors)

Distribution of genetic diversity in relation to chromosomal inversions in the malaria mosquito Anopheles gambiae.

PubMed

Mathiopoulos, K D; Lanzaro, G C

1995-06-01

The epidemiology of malaria in Africa is complicated by the fact that its principal vector, the mosquito Anopheles gambiae, constitutes a complex of six sibling species. Each species is characterized by a unique array of paracentric inversions, as deduced by karyotypic analysis. In addition, most of the species carry a number of polymorphic inversions. In order to develop an understanding of the evolutionary histories of different parts of the genome, we compared the genetic variation of areas inside and outside inversions in two distinct inversion karyotypes of A. gambiae. Thirty-five cDNA clones were mapped on the five arms of the A. gambiae chromosomes with divisional probes. Sixteen of these clones, localized both inside and outside inversions of chromosome 2, were used as probes in order to determine the nucleotide diversity of different parts of the genome in the two inversion karyotypes. We observed that the sequence diversity inside the inversion is more than three-fold lower than in areas outside the inversion and that the degree of divergence increases gradually at loci at increasing distance from the inversion. To interpret the data we present a selectionist and a stochastic model, both of which point to a relatively recent origin of the studied inversion and may suggest differences between the evolutionary history of inversions in Anopheles and Drosophila species.

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…

Solving the problem of negative populations in approximate accelerated stochastic simulations using the representative reaction approach.

PubMed

Kadam, Shantanu; Vanka, Kumar

2013-02-15

Methods based on the stochastic formulation of chemical kinetics have the potential to accurately reproduce the dynamical behavior of various biochemical systems of interest. However, the computational expense makes them impractical for the study of real systems. Attempts to render these methods practical have led to the development of accelerated methods, where the reaction numbers are modeled by Poisson random numbers. However, for certain systems, such methods give rise to physically unrealistic negative numbers for species populations. The methods which make use of binomial variables, in place of Poisson random numbers, have since become popular, and have been partially successful in addressing this problem. In this manuscript, the development of two new computational methods, based on the representative reaction approach (RRA), has been discussed. The new methods endeavor to solve the problem of negative numbers, by making use of tools like the stochastic simulation algorithm and the binomial method, in conjunction with the RRA. It is found that these newly developed methods perform better than other binomial methods used for stochastic simulations, in resolving the problem of negative populations. Copyright © 2012 Wiley Periodicals, Inc.

Bayesian inference of spectral induced polarization parameters for laboratory complex resistivity measurements of rocks and soils

NASA Astrophysics Data System (ADS)

Bérubé, Charles L.; Chouteau, Michel; Shamsipour, Pejman; Enkin, Randolph J.; Olivo, Gema R.

2017-08-01

Spectral induced polarization (SIP) measurements are now widely used to infer mineralogical or hydrogeological properties from the low-frequency electrical properties of the subsurface in both mineral exploration and environmental sciences. We present an open-source program that performs fast multi-model inversion of laboratory complex resistivity measurements using Markov-chain Monte Carlo simulation. Using this stochastic method, SIP parameters and their uncertainties may be obtained from the Cole-Cole and Dias models, or from the Debye and Warburg decomposition approaches. The program is tested on synthetic and laboratory data to show that the posterior distribution of a multiple Cole-Cole model is multimodal in particular cases. The Warburg and Debye decomposition approaches yield unique solutions in all cases. It is shown that an adaptive Metropolis algorithm performs faster and is less dependent on the initial parameter values than the Metropolis-Hastings step method when inverting SIP data through the decomposition schemes. There are no advantages in using an adaptive step method for well-defined Cole-Cole inversion. Finally, the influence of measurement noise on the recovered relaxation time distribution is explored. We provide the geophysics community with a open-source platform that can serve as a base for further developments in stochastic SIP data inversion and that may be used to perform parameter analysis with various SIP models.

An estimator for the relative entropy rate of path measures for stochastic differential equations

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

Opper, Manfred, E-mail: manfred.opper@tu-berlin.de

2017-02-01

We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.

Bowl Inversion and Electronic Switching of Buckybowls on Gold.

PubMed

Fujii, Shintaro; Ziatdinov, Maxim; Higashibayashi, Shuhei; Sakurai, Hidehiro; Kiguchi, Manabu

2016-09-21

Bowl-shaped π-conjugated compounds, or buckybowls, are a novel class of sp(2)-hybridized nanocarbon materials. In contrast to tubular carbon nanotubes and ball-shaped fullerenes, the buckybowls feature structural flexibility. Bowl-to-bowl structural inversion is one of the unique properties of the buckybowls in solutions. Bowl inversion on a surface modifies the metal-molecule interactions through bistable switching between bowl-up and bowl-down states on the surface, which makes surface-adsorbed buckybowls a relevant model system for elucidation of the mechano-electronic properties of nanocarbon materials. Here, we report a combination of scanning tunneling microscopy (STM) measurements and ab initio atomistic simulations to identify the adlayer structure of the sumanene buckybowl on Au(111) and reveal its unique bowl inversion behavior. We demonstrate that the bowl inversion can be induced by approaching the STM tip toward the molecule. By tuning the local metal-molecule interaction using the STM tip, the sumanene buckybowl exhibits structural bistability with a switching rate that is two orders of magnitude faster than that of the stochastic inversion process.

Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon

NASA Astrophysics Data System (ADS)

Wu, Jiang; Liao, Fucheng; Tomizuka, Masayoshi

2017-01-01

This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.

Some variance reduction methods for numerical stochastic homogenization.

PubMed

Blanc, X; Le Bris, C; Legoll, F

2016-04-28

We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here. © 2016 The Author(s).

Inverse estimation of the spheroidal particle size distribution using Ant Colony Optimization algorithms in multispectral extinction technique

NASA Astrophysics Data System (ADS)

He, Zhenzong; Qi, Hong; Wang, Yuqing; Ruan, Liming

2014-10-01

Four improved Ant Colony Optimization (ACO) algorithms, i.e. the probability density function based ACO (PDF-ACO) algorithm, the Region ACO (RACO) algorithm, Stochastic ACO (SACO) algorithm and Homogeneous ACO (HACO) algorithm, are employed to estimate the particle size distribution (PSD) of the spheroidal particles. The direct problems are solved by the extended Anomalous Diffraction Approximation (ADA) and the Lambert-Beer law. Three commonly used monomodal distribution functions i.e. the Rosin-Rammer (R-R) distribution function, the normal (N-N) distribution function, and the logarithmic normal (L-N) distribution function are estimated under dependent model. The influence of random measurement errors on the inverse results is also investigated. All the results reveal that the PDF-ACO algorithm is more accurate than the other three ACO algorithms and can be used as an effective technique to investigate the PSD of the spheroidal particles. Furthermore, the Johnson's SB (J-SB) function and the modified beta (M-β) function are employed as the general distribution functions to retrieve the PSD of spheroidal particles using PDF-ACO algorithm. The investigation shows a reasonable agreement between the original distribution function and the general distribution function when only considering the variety of the length of the rotational semi-axis.

A Global Existence and Uniqueness Theorem for a Riccati Equation.

DTIC Science & Technology

1981-01-01

made to an asymptotic stochastic analysis of a noisy duel problem. / DTICELECTE[I JUN 2 3 19820 !--i *This w paper was partially supported by AFOSR Grant...of these results is made to an asymptotic stochastic analysis of I ntssy duel problem. DD ,OR 1473 EDITION O, 1.OV 1SIS OSOLTE UNCLASTFIED SCUJRITY...motivated by the approach used in [3] and [6] to analyze the equal-accuracy noisy duel problem for two players having finite unequal units of ammunition

Stochastic noncooperative and cooperative evolutionary game strategies of a population of biological networks under natural selection.

PubMed

Chen, Bor-Sen; Yeh, Chin-Hsun

2017-12-01

We review current static and dynamic evolutionary game strategies of biological networks and discuss the lack of random genetic variations and stochastic environmental disturbances in these models. To include these factors, a population of evolving biological networks is modeled as a nonlinear stochastic biological system with Poisson-driven genetic variations and random environmental fluctuations (stimuli). To gain insight into the evolutionary game theory of stochastic biological networks under natural selection, the phenotypic robustness and network evolvability of noncooperative and cooperative evolutionary game strategies are discussed from a stochastic Nash game perspective. The noncooperative strategy can be transformed into an equivalent multi-objective optimization problem and is shown to display significantly improved network robustness to tolerate genetic variations and buffer environmental disturbances, maintaining phenotypic traits for longer than the cooperative strategy. However, the noncooperative case requires greater effort and more compromises between partly conflicting players. Global linearization is used to simplify the problem of solving nonlinear stochastic evolutionary games. Finally, a simple stochastic evolutionary model of a metabolic pathway is simulated to illustrate the procedure of solving for two evolutionary game strategies and to confirm and compare their respective characteristics in the evolutionary process. Copyright © 2017 Elsevier B.V. All rights reserved.

Biochemical simulations: stochastic, approximate stochastic and hybrid approaches.

PubMed

Pahle, Jürgen

2009-01-01

Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem.

Biochemical simulations: stochastic, approximate stochastic and hybrid approaches

PubMed Central

2009-01-01

Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem. PMID:19151097

Gaussian process-based Bayesian nonparametric inference of population size trajectories from gene genealogies.

PubMed

Palacios, Julia A; Minin, Vladimir N

2013-03-01

Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method. Copyright © 2013, The International Biometric Society.

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.

Evaluation of the inverse dispersion modelling method for estimating ammonia multi-source emissions using low-cost long time averaging sensor

NASA Astrophysics Data System (ADS)

Loubet, Benjamin; Carozzi, Marco

2015-04-01

Tropospheric ammonia (NH3) is a key player in atmospheric chemistry and its deposition is a threat for the environment (ecosystem eutrophication, soil acidification and reduction in species biodiversity). Most of the NH3 global emissions derive from agriculture, mainly from livestock manure (storage and field application) but also from nitrogen-based fertilisers. Inverse dispersion modelling has been widely used to infer emission sources from a homogeneous source of known geometry. When the emission derives from different sources inside of the measured footprint, the emission should be treated as multi-source problem. This work aims at estimating whether multi-source inverse dispersion modelling can be used to infer NH3 emissions from different agronomic treatment, composed of small fields (typically squares of 25 m side) located near to each other, using low-cost NH3 measurements (diffusion samplers). To do that, a numerical experiment was designed with a combination of 3 x 3 square field sources (625 m2), and a set of sensors placed at the centre of each field at several heights as well as at 200 m away from the sources in each cardinal directions. The concentration at each sensor location was simulated with a forward Lagrangian Stochastic (WindTrax) and a Gaussian-like (FIDES) dispersion model. The concentrations were averaged over various integration times (3 hours to 28 days), to mimic the diffusion sampler behaviour with several sampling strategy. The sources were then inferred by inverse modelling using the averaged concentration and the same models in backward mode. The sources patterns were evaluated using a soil-vegetation-atmosphere model (SurfAtm-NH3) that incorporates the response of the NH3 emissions to surface temperature. A combination emission patterns (constant, linear decreasing, exponential decreasing and Gaussian type) and strengths were used to evaluate the uncertainty of the inversion method. Each numerical experiment covered a period of 28 days. The meteorological dataset of the fluxnet FR-Gri site (Grignon, FR) in 2008 was employed. Several sensor heights were tested, from 0.25 m to 2 m. The multi-source inverse problem was solved based on several sampling and field trial strategies: considering 1 or 2 heights over each field, considering the background concentration as known or unknown, and considering block-repetitions in the field set-up (3 repetitions). The inverse modelling approach demonstrated to be adapted for discriminating large differences in NH3 emissions from small agronomic plots using integrating sensors. The method is sensitive to sensor heights. The uncertainties and systematic biases are evaluated and discussed.

Estimating rare events in biochemical systems using conditional sampling.

PubMed

Sundar, V S

2017-01-28

The paper focuses on development of variance reduction strategies to estimate rare events in biochemical systems. Obtaining this probability using brute force Monte Carlo simulations in conjunction with the stochastic simulation algorithm (Gillespie's method) is computationally prohibitive. To circumvent this, important sampling tools such as the weighted stochastic simulation algorithm and the doubly weighted stochastic simulation algorithm have been proposed. However, these strategies require an additional step of determining the important region to sample from, which is not straightforward for most of the problems. In this paper, we apply the subset simulation method, developed as a variance reduction tool in the context of structural engineering, to the problem of rare event estimation in biochemical systems. The main idea is that the rare event probability is expressed as a product of more frequent conditional probabilities. These conditional probabilities are estimated with high accuracy using Monte Carlo simulations, specifically the Markov chain Monte Carlo method with the modified Metropolis-Hastings algorithm. Generating sample realizations of the state vector using the stochastic simulation algorithm is viewed as mapping the discrete-state continuous-time random process to the standard normal random variable vector. This viewpoint opens up the possibility of applying more sophisticated and efficient sampling schemes developed elsewhere to problems in stochastic chemical kinetics. The results obtained using the subset simulation method are compared with existing variance reduction strategies for a few benchmark problems, and a satisfactory improvement in computational time is demonstrated.

Optimal Computing Budget Allocation for Particle Swarm Optimization in Stochastic Optimization.

PubMed

Zhang, Si; Xu, Jie; Lee, Loo Hay; Chew, Ek Peng; Wong, Wai Peng; Chen, Chun-Hung

2017-04-01

Particle Swarm Optimization (PSO) is a popular metaheuristic for deterministic optimization. Originated in the interpretations of the movement of individuals in a bird flock or fish school, PSO introduces the concept of personal best and global best to simulate the pattern of searching for food by flocking and successfully translate the natural phenomena to the optimization of complex functions. Many real-life applications of PSO cope with stochastic problems. To solve a stochastic problem using PSO, a straightforward approach is to equally allocate computational effort among all particles and obtain the same number of samples of fitness values. This is not an efficient use of computational budget and leaves considerable room for improvement. This paper proposes a seamless integration of the concept of optimal computing budget allocation (OCBA) into PSO to improve the computational efficiency of PSO for stochastic optimization problems. We derive an asymptotically optimal allocation rule to intelligently determine the number of samples for all particles such that the PSO algorithm can efficiently select the personal best and global best when there is stochastic estimation noise in fitness values. We also propose an easy-to-implement sequential procedure. Numerical tests show that our new approach can obtain much better results using the same amount of computational effort.

Optimal Computing Budget Allocation for Particle Swarm Optimization in Stochastic Optimization

PubMed Central

Zhang, Si; Xu, Jie; Lee, Loo Hay; Chew, Ek Peng; Chen, Chun-Hung

2017-01-01

Particle Swarm Optimization (PSO) is a popular metaheuristic for deterministic optimization. Originated in the interpretations of the movement of individuals in a bird flock or fish school, PSO introduces the concept of personal best and global best to simulate the pattern of searching for food by flocking and successfully translate the natural phenomena to the optimization of complex functions. Many real-life applications of PSO cope with stochastic problems. To solve a stochastic problem using PSO, a straightforward approach is to equally allocate computational effort among all particles and obtain the same number of samples of fitness values. This is not an efficient use of computational budget and leaves considerable room for improvement. This paper proposes a seamless integration of the concept of optimal computing budget allocation (OCBA) into PSO to improve the computational efficiency of PSO for stochastic optimization problems. We derive an asymptotically optimal allocation rule to intelligently determine the number of samples for all particles such that the PSO algorithm can efficiently select the personal best and global best when there is stochastic estimation noise in fitness values. We also propose an easy-to-implement sequential procedure. Numerical tests show that our new approach can obtain much better results using the same amount of computational effort. PMID:29170617

H∞ state estimation for discrete-time memristive recurrent neural networks with stochastic time-delays

NASA Astrophysics Data System (ADS)

Liu, Hongjian; Wang, Zidong; Shen, Bo; Alsaadi, Fuad E.

2016-07-01

This paper deals with the robust H∞ state estimation problem for a class of memristive recurrent neural networks with stochastic time-delays. The stochastic time-delays under consideration are governed by a Bernoulli-distributed stochastic sequence. The purpose of the addressed problem is to design the robust state estimator such that the dynamics of the estimation error is exponentially stable in the mean square, and the prescribed ? performance constraint is met. By utilizing the difference inclusion theory and choosing a proper Lyapunov-Krasovskii functional, the existence condition of the desired estimator is derived. Based on it, the explicit expression of the estimator gain is given in terms of the solution to a linear matrix inequality. Finally, a numerical example is employed to demonstrate the effectiveness and applicability of the proposed estimation approach.

A comparison between Gauss-Newton and Markov chain Monte Carlo basedmethods for inverting spectral induced polarization data for Cole-Coleparameters

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

Chen, Jinsong; Kemna, Andreas; Hubbard, Susan S.

2008-05-15

We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive globalmore » information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters.« less

Stochastic models for inferring genetic regulation from microarray gene expression data.

PubMed

Tian, Tianhai

2010-03-01

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information. 2009 Elsevier Ireland Ltd. All rights reserved.

An optimal repartitioning decision policy

NASA Technical Reports Server (NTRS)

Nicol, D. M.; Reynolds, P. F., Jr.

1986-01-01

A central problem to parallel processing is the determination of an effective partitioning of workload to processors. The effectiveness of any given partition is dependent on the stochastic nature of the workload. The problem of determining when and if the stochastic behavior of the workload has changed enough to warrant the calculation of a new partition is treated. The problem is modeled as a Markov decision process, and an optimal decision policy is derived. Quantification of this policy is usually intractable. A heuristic policy which performs nearly optimally is investigated empirically. The results suggest that the detection of change is the predominant issue in this problem.

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa

NASA Astrophysics Data System (ADS)

Deng, Zhaojie; Arsenault, Sam; Caranica, Cristian; Griffith, James; Zhu, Taotao; Al-Omari, Ahmad; Schüttler, Heinz-Bernd; Arnold, Jonathan; Mao, Leidong

2016-10-01

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype.

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa

PubMed Central

Deng, Zhaojie; Arsenault, Sam; Caranica, Cristian; Griffith, James; Zhu, Taotao; Al-Omari, Ahmad; Schüttler, Heinz-Bernd; Arnold, Jonathan; Mao, Leidong

2016-01-01

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype. PMID:27786253

Downscaling the NOAA CarbonTracker Inversion for North America

NASA Astrophysics Data System (ADS)

Petron, G.; Andrews, A. E.; Chen, H.; Trudeau, M. E.; Eluszkiewicz, J.; Nehrkorn, T.; Henderson, J.; Sweeney, C.; Karion, A.; Masarie, K.; Bruhwiler, L.; Miller, J. B.; Miller, B. R.; Peters, W.; Gourdji, S. M.; Mueller, K. L.; Michalak, A. M.; Tans, P. P.

2011-12-01

We are developing a regional extension of the NOAA CarbonTracker CO2 data-assimilation system for a limited domain covering North America. The regional assimilation will use pre-computed and species-independent atmospheric sampling footprints from a Lagrangian Particle Dispersion Model. Each footprint relates an observed trace gas concentration to upwind fluxes. Once a footprint library has been computed, it can be used repeatedly to quickly test different inversion strategies and, importantly, for inversions using multiple species data (e.g., anthropogenic tracers such as radiocarbon and carbon monoxide and biological tracers such as carbonyl sulfide and stable isotopes of CO2). The current global CarbonTracker (CT) assimilation framework has some important limitations. For example, the assimilation adjusts scaling factors for different vegetation classes within large regions. This means, for example, that all crops within temperate North America are scaled together. There is currently no distinction between crops such as corn and sorghum, which utilize the C4 photosynthesis pathway and C3 crops like soybeans, wheat, cotton, etc. The optimization scales only the net CO2 flux, rather than adjusting photosynthesis and respiration fluxes separately, which limits the flexibility of the inversion and sometimes results in unrealistic diurnal cycles of CO2 flux. The time-series of residuals (CT - observed) for continental sites in North America reveals a persistent excess of CO2 during summer. This summertime positive bias is also apparent in the comparison of CT posterior CO2 with aircraft data and with data from Pacific marine boundary layer sites, suggesting that some of the problem may originate outside of North America. For the regional inversion, we will use footprints from the Stochastic Time-Inverted Lagrangian Transport Model driven by meteorological fields from a customized high-resolution simulation with the Weather Research Forecast (WRF) model. We will use empirically corrected boundary conditions in order to minimize sensitivity to inaccurate fluxes or transport outside of our domain. We plan to test a variety of inversion strategies that effectively exploit CO2 and isotopic data from the relatively dense North American sampling network for 2007-2010.

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.

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.

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

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

Aguilo Valentin, Miguel Alejandro

2016-07-01

This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

Continuous-time mean-variance portfolio selection with value-at-risk and no-shorting constraints

NASA Astrophysics Data System (ADS)

Yan, Wei

2012-01-01

An investment problem is considered with dynamic mean-variance(M-V) portfolio criterion under discontinuous prices which follow jump-diffusion processes according to the actual prices of stocks and the normality and stability of the financial market. The short-selling of stocks is prohibited in this mathematical model. Then, the corresponding stochastic Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and the solution of the stochastic HJB equation based on the theory of stochastic LQ control and viscosity solution is obtained. The efficient frontier and optimal strategies of the original dynamic M-V portfolio selection problem are also provided. And then, the effects on efficient frontier under the value-at-risk constraint are illustrated. Finally, an example illustrating the discontinuous prices based on M-V portfolio selection is presented.

A framework for discrete stochastic simulation on 3D moving boundary domains

DOE PAGES

Drawert, Brian; Hellander, Stefan; Trogdon, Michael; ...

2016-11-14

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. Finally, we demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formationmore » during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical.« less

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

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

Ma, Xiao; Dong, Jin; Djouadi, Seddik M

2015-01-01

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, wheremore » the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.« less

Optimal Strategy for Integrated Dynamic Inventory Control and Supplier Selection in Unknown Environment via Stochastic Dynamic Programming

NASA Astrophysics Data System (ADS)

Sutrisno; Widowati; Solikhin

2016-06-01

In this paper, we propose a mathematical model in stochastic dynamic optimization form to determine the optimal strategy for an integrated single product inventory control problem and supplier selection problem where the demand and purchasing cost parameters are random. For each time period, by using the proposed model, we decide the optimal supplier and calculate the optimal product volume purchased from the optimal supplier so that the inventory level will be located at some point as close as possible to the reference point with minimal cost. We use stochastic dynamic programming to solve this problem and give several numerical experiments to evaluate the model. From the results, for each time period, the proposed model was generated the optimal supplier and the inventory level was tracked the reference point well.

Physics-based Inverse Problem to Deduce Marine Atmospheric Boundary Layer Parameters

DTIC Science & Technology

2017-03-07

please find the Final Technical Report with SF 298 for Dr. Erin E. Hackett’s ONR grant entitled Physics-based Inverse Problem to Deduce Marine...From- To) 07/03/2017 Final Technica l Dec 2012- Dec 2016 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Physics-based Inverse Problem to Deduce Marine...SUPPLEMENTARY NOTES 14. ABSTRACT This report describes research results related to the development and implementation of an inverse problem approach for

FRACTIONAL PEARSON DIFFUSIONS.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-07-15

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

A decoupled approach to filter design for stochastic systems

NASA Astrophysics Data System (ADS)

Barbata, A.; Zasadzinski, M.; Ali, H. Souley; Messaoud, H.

2016-08-01

This paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems. This result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept. Two kinds of observers are treated: the full-order and reduced-order cases.

Advanced Dynamically Adaptive Algorithms for Stochastic Simulations on Extreme Scales

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

Xiu, Dongbin

2017-03-03

The focus of the project is the development of mathematical methods and high-performance computational tools for stochastic simulations, with a particular emphasis on computations on extreme scales. The core of the project revolves around the design of highly efficient and scalable numerical algorithms that can adaptively and accurately, in high dimensional spaces, resolve stochastic problems with limited smoothness, even containing discontinuities.

Active stability augmentation of large space structures: A stochastic control problem

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1987-01-01

A problem in SCOLE is that of slewing an offset antenna on a long flexible beam-like truss attached to the space shuttle, with rather stringent pointing accuracy requirements. The relevant methodology aspects in robust feedback-control design for stability augmentation of the beam using on-board sensors is examined. It is framed as a stochastic control problem, boundary control of a distributed parameter system described by partial differential equations. While the framework is mathematical, the emphasis is still on an engineering solution. An abstract mathematical formulation is developed as a nonlinear wave equation in a Hilbert space. That the system is controllable is shown and a feedback control law that is robust in the sense that it does not require quantitative knowledge of system parameters is developed. The stochastic control problem that arises in instrumenting this law using appropriate sensors is treated. Using an engineering first approximation which is valid for small damping, formulas for optimal choice of the control gain are developed.

On the decentralized control of large-scale systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chong, C.

1973-01-01

The decentralized control of stochastic large scale systems was considered. Particular emphasis was given to control strategies which utilize decentralized information and can be computed in a decentralized manner. The deterministic constrained optimization problem is generalized to the stochastic case when each decision variable depends on different information and the constraint is only required to be satisfied on the average. For problems with a particular structure, a hierarchical decomposition is obtained. For the stochastic control of dynamic systems with different information sets, a new kind of optimality is proposed which exploits the coupled nature of the dynamic system. The subsystems are assumed to be uncoupled and then certain constraints are required to be satisfied, either in a off-line or on-line fashion. For off-line coordination, a hierarchical approach of solving the problem is obtained. The lower level problems are all uncoupled. For on-line coordination, distinction is made between open loop feedback optimal coordination and closed loop optimal coordination.

Stochastic Methods for Aircraft Design

NASA Technical Reports Server (NTRS)

Pelz, Richard B.; Ogot, Madara

1998-01-01

The global stochastic optimization method, simulated annealing (SA), was adapted and applied to various problems in aircraft design. The research was aimed at overcoming the problem of finding an optimal design in a space with multiple minima and roughness ubiquitous to numerically generated nonlinear objective functions. SA was modified to reduce the number of objective function evaluations for an optimal design, historically the main criticism of stochastic methods. SA was applied to many CFD/MDO problems including: low sonic-boom bodies, minimum drag on supersonic fore-bodies, minimum drag on supersonic aeroelastic fore-bodies, minimum drag on HSCT aeroelastic wings, FLOPS preliminary design code, another preliminary aircraft design study with vortex lattice aerodynamics, HSR complete aircraft aerodynamics. In every case, SA provided a simple, robust and reliable optimization method which found optimal designs in order 100 objective function evaluations. Perhaps most importantly, from this academic/industrial project, technology has been successfully transferred; this method is the method of choice for optimization problems at Northrop Grumman.

Genetic Algorithm and Tabu Search for Vehicle Routing Problems with Stochastic Demand

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

Ismail, Zuhaimy, E-mail: zuhaimyi@yahoo.com, E-mail: irhamahn@yahoo.com; Irhamah, E-mail: zuhaimyi@yahoo.com, E-mail: irhamahn@yahoo.com

2010-11-11

This paper presents a problem of designing solid waste collection routes, involving scheduling of vehicles where each vehicle begins at the depot, visits customers and ends at the depot. It is modeled as a Vehicle Routing Problem with Stochastic Demands (VRPSD). A data set from a real world problem (a case) is used in this research. We developed Genetic Algorithm (GA) and Tabu Search (TS) procedure and these has produced the best possible result. The problem data are inspired by real case of VRPSD in waste collection. Results from the experiment show the advantages of the proposed algorithm that aremore » its robustness and better solution qualities.« less

Simulated Stochastic Approximation Annealing for Global Optimization with a Square-Root Cooling Schedule

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

Liang, Faming; Cheng, Yichen; Lin, Guang

2014-06-13

Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to have such a long CPU time. This paper proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which is a combination of simulated annealing and the stochastic approximation Monte Carlo algorithm. Under the framework of stochastic approximation Markov chain Monte Carlo, it is shown that themore » new algorithm can work with a cooling schedule in which the temperature can decrease much faster than in the logarithmic cooling schedule, e.g., a square-root cooling schedule, while guaranteeing the global optima to be reached when the temperature tends to zero. The new algorithm has been tested on a few benchmark optimization problems, including feed-forward neural network training and protein-folding. The numerical results indicate that the new algorithm can significantly outperform simulated annealing and other competitors.« less

Disentangling the stochastic behavior of complex time series

NASA Astrophysics Data System (ADS)

Anvari, Mehrnaz; Tabar, M. Reza Rahimi; Peinke, Joachim; Lehnertz, Klaus

2016-10-01

Complex systems involving a large number of degrees of freedom, generally exhibit non-stationary dynamics, which can result in either continuous or discontinuous sample paths of the corresponding time series. The latter sample paths may be caused by discontinuous events - or jumps - with some distributed amplitudes, and disentangling effects caused by such jumps from effects caused by normal diffusion processes is a main problem for a detailed understanding of stochastic dynamics of complex systems. Here we introduce a non-parametric method to address this general problem. By means of a stochastic dynamical jump-diffusion modelling, we separate deterministic drift terms from different stochastic behaviors, namely diffusive and jumpy ones, and show that all of the unknown functions and coefficients of this modelling can be derived directly from measured time series. We demonstrate appli- cability of our method to empirical observations by a data-driven inference of the deterministic drift term and of the diffusive and jumpy behavior in brain dynamics from ten epilepsy patients. Particularly these different stochastic behaviors provide extra information that can be regarded valuable for diagnostic purposes.

A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

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

Chen, Luoping; Zheng, Bin; Lin, Guang

In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse meshmore » $$\\mathcal{T}_H$$ with a low level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_{P}$$) and solve linearized equations on a fine mesh $$\\mathcal{T}_h$$ using high level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_p$$). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with $$\\mathcal{T}_h$$ and $$\\mathcal{P}_p$$. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.« less

A combined stochastic feedforward and feedback control design methodology with application to autoland design

NASA Technical Reports Server (NTRS)

Halyo, Nesim

1987-01-01

A combined stochastic feedforward and feedback control design methodology was developed. The objective of the feedforward control law is to track the commanded trajectory, whereas the feedback control law tries to maintain the plant state near the desired trajectory in the presence of disturbances and uncertainties about the plant. The feedforward control law design is formulated as a stochastic optimization problem and is embedded into the stochastic output feedback problem where the plant contains unstable and uncontrollable modes. An algorithm to compute the optimal feedforward is developed. In this approach, the use of error integral feedback, dynamic compensation, control rate command structures are an integral part of the methodology. An incremental implementation is recommended. Results on the eigenvalues of the implemented versus designed control laws are presented. The stochastic feedforward/feedback control methodology is used to design a digital automatic landing system for the ATOPS Research Vehicle, a Boeing 737-100 aircraft. The system control modes include localizer and glideslope capture and track, and flare to touchdown. Results of a detailed nonlinear simulation of the digital control laws, actuator systems, and aircraft aerodynamics are presented.

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

Malikopoulos, Andreas; Djouadi, Seddik M; Kuruganti, Teja

We consider the optimal stochastic control problem for home energy systems with solar and energy storage devices when the demand is realized from the grid. The demand is subject to Brownian motions with both drift and variance parameters modulated by a continuous-time Markov chain that represents the regime of electricity price. We model the systems as pure stochastic differential equation models, and then we follow the completing square technique to solve the stochastic home energy management problem. The effectiveness of the efficiency of the proposed approach is validated through a simulation example. For practical situations with constraints consistent to thosemore » studied here, our results imply the proposed framework could reduce the electricity cost from short-term purchase in peak hour market.« less

The complexity of divisibility.

PubMed

Bausch, Johannes; Cubitt, Toby

2016-09-01

We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive trace-preserving maps, i.e. the quantum analogue of stochastic matrices. We further prove a complexity hierarchy for the divisibility and decomposability of probability distributions, showing that finite distribution divisibility is in P, but decomposability is NP-hard. For the former, we give an explicit polynomial-time algorithm. All results on distributions extend to weak-membership formulations, proving that the complexity of these problems is robust to perturbations.

Constructing a starting 3D shear velocity model with sharp interfaces for SEM-based upper mantle tomography in North America

NASA Astrophysics Data System (ADS)

Calo, M.; Bodin, T.; Yuan, H.; Romanowicz, B. A.; Larmat, C. S.; Maceira, M.

2013-12-01

Seismic tomography is currently evolving towards 3D earth models that satisfy full seismic waveforms at increasingly high frequencies. This evolution is possible thanks to the advent of powerful numerical methods such as the Spectral Element Method (SEM) that allow accurate computation of the seismic wavefield in complex media, and the drastic increase of computational resources. However, the production of such models requires handling complex misfit functions with more than one local minimum. Standard linearized inversion methods (such as gradient methods) have two main drawbacks: 1) they produce solution models highly dependent on the starting model; 2) they do not provide a means of estimating true model uncertainties. However, these issues can be addressed with stochastic methods that can sample the space of possible solutions efficiently. Such methods are prohibitively challenging computationally in 3D, but increasingly accessible in 1D. In previous work (Yuan and Romanowicz, 2010; Yuan et al., 2011) we developed a continental scale anisotropic upper mantle model of north America based on a combination of long period seismic waveforms and SKS splitting measurements, showing the pervasive presence of layering of anisotropy in the cratonic lithosphere with significant variations in depth of the mid-lithospheric boundary. The radial anisotropy part of the model has been recently updated using the spectral element method for forward wavefield computations and waveform data from the latest deployments of USarray (Yuan and Romanowicz, 2013). However, the long period waveforms (periods > 40s) themselves only provide a relatively smooth view of the mantle if the starting model is smooth, and the mantle discontinuities necessary for geodynamical interpretation are not imaged. Increasing the frequency of the computations to constrain smaller scale features is possible, but challenging computationally, and at the risk of falling in local minima of the misfit function. In this work we propose instead to directly tackle the non-linearity of the inverse problem by using stochastic methods to construct a 3D starting model with a good estimate of the depths of the main layering interfaces. We present preliminary results of the construction of such a starting 3D model based on: (1) Regionalizing the study area to define provinces within which lateral variations are smooth; (2) Applying trans-dimensional stochastic inversion (Bodin et al., 2012) to obtain accurate 1D models in each province as well as the corresponding error distribution, constrained by receiver function and surface wave dispersion data as well as the previously constructed 3D model (name), and (3) connecting these models laterally using data-driven smoothing operators to obtain a starting 3D model with errors. References Bodin, T.,et al. 2012, Transdimensional inversion of receiver functions and surface wave dispersion, J. Geophys. Res., 117, B02301, doi:10.1029/2011JB008560. Yuan and Romanowicz, 2013, in revison. Yuan, H., et al. 2011, 3-D shear wave radially and azimuthally anisotropic velocity model of the North American upper mantle. Geophysical Journal International, 184: 1237-1260. doi: 10.1111/j.1365-246X.2010.04901.x Yuan, H. & Romanowicz, B., 2010. Lithospheric layering in the North American Craton, Nature, 466, 1063-1068.

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.)

Idempotent Methods for Continuous Time Nonlinear Stochastic Control

DTIC Science & Technology

2012-09-13

AND ADDRESS(ES) dba AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER Stochastech Corporation dba Tempest Technologies 8939 S...Stochastic Control Problems Ben G. Fitzpatrick Tempest Technologies 8939 S. Sepulveda Boulevard, Suite 506 Los Angeles, CA 90045 Sponsored by

Impact of a Stochastic Parameterization Scheme on El Nino-Southern Oscillation in the Community Climate System Model

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Berner, J.; Sardeshmukh, P. D.

2017-12-01

Stochastic parameterizations have been used for more than a decade in atmospheric models. They provide a way to represent model uncertainty through representing the variability of unresolved sub-grid processes, and have been shown to have a beneficial effect on the spread and mean state for medium- and extended-range forecasts. There is increasing evidence that stochastic parameterization of unresolved processes can improve the bias in mean and variability, e.g. by introducing a noise-induced drift (nonlinear rectification), and by changing the residence time and structure of flow regimes. We present results showing the impact of including the Stochastically Perturbed Parameterization Tendencies scheme (SPPT) in coupled runs of the National Center for Atmospheric Research (NCAR) Community Atmosphere Model, version 4 (CAM4) with historical forcing. SPPT results in a significant improvement in the representation of the El Nino-Southern Oscillation in CAM4, improving the power spectrum, as well as both the inter- and intra-annual variability of tropical pacific sea surface temperatures. We use a Linear Inverse Modelling framework to gain insight into the mechanisms by which SPPT has improved ENSO-variability.

Clinical Applications of Stochastic Dynamic Models of the Brain, Part I: A Primer.

PubMed

Roberts, James A; Friston, Karl J; Breakspear, Michael

2017-04-01

Biological phenomena arise through interactions between an organism's intrinsic dynamics and stochastic forces-random fluctuations due to external inputs, thermal energy, or other exogenous influences. Dynamic processes in the brain derive from neurophysiology and anatomical connectivity; stochastic effects arise through sensory fluctuations, brainstem discharges, and random microscopic states such as thermal noise. The dynamic evolution of systems composed of both dynamic and random effects can be studied with stochastic dynamic models (SDMs). This article, Part I of a two-part series, offers a primer of SDMs and their application to large-scale neural systems in health and disease. The companion article, Part II, reviews the application of SDMs to brain disorders. SDMs generate a distribution of dynamic states, which (we argue) represent ideal candidates for modeling how the brain represents states of the world. When augmented with variational methods for model inversion, SDMs represent a powerful means of inferring neuronal dynamics from functional neuroimaging data in health and disease. Together with deeper theoretical considerations, this work suggests that SDMs will play a unique and influential role in computational psychiatry, unifying empirical observations with models of perception and behavior. Copyright © 2017 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.

Rupture Propagation for Stochastic Fault Models

NASA Astrophysics Data System (ADS)

Favreau, P.; Lavallee, D.; Archuleta, R.

2003-12-01

The inversion of strong motion data of large earhquakes give the spatial distribution of pre-stress on the ruptured faults and it can be partially reproduced by stochastic models, but a fundamental question remains: how rupture propagates, constrained by the presence of spatial heterogeneity? For this purpose we investigate how the underlying random variables, that control the pre-stress spatial variability, condition the propagation of the rupture. Two stochastic models of prestress distributions are considered, respectively based on Cauchy and Gaussian random variables. The parameters of the two stochastic models have values corresponding to the slip distribution of the 1979 Imperial Valley earthquake. We use a finite difference code to simulate the spontaneous propagation of shear rupture on a flat fault in a 3D continuum elastic body. The friction law is the slip dependent friction law. The simulations show that the propagation of the rupture front is more complex, incoherent or snake-like for a prestress distribution based on Cauchy random variables. This may be related to the presence of a higher number of asperities in this case. These simulations suggest that directivity is stronger in the Cauchy scenario, compared to the smoother rupture of the Gauss scenario.

Non-Gaussianity in a quasiclassical electronic circuit

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi J.; Hayakawa, Hisao

2017-05-01

We study the non-Gaussian dynamics of a quasiclassical electronic circuit coupled to a mesoscopic conductor. Non-Gaussian noise accompanying the nonequilibrium transport through the conductor significantly modifies the stationary probability density function (PDF) of the flux in the dissipative circuit. We incorporate weak quantum fluctuation of the dissipative LC circuit with a stochastic method and evaluate the quantum correction of the stationary PDF. Furthermore, an inverse formula to infer the statistical properties of the non-Gaussian noise from the stationary PDF is derived in the classical-quantum crossover regime. The quantum correction is indispensable to correctly estimate the microscopic transfer events in the QPC with the quasiclassical inverse formula.

Coordinated phenotype switching with large-scale chromosome flip-flop inversion observed in bacteria.

PubMed

Cui, Longzhu; Neoh, Hui-min; Iwamoto, Akira; Hiramatsu, Keiichi

2012-06-19

Genome inversions are ubiquitous in organisms ranging from prokaryotes to eukaryotes. Typical examples can be identified by comparing the genomes of two or more closely related organisms, where genome inversion footprints are clearly visible. Although the evolutionary implications of this phenomenon are huge, little is known about the function and biological meaning of this process. Here, we report our findings on a bacterium that generates a reversible, large-scale inversion of its chromosome (about half of its total genome) at high frequencies of up to once every four generations. This inversion switches on or off bacterial phenotypes, including colony morphology, antibiotic susceptibility, hemolytic activity, and expression of dozens of genes. Quantitative measurements and mathematical analyses indicate that this reversible switching is stochastic but self-organized so as to maintain two forms of stable cell populations (i.e., small colony variant, normal colony variant) as a bet-hedging strategy. Thus, this heritable and reversible genome fluctuation seems to govern the bacterial life cycle; it has a profound impact on the course and outcomes of bacterial infections.

Optimal growth trajectories with finite carrying capacity.

PubMed

Caravelli, F; Sindoni, L; Caccioli, F; Ududec, C

2016-08-01

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Multiobjective optimization in structural design with uncertain parameters and stochastic processes

NASA Technical Reports Server (NTRS)

Rao, S. S.

1984-01-01

The application of multiobjective optimization techniques to structural design problems involving uncertain parameters and random processes is studied. The design of a cantilever beam with a tip mass subjected to a stochastic base excitation is considered for illustration. Several of the problem parameters are assumed to be random variables and the structural mass, fatigue damage, and negative of natural frequency of vibration are considered for minimization. The solution of this three-criteria design problem is found by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It is observed that the game theory approach is superior in finding a better optimum solution, assuming the proper balance of the various objective functions. The procedures used in the present investigation are expected to be useful in the design of general dynamic systems involving uncertain parameters, stochastic process, and multiple objectives.

A quantile-based scenario analysis approach to biomass supply chain optimization under uncertainty

DOE PAGES

Zamar, David S.; Gopaluni, Bhushan; Sokhansanj, Shahab; ...

2016-11-21

Supply chain optimization for biomass-based power plants is an important research area due to greater emphasis on renewable power energy sources. Biomass supply chain design and operational planning models are often formulated and studied using deterministic mathematical models. While these models are beneficial for making decisions, their applicability to real world problems may be limited because they do not capture all the complexities in the supply chain, including uncertainties in the parameters. This study develops a statistically robust quantile-based approach for stochastic optimization under uncertainty, which builds upon scenario analysis. We apply and evaluate the performance of our approach tomore » address the problem of analyzing competing biomass supply chains subject to stochastic demand and supply. Finally, the proposed approach was found to outperform alternative methods in terms of computational efficiency and ability to meet the stochastic problem requirements.« less

Finite-time synchronization of stochastic coupled neural networks subject to Markovian switching and input saturation.

PubMed

Selvaraj, P; Sakthivel, R; Kwon, O M

2018-06-07

This paper addresses the problem of finite-time synchronization of stochastic coupled neural networks (SCNNs) subject to Markovian switching, mixed time delay, and actuator saturation. In addition, coupling strengths of the SCNNs are characterized by mutually independent random variables. By utilizing a simple linear transformation, the problem of stochastic finite-time synchronization of SCNNs is converted into a mean-square finite-time stabilization problem of an error system. By choosing a suitable mode dependent switched Lyapunov-Krasovskii functional, a new set of sufficient conditions is derived to guarantee the finite-time stability of the error system. Subsequently, with the help of anti-windup control scheme, the actuator saturation risks could be mitigated. Moreover, the derived conditions help to optimize estimation of the domain of attraction by enlarging the contractively invariant set. Furthermore, simulations are conducted to exhibit the efficiency of proposed control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

A Novel Biobjective Risk-Based Model for Stochastic Air Traffic Network Flow Optimization Problem.

PubMed

Cai, Kaiquan; Jia, Yaoguang; Zhu, Yanbo; Xiao, Mingming

2015-01-01

Network-wide air traffic flow management (ATFM) is an effective way to alleviate demand-capacity imbalances globally and thereafter reduce airspace congestion and flight delays. The conventional ATFM models assume the capacities of airports or airspace sectors are all predetermined. However, the capacity uncertainties due to the dynamics of convective weather may make the deterministic ATFM measures impractical. This paper investigates the stochastic air traffic network flow optimization (SATNFO) problem, which is formulated as a weighted biobjective 0-1 integer programming model. In order to evaluate the effect of capacity uncertainties on ATFM, the operational risk is modeled via probabilistic risk assessment and introduced as an extra objective in SATNFO problem. Computation experiments using real-world air traffic network data associated with simulated weather data show that presented model has far less constraints compared to stochastic model with nonanticipative constraints, which means our proposed model reduces the computation complexity.

A quantile-based scenario analysis approach to biomass supply chain optimization under uncertainty

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

Zamar, David S.; Gopaluni, Bhushan; Sokhansanj, Shahab

Supply chain optimization for biomass-based power plants is an important research area due to greater emphasis on renewable power energy sources. Biomass supply chain design and operational planning models are often formulated and studied using deterministic mathematical models. While these models are beneficial for making decisions, their applicability to real world problems may be limited because they do not capture all the complexities in the supply chain, including uncertainties in the parameters. This study develops a statistically robust quantile-based approach for stochastic optimization under uncertainty, which builds upon scenario analysis. We apply and evaluate the performance of our approach tomore » address the problem of analyzing competing biomass supply chains subject to stochastic demand and supply. Finally, the proposed approach was found to outperform alternative methods in terms of computational efficiency and ability to meet the stochastic problem requirements.« less

An improved stochastic fractal search algorithm for 3D protein structure prediction.

PubMed

Zhou, Changjun; Sun, Chuan; Wang, Bin; Wang, Xiaojun

2018-05-03

Protein structure prediction (PSP) is a significant area for biological information research, disease treatment, and drug development and so on. In this paper, three-dimensional structures of proteins are predicted based on the known amino acid sequences, and the structure prediction problem is transformed into a typical NP problem by an AB off-lattice model. This work applies a novel improved Stochastic Fractal Search algorithm (ISFS) to solve the problem. The Stochastic Fractal Search algorithm (SFS) is an effective evolutionary algorithm that performs well in exploring the search space but falls into local minimums sometimes. In order to avoid the weakness, Lvy flight and internal feedback information are introduced in ISFS. In the experimental process, simulations are conducted by ISFS algorithm on Fibonacci sequences and real peptide sequences. Experimental results prove that the ISFS performs more efficiently and robust in terms of finding the global minimum and avoiding getting stuck in local minimums.

Optimal growth trajectories with finite carrying capacity

NASA Astrophysics Data System (ADS)

Caravelli, F.; Sindoni, L.; Caccioli, F.; Ududec, C.

2016-08-01

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults.

PubMed

Li, Yongming; Ma, Zhiyao; Tong, Shaocheng

2017-09-01

The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Stochastic Dynamic Mixed-Integer Programming (SD-MIP)

DTIC Science & Technology

2015-05-05

stochastic linear programming ( SLP ) problems. By using a combination of ideas from cutting plane theory of deterministic MIP (especially disjunctive...developed to date. b) As part of this project, we have also developed tools for very large scale Stochastic Linear Programming ( SLP ). There are...several reasons for this. First, SLP models continue to challenge many of the fastest computers to date, and many applications within the DoD (e.g

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.

Stochastic Representations of Seismic Anisotropy: Verification of Effective Media Models and Application to the Continental Crust

NASA Astrophysics Data System (ADS)

Song, X.; Jordan, T. H.

2017-12-01

The seismic anisotropy of the continental crust is dominated by two mechanisms: the local (intrinsic) anisotropy of crustal rocks caused by the lattice-preferred orientation of their constituent minerals, and the geometric (extrinsic) anisotropy caused by the alignment and layering of elastic heterogeneities by sedimentation and deformation. To assess the relative importance of these mechanisms, we have applied Jordan's (GJI, 2015) self-consistent, second-order theory to compute the effective elastic parameters of stochastic media with hexagonal local anisotropy and small-scale 3D heterogeneities that have transversely isotropic (TI) statistics. The theory pertains to stochastic TI media in which the eighth-order covariance tensor of the elastic moduli can be separated into a one-point variance tensor that describes the local anisotropy in terms of a anisotropy orientation ratio (ξ from 0 to ∞), and a two-point correlation function that describes the geometric anisotropy in terms of a heterogeneity aspect ratio (η from 0 to ∞). If there is no local anisotropy, then, in the limiting case of a horizontal stochastic laminate (η→∞), the effective-medium equations reduce to the second-order equations derived by Backus (1962) for a stochastically layered medium. This generalization of the Backus equations to 3D stochastic media, as well as the introduction of local, stochastically rotated anisotropy, provides a powerful theory for interpreting the anisotropic signatures of sedimentation and deformation in continental environments; in particular, the parameterizations that we propose are suitable for tomographic inversions. We have verified this theory through a series high-resolution numerical experiments using both isotropic and anisotropic wave-propagation codes.

Stochastic von Bertalanffy models, with applications to fish recruitment.

PubMed

Lv, Qiming; Pitchford, Jonathan W

2007-02-21

We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalanffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed.

A hybrid meta-heuristic algorithm for the vehicle routing problem with stochastic travel times considering the driver's satisfaction

NASA Astrophysics Data System (ADS)

Tavakkoli-Moghaddam, Reza; Alinaghian, Mehdi; Salamat-Bakhsh, Alireza; Norouzi, Narges

2012-05-01

A vehicle routing problem is a significant problem that has attracted great attention from researchers in recent years. The main objectives of the vehicle routing problem are to minimize the traveled distance, total traveling time, number of vehicles and cost function of transportation. Reducing these variables leads to decreasing the total cost and increasing the driver's satisfaction level. On the other hand, this satisfaction, which will decrease by increasing the service time, is considered as an important logistic problem for a company. The stochastic time dominated by a probability variable leads to variation of the service time, while it is ignored in classical routing problems. This paper investigates the problem of the increasing service time by using the stochastic time for each tour such that the total traveling time of the vehicles is limited to a specific limit based on a defined probability. Since exact solutions of the vehicle routing problem that belong to the category of NP-hard problems are not practical in a large scale, a hybrid algorithm based on simulated annealing with genetic operators was proposed to obtain an efficient solution with reasonable computational cost and time. Finally, for some small cases, the related results of the proposed algorithm were compared with results obtained by the Lingo 8 software. The obtained results indicate the efficiency of the proposed hybrid simulated annealing algorithm.

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.

Development and Tuning of a 3D Stochastic Inversion Methodology to the European Arctic

DTIC Science & Technology

2010-09-01

from previous studies covering the region, in particular from Breivik et al. (2002). Our MCMC algorithm shown in Figure 3 has two major components...criteria, Geophys. J. Int., 156: 483–496, doi:10.1111/j.1365-246X.2004.570 02070.x. Breivik , A., R. Mjelde, P. Grogan, H. Shimamura, Y. Murai, Y

Finding optimal vaccination strategies under parameter uncertainty using stochastic programming.

PubMed

Tanner, Matthew W; Sattenspiel, Lisa; Ntaimo, Lewis

2008-10-01

We present a stochastic programming framework for finding the optimal vaccination policy for controlling infectious disease epidemics under parameter uncertainty. Stochastic programming is a popular framework for including the effects of parameter uncertainty in a mathematical optimization model. The problem is initially formulated to find the minimum cost vaccination policy under a chance-constraint. The chance-constraint requires that the probability that R(*)

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.

Quantum learning of classical stochastic processes: The completely positive realization problem

NASA Astrophysics Data System (ADS)

Monràs, Alex; Winter, Andreas

2016-01-01

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651-664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print arXiv:1303.3771(2013)].

Agonist-induced modulation of inverse agonist efficacy at the beta 2-adrenergic receptor.

PubMed

Chidiac, P; Nouet, S; Bouvier, M

1996-09-01

Sustained stimulation of several G protein-coupled receptors is known to lead to a reduction in the signaling efficacy. This phenomenon, named agonist-induced desensitization, has been best studied for the beta 2-adrenergic receptor (AR) and is characterized by a decreased efficacy of beta-adrenergic agonists to stimulate the adenylyl cyclase activity. Recently, several beta-adrenergic ligands were found to inhibit the spontaneous agonist-independent activity of the beta 2AR. These compounds, termed inverse agonists, have different inhibitory efficacies, ranging from almost neutral antagonists to full inverse agonists. The current study was undertaken to determine whether, as is the case for agonists, desensitization can affect the efficacies of inverse agonists. Agonist-promoted desensitization of the human beta 2AR expressed in Sf9 cells potentiated the inhibitory actions of the inverse agonists, with the extent of the potentiation being inversely proportional to their intrinsic activity. For example, desensitization increased the inhibitory action of the weak inverse agonist labetalol by 29%, whereas inhibition of the spontaneous activity by the strong inverse agonist timolol was not enhanced by the desensitizing stimuli. Interestingly, dichloroisoproterenol acted stochastically as either a weak partial agonist or a weak inverse agonist in control conditions but always behaved as an inverse agonist after desensitization. These data demonstrate that like for agonists, the efficacies of inverse agonists can be modulated by a desensitizing treatment. Also, the data show that the initial state of the receptor can determine whether a ligand behaves as a partial agonist or an inverse agonist.

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.

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

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

Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

Few-body problem in terms of correlated Gaussians

NASA Astrophysics Data System (ADS)

Silvestre-Brac, Bernard; Mathieu, Vincent

2007-10-01

In their textbook, Suzuki and Varga [Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems (Springer, Berlin, 1998)] present the stochastic variational method with the correlated Gaussian basis in a very exhaustive way. However, the Fourier transform of these functions and their application to the management of a relativistic kinetic energy operator are missing and cannot be found in the literature. In this paper we present these interesting formulas. We also give a derivation for formulations concerning central potentials.

Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

NASA Astrophysics Data System (ADS)

Yan, Wei; Chang, Yuwen

2016-12-01

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

Solving multistage stochastic programming models of portfolio selection with outstanding liabilities

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

Edirisinghe, C.

1994-12-31

Models for portfolio selection in the presence of an outstanding liability have received significant attention, for example, models for pricing options. The problem may be described briefly as follows: given a set of risky securities (and a riskless security such as a bond), and given a set of cash flows, i.e., outstanding liability, to be met at some future date, determine an initial portfolio and a dynamic trading strategy for the underlying securities such that the initial cost of the portfolio is within a prescribed wealth level and the expected cash surpluses arising from trading is maximized. While the tradingmore » strategy should be self-financing, there may also be other restrictions such as leverage and short-sale constraints. Usually the treatment is limited to binomial evolution of uncertainty (of stock price), with possible extensions for developing computational bounds for multinomial generalizations. Posing as stochastic programming models of decision making, we investigate alternative efficient solution procedures under continuous evolution of uncertainty, for discrete time economies. We point out an important moment problem arising in the portfolio selection problem, the solution (or bounds) on which provides the basis for developing efficient computational algorithms. While the underlying stochastic program may be computationally tedious even for a modest number of trading opportunities (i.e., time periods), the derived algorithms may used to solve problems whose sizes are beyond those considered within stochastic optimization.« less

Adaptive control of stochastic linear systems with unknown parameters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Ku, R. T.

1972-01-01

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.

PubMed

Gao, Qing; Liu, Lu; Feng, Gang; Wang, Yong

2014-12-01

In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.

Sampling-Based Stochastic Sensitivity Analysis Using Score Functions for RBDO Problems with Correlated Random Variables

DTIC Science & Technology

2010-08-01

a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. a ...SECURITY CLASSIFICATION OF: This study presents a methodology for computing stochastic sensitivities with respect to the design variables, which are the...Random Variables Report Title ABSTRACT This study presents a methodology for computing stochastic sensitivities with respect to the design variables

Theory of Stochastic Duels - Miscellaneous Results

DTIC Science & Technology

1978-03-01

TECHNICAL MEMORANDUM 2-77, "THEORY OF STOCHASTIC DUELS - MISCELLANEOUS RESULTS"______________ 6. PERFORMING ORG. REPORT NUMBER _USA TRASANA 7. AUT)IOR...Identify by block number) This memorandum presents particular applications of various aspects of the theory of stochastic duels that the author has...Marksman Problem with Erlang n Firing Time 1 Distribution 2.3 Tactical Equity Duel with Erlang 2 Firing Times 4 2.4 Different Tactical Equity Duel 6 S2.5

The cardiorespiratory interaction: a nonlinear stochastic model and its synchronization properties

NASA Astrophysics Data System (ADS)

Bahraminasab, A.; Kenwright, D.; Stefanovska, A.; McClintock, P. V. E.

2007-06-01

We address the problem of interactions between the phase of cardiac and respiration oscillatory components. The coupling between these two quantities is experimentally investigated by the theory of stochastic Markovian processes. The so-called Markov analysis allows us to derive nonlinear stochastic equations for the reconstruction of the cardiorespiratory signals. The properties of these equations provide interesting new insights into the strength and direction of coupling which enable us to divide the couplings to two parts: deterministic and stochastic. It is shown that the synchronization behaviors of the reconstructed signals are statistically identical with original one.

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.

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.

Digital program for solving the linear stochastic optimal control and estimation problem

NASA Technical Reports Server (NTRS)

Geyser, L. C.; Lehtinen, B.

1975-01-01

A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.

Training-based descreening.

PubMed

Siddiqui, Hasib; Bouman, Charles A

2007-03-01

Conventional halftoning methods employed in electrophotographic printers tend to produce Moiré artifacts when used for printing images scanned from printed material, such as books and magazines. We present a novel approach for descreening color scanned documents aimed at providing an efficient solution to the Moiré problem in practical imaging devices, including copiers and multifunction printers. The algorithm works by combining two nonlinear image-processing techniques, resolution synthesis-based denoising (RSD), and modified smallest univalue segment assimilating nucleus (SUSAN) filtering. The RSD predictor is based on a stochastic image model whose parameters are optimized beforehand in a separate training procedure. Using the optimized parameters, RSD classifies the local window around the current pixel in the scanned image and applies filters optimized for the selected classes. The output of the RSD predictor is treated as a first-order estimate to the descreened image. The modified SUSAN filter uses the output of RSD for performing an edge-preserving smoothing on the raw scanned data and produces the final output of the descreening algorithm. Our method does not require any knowledge of the screening method, such as the screen frequency or dither matrix coefficients, that produced the printed original. The proposed scheme not only suppresses the Moiré artifacts, but, in addition, can be trained with intrinsic sharpening for deblurring scanned documents. Finally, once optimized for a periodic clustered-dot halftoning method, the same algorithm can be used to inverse halftone scanned images containing stochastic error diffusion halftone noise.

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

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

Chen, Peng, E-mail: peng@ices.utexas.edu; Schwab, Christoph, E-mail: christoph.schwab@sam.math.ethz.ch

2016-07-01

We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by themore » so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation and for Bayesian estimation. They also open a perspective for optimal experimental design.« less

Interparameter trade-off quantification and reduction in isotropic-elastic full-waveform inversion: synthetic experiments and Hussar land data set application

NASA Astrophysics Data System (ADS)

Pan, Wenyong; Geng, Yu; Innanen, Kristopher A.

2018-05-01

The problem of inverting for multiple physical parameters in the subsurface using seismic full-waveform inversion (FWI) is complicated by interparameter trade-off arising from inherent ambiguities between different physical parameters. Parameter resolution is often characterized using scattering radiation patterns, but these neglect some important aspects of interparameter trade-off. More general analysis and mitigation of interparameter trade-off in isotropic-elastic FWI is possible through judiciously chosen multiparameter Hessian matrix-vector products. We show that products of multiparameter Hessian off-diagonal blocks with model perturbation vectors, referred to as interparameter contamination kernels, are central to the approach. We apply the multiparameter Hessian to various vectors designed to provide information regarding the strengths and characteristics of interparameter contamination, both locally and within the whole volume. With numerical experiments, we observe that S-wave velocity perturbations introduce strong contaminations into density and phase-reversed contaminations into P-wave velocity, but themselves experience only limited contaminations from other parameters. Based on these findings, we introduce a novel strategy to mitigate the influence of interparameter trade-off with approximate contamination kernels. Furthermore, we recommend that the local spatial and interparameter trade-off of the inverted models be quantified using extended multiparameter point spread functions (EMPSFs) obtained with pre-conditioned conjugate-gradient algorithm. Compared to traditional point spread functions, the EMPSFs appear to provide more accurate measurements for resolution analysis, by de-blurring the estimations, scaling magnitudes and mitigating interparameter contamination. Approximate eigenvalue volumes constructed with stochastic probing approach are proposed to evaluate the resolution of the inverted models within the whole model. With a synthetic Marmousi model example and a land seismic field data set from Hussar, Alberta, Canada, we confirm that the new inversion strategy suppresses the interparameter contamination effectively and provides more reliable density estimations in isotropic-elastic FWI as compared to standard simultaneous inversion approach.

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.

Tracking plastics in the Mediterranean: 2D Lagrangian model.

PubMed

Liubartseva, S; Coppini, G; Lecci, R; Clementi, E

2018-04-01

Drift of floating debris is studied with a 2D Lagrangian model with stochastic beaching and sedimentation of plastics. An ensemble of >10 10 virtual particles is tracked from anthropogenic sources (coastal human populations, rivers, shipping lanes) to environmental destinations (sea surface, coastlines, seabed). Daily analyses of ocean currents and waves provided by CMEMS at a horizontal resolution of 1/16° are used to force the plastics. High spatio-temporal variability in sea-surface plastic concentrations without any stable long-term accumulations is found. Substantial accumulation of plastics is detected on coastlines and the sea bottom. The most contaminated areas are in the Cilician subbasin, Catalan Sea, and near the Po River Delta. Also, highly polluted local patches in the vicinity of sources with limited circulation are identified. An inverse problem solution, used to quantify the origins of plastics, shows that plastic pollution of every Mediterranean country is caused primarily by its own terrestrial sources. Copyright © 2018 Elsevier Ltd. All rights reserved.

Research in Stochastic Processes.

DTIC Science & Technology

1982-10-31

Office of Scientific Research Grant AFOSR F49620 82 C 0009 Period: 1 Noveber 1981 through 31 October 1982 Title: Research in Stochastic Processes Co...STA4ATIS CAMBANIS The work briefly described here was developed in connection with problems arising from and related to the statistical comunication

An efficient distribution method for nonlinear transport problems in highly heterogeneous stochastic porous media

NASA Astrophysics Data System (ADS)

Ibrahima, Fayadhoi; Meyer, Daniel; Tchelepi, Hamdi

2016-04-01

Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are crucial to explore possible scenarios and assess risks in subsurface problems. In particular, nonlinear two-phase flows in porous media are essential, yet challenging, in reservoir simulation and hydrology. Adding highly heterogeneous and uncertain input, such as the permeability and porosity fields, transforms the estimation of the flow response into a tough stochastic problem for which computationally expensive Monte Carlo (MC) simulations remain the preferred option.We propose an alternative approach to evaluate the probability distribution of the (water) saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the (water) saturation. The distribution method draws inspiration from a Lagrangian approach of the stochastic transport problem and expresses the saturation PDF and CDF essentially in terms of a deterministic mapping and the distribution and statistics of scalar random fields. In a large class of applications these random fields can be estimated at low computational costs (few MC runs), thus making the distribution method attractive. Even though the method relies on a key assumption of fixed streamlines, we show that it performs well for high input variances, which is the case of interest. Once the saturation distribution is determined, any one-point statistics thereof can be obtained, especially the saturation average and standard deviation. Moreover, the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be efficiently derived from the distribution method. These statistics can then be used for risk assessment, as well as data assimilation and uncertainty reduction in the prior knowledge of input distributions. We provide various examples and comparisons with MC simulations to illustrate the performance of the method.

Fitting of full Cobb-Douglas and full VRTS cost frontiers by solving goal programming problem

NASA Astrophysics Data System (ADS)

Venkateswarlu, B.; Mahaboob, B.; Subbarami Reddy, C.; Madhusudhana Rao, B.

2017-11-01

The present research article first defines two popular production functions viz, Cobb-Douglas and VRTS production frontiers and their dual cost functions and then derives their cost limited maximal outputs. This paper tells us that the cost limited maximal output is cost efficient. Here the one side goal programming problem is proposed by which the full Cobb-Douglas cost frontier, full VRTS frontier can be fitted. This paper includes the framing of goal programming by which stochastic cost frontier and stochastic VRTS frontiers are fitted. Hasan et al. [1] used a parameter approach Stochastic Frontier Approach (SFA) to examine the technical efficiency of the Malaysian domestic banks listed in the Kuala Lumpur stock Exchange (KLSE) market over the period 2005-2010. AshkanHassani [2] exposed Cobb-Douglas Production Functions application in construction schedule crashing and project risk analysis related to the duration of construction projects. Nan Jiang [3] applied Stochastic Frontier analysis to a panel of New Zealand dairy forms in 1998/99-2006/2007.

Optimization Testbed Cometboards Extended into Stochastic Domain

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Pai, Shantaram S.; Coroneos, Rula M.; Patnaik, Surya N.

2010-01-01

COMparative Evaluation Testbed of Optimization and Analysis Routines for the Design of Structures (CometBoards) is a multidisciplinary design optimization software. It was originally developed for deterministic calculation. It has now been extended into the stochastic domain for structural design problems. For deterministic problems, CometBoards is introduced through its subproblem solution strategy as well as the approximation concept in optimization. In the stochastic domain, a design is formulated as a function of the risk or reliability. Optimum solution including the weight of a structure, is also obtained as a function of reliability. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to 50 percent probability of success, or one failure in two samples. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure that corresponded to unity for reliability. Weight can be reduced to a small value for the most failure-prone design with a compromised reliability approaching zero. The stochastic design optimization (SDO) capability for an industrial problem was obtained by combining three codes: MSC/Nastran code was the deterministic analysis tool, fast probabilistic integrator, or the FPI module of the NESSUS software, was the probabilistic calculator, and CometBoards became the optimizer. The SDO capability requires a finite element structural model, a material model, a load model, and a design model. The stochastic optimization concept is illustrated considering an academic example and a real-life airframe component made of metallic and composite materials.

Quantum-field-theoretical approach to phase-space techniques: Generalizing the positive-P representation

NASA Astrophysics Data System (ADS)

Plimak, L. I.; Fleischhauer, M.; Olsen, M. K.; Collett, M. J.

2003-01-01

We present an introduction to phase-space techniques (PST) based on a quantum-field-theoretical (QFT) approach. In addition to bridging the gap between PST and QFT, our approach results in a number of generalizations of the PST. First, for problems where the usual PST do not result in a genuine Fokker-Planck equation (even after phase-space doubling) and hence fail to produce a stochastic differential equation (SDE), we show how the system in question may be approximated via stochastic difference equations (SΔE). Second, we show that introducing sources into the SDE’s (or SΔE’s) generalizes them to a full quantum nonlinear stochastic response problem (thus generalizing Kubo’s linear reaction theory to a quantum nonlinear stochastic response theory). Third, we establish general relations linking quantum response properties of the system in question to averages of operator products ordered in a way different from time normal. This extends PST to a much wider assemblage of operator products than are usually considered in phase-space approaches. In all cases, our approach yields a very simple and straightforward way of deriving stochastic equations in phase space.

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.

A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media

NASA Astrophysics Data System (ADS)

Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi

2017-02-01

A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod-Patterson-Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiency of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.

New Additions to the Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment.

PubMed

Coll-Font, Jaume; Burton, Brett M; Tate, Jess D; Erem, Burak; Swenson, Darrel J; Wang, Dafang; Brooks, Dana H; van Dam, Peter; Macleod, Rob S

2014-09-01

Cardiac electrical imaging often requires the examination of different forward and inverse problem formulations based on mathematical and numerical approximations of the underlying source and the intervening volume conductor that can generate the associated voltages on the surface of the body. If the goal is to recover the source on the heart from body surface potentials, the solution strategy must include numerical techniques that can incorporate appropriate constraints and recover useful solutions, even though the problem is badly posed. Creating complete software solutions to such problems is a daunting undertaking. In order to make such tools more accessible to a broad array of researchers, the Center for Integrative Biomedical Computing (CIBC) has made an ECG forward/inverse toolkit available within the open source SCIRun system. Here we report on three new methods added to the inverse suite of the toolkit. These new algorithms, namely a Total Variation method, a non-decreasing TMP inverse and a spline-based inverse, consist of two inverse methods that take advantage of the temporal structure of the heart potentials and one that leverages the spatial characteristics of the transmembrane potentials. These three methods further expand the possibilities of researchers in cardiology to explore and compare solutions to their particular imaging problem.

Modelisations et inversions tri-dimensionnelles en prospections gravimetrique et electrique

NASA Astrophysics Data System (ADS)

Boulanger, Olivier

The aim of this thesis is the application of gravity and resistivity methods for mining prospecting. The objectives of the present study are: (1) to build a fast gravity inversion method to interpret surface data; (2) to develop a tool for modelling the electrical potential acquired at surface and in boreholes when the resistivity distribution is heterogeneous; and (3) to define and implement a stochastic inversion scheme allowing the estimation of the subsurface resistivity from electrical data. The first technique concerns the elaboration of a three dimensional (3D) inversion program allowing the interpretation of gravity data using a selection of constraints such as the minimum distance, the flatness, the smoothness and the compactness. These constraints are integrated in a Lagrangian formulation. A multi-grid technique is also implemented to resolve separately large and short gravity wavelengths. The subsurface in the survey area is divided into juxtaposed rectangular prismatic blocks. The problem is solved by calculating the model parameters, i.e. the densities of each block. Weights are given to each block depending on depth, a priori information on density, and density range allowed for the region under investigation. The present code is tested on synthetic data. Advantages and behaviour of each method are compared in the 3D reconstruction. Recovery of geometry (depth, size) and density distribution of the original model is dependent on the set of constraints used. The best combination of constraints experimented for multiple bodies seems to be flatness and minimum volume for multiple bodies. The inversion method is tested on real gravity data. The second tool developed in this thesis is a three-dimensional electrical resistivity modelling code to interpret surface and subsurface data. Based on the integral equation, it calculates the charge density caused by conductivity gradients at each interface of the mesh allowing an exact estimation of the potential. Modelling generates a huge matrix made of Green's functions which is stored by using the method of pyramidal compression. The third method consists to interpret electrical potential measurements from a non-linear geostatistical approach including new constraints. This method estimates an analytical covariance model for the resistivity parameters from the potential data. (Abstract shortened by UMI.)

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…

A Volunteer Computing Project for Solving Geoacoustic Inversion Problems

NASA Astrophysics Data System (ADS)

Zaikin, Oleg; Petrov, Pavel; Posypkin, Mikhail; Bulavintsev, Vadim; Kurochkin, Ilya

2017-12-01

A volunteer computing project aimed at solving computationally hard inverse problems in underwater acoustics is described. This project was used to study the possibilities of the sound speed profile reconstruction in a shallow-water waveguide using a dispersion-based geoacoustic inversion scheme. The computational capabilities provided by the project allowed us to investigate the accuracy of the inversion for different mesh sizes of the sound speed profile discretization grid. This problem suits well for volunteer computing because it can be easily decomposed into independent simpler subproblems.

A Resume of Stochastic, Time-Varying, Linear System Theory with Application to Active-Sonar Signal-Processing Problems

DTIC Science & Technology

1981-06-15

relationships 5 3. Normalized energy in ambiguity function for i = 0 14 k ilI SACLANTCEN SR-50 A RESUME OF STOCHASTIC, TIME-VARYING, LINEAR SYSTEM THEORY WITH...the order in which systems are concatenated is unimportant. These results are exactly analogous to the results of time-invariant linear system theory in...REFERENCES 1. MEIER, L. A rdsum6 of deterministic time-varying linear system theory with application to active sonar signal processing problems, SACLANTCEN

A Fast Fourier transform stochastic analysis of the contaminant transport problem

USGS Publications Warehouse

Deng, F.W.; Cushman, J.H.; Delleur, J.W.

1993-01-01

A three-dimensional stochastic analysis of the contaminant transport problem is developed in the spirit of Naff (1990). The new derivation is more general and simpler than previous analysis. The fast Fourier transformation is used extensively to obtain numerical estimates of the mean concentration and various spatial moments. Data from both the Borden and Cape Cod experiments are used to test the methodology. Results are comparable to results obtained by other methods, and to the experiments themselves.

Solving a Class of Stochastic Mixed-Integer Programs With Branch and Price

DTIC Science & Technology

2006-01-01

a two-dimensional knapsack problem, but for a given m, the objective value gi does not depend on the variance index v. This will be used in a final...optimization. Journal of Multicriteria Decision Analysis 11, 139–150 (2002) 29. Ford, L.R., Fulkerson, D.R.: A suggested computation for the maximal...for solution by a branch-and-price algorithm (B&P). We then survey a number of examples, and use a stochastic facility-location problem (SFLP) for a

A well-posed and stable stochastic Galerkin formulation of the incompressible Navier–Stokes equations with random data

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

Pettersson, Per, E-mail: per.pettersson@uib.no; Nordström, Jan, E-mail: jan.nordstrom@liu.se; Doostan, Alireza, E-mail: alireza.doostan@colorado.edu

2016-02-01

We present a well-posed stochastic Galerkin formulation of the incompressible Navier–Stokes equations with uncertainty in model parameters or the initial and boundary conditions. The stochastic Galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions, resulting in an extended system of equations. A relatively low-order generalized polynomial chaos expansion is sufficient to capture the stochastic solution for the problem considered. We derive boundary conditions for the continuous form of the stochastic Galerkin formulation of the velocity and pressure equations. The resulting problem formulation leads to an energy estimatemore » for the divergence. With suitable boundary data on the pressure and velocity, the energy estimate implies zero divergence of the velocity field. Based on the analysis of the continuous equations, we present a semi-discretized system where the spatial derivatives are approximated using finite difference operators with a summation-by-parts property. With a suitable choice of dissipative boundary conditions imposed weakly through penalty terms, the semi-discrete scheme is shown to be stable. Numerical experiments in the laminar flow regime corroborate the theoretical results and we obtain high-order accurate results for the solution variables and the velocity divergence converges to zero as the mesh is refined.« less

FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management.

PubMed

Li, Pu; Chen, Bing

2011-04-01

Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk. Copyright © 2010 Elsevier Ltd. All rights reserved.

UXO Navigation Technology

DTIC Science & Technology

2008-10-01

modeling operator and dobs is the observed data (details in Pasion 2007). Figure 42. Geometry of EM61HH-MK2 sensor. The transmitter and receiver...1979. Stochastic models, estimation, and control (Vol. 141). Pasion , L. R., 2007. Inversion of Time Domain Electromagnetic Data for the Detection of...Unexploded Ordnance. Ph.D. Thesis, The University of British Columbia. Pasion , L. R., Oldenburg, D. W., 2001. A Discrimination Algorithm for UXO

XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Dennis, Graham R.; Hope, Joseph J.; Johnsson, Mattias T.

2013-01-01

XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code. Program summaryProgram title: XMDS2 Catalogue identifier: AENK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 872490 No. of bytes in distributed program, including test data, etc.: 45522370 Distribution format: tar.gz Programming language: Python and C++. Computer: Any computer with a Unix-like system, a C++ compiler and Python. Operating system: Any Unix-like system; developed under Mac OS X and GNU/Linux. RAM: Problem dependent (roughly 50 bytes per grid point) Classification: 4.3, 6.5. External routines: The external libraries required are problem-dependent. Uses FFTW3 Fourier transforms (used only for FFT-based spectral methods), dSFMT random number generation (used only for stochastic problems), MPI message-passing interface (used only for distributed problems), HDF5, GNU Scientific Library (used only for Bessel-based spectral methods) and a BLAS implementation (used only for non-FFT-based spectral methods). Nature of problem: General coupled initial-value stochastic partial differential equations. Solution method: Spectral method with method-of-lines integration Running time: Determined by the size of the problem

Stochastic Processes in Physics: Deterministic Origins and Control

NASA Astrophysics Data System (ADS)

Demers, Jeffery

Stochastic processes are ubiquitous in the physical sciences and engineering. While often used to model imperfections and experimental uncertainties in the macroscopic world, stochastic processes can attain deeper physical significance when used to model the seemingly random and chaotic nature of the underlying microscopic world. Nowhere more prevalent is this notion than in the field of stochastic thermodynamics - a modern systematic framework used describe mesoscale systems in strongly fluctuating thermal environments which has revolutionized our understanding of, for example, molecular motors, DNA replication, far-from equilibrium systems, and the laws of macroscopic thermodynamics as they apply to the mesoscopic world. With progress, however, come further challenges and deeper questions, most notably in the thermodynamics of information processing and feedback control. Here it is becoming increasingly apparent that, due to divergences and subtleties of interpretation, the deterministic foundations of the stochastic processes themselves must be explored and understood. This thesis presents a survey of stochastic processes in physical systems, the deterministic origins of their emergence, and the subtleties associated with controlling them. First, we study time-dependent billiards in the quivering limit - a limit where a billiard system is indistinguishable from a stochastic system, and where the simplified stochastic system allows us to view issues associated with deterministic time-dependent billiards in a new light and address some long-standing problems. Then, we embark on an exploration of the deterministic microscopic Hamiltonian foundations of non-equilibrium thermodynamics, and we find that important results from mesoscopic stochastic thermodynamics have simple microscopic origins which would not be apparent without the benefit of both the micro and meso perspectives. Finally, we study the problem of stabilizing a stochastic Brownian particle with feedback control, and we find that in order to avoid paradoxes involving the first law of thermodynamics, we need a model for the fine details of the thermal driving noise. The underlying theme of this thesis is the argument that the deterministic microscopic perspective and stochastic mesoscopic perspective are both important and useful, and when used together, we can more deeply and satisfyingly understand the physics occurring over either scale.

Stochastic Robust Mathematical Programming Model for Power System Optimization

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

Liu, Cong; Changhyeok, Lee; Haoyong, Chen

2016-01-01

This paper presents a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with ifferent uncertainty sets. A case study of unit commitment shows the effectiveness of the proposed model and algorithms.

Pricing European option with transaction costs under the fractional long memory stochastic volatility model

NASA Astrophysics Data System (ADS)

Wang, Xiao-Tian; Wu, Min; Zhou, Ze-Min; Jing, Wei-Shu

2012-02-01

This paper deals with the problem of discrete time option pricing using the fractional long memory stochastic volatility model with transaction costs. Through the 'anchoring and adjustment' argument in a discrete time setting, a European call option pricing formula is obtained.

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

Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost

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

Bokanowski, Olivier, E-mail: boka@math.jussieu.fr; Picarelli, Athena, E-mail: athena.picarelli@inria.fr; Zidani, Hasnaa, E-mail: hasnaa.zidani@ensta.fr

2015-02-15

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system ofmore » controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.« less

Adaptive Fuzzy Output Constrained Control Design for Multi-Input Multioutput Stochastic Nonstrict-Feedback Nonlinear Systems.

PubMed

Li, Yongming; Tong, Shaocheng

2017-12-01

In this paper, an adaptive fuzzy output constrained control design approach is addressed for multi-input multioutput uncertain stochastic nonlinear systems in nonstrict-feedback form. The nonlinear systems addressed in this paper possess unstructured uncertainties, unknown gain functions and unknown stochastic disturbances. Fuzzy logic systems are utilized to tackle the problem of unknown nonlinear uncertainties. The barrier Lyapunov function technique is employed to solve the output constrained problem. In the framework of backstepping design, an adaptive fuzzy control design scheme is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Multi-period natural gas market modeling Applications, stochastic extensions and solution approaches

NASA Astrophysics Data System (ADS)

Egging, Rudolf Gerardus

This dissertation develops deterministic and stochastic multi-period mixed complementarity problems (MCP) for the global natural gas market, as well as solution approaches for large-scale stochastic MCP. The deterministic model is unique in the combination of the level of detail of the actors in the natural gas markets and the transport options, the detailed regional and global coverage, the multi-period approach with endogenous capacity expansions for transportation and storage infrastructure, the seasonal variation in demand and the representation of market power according to Nash-Cournot theory. The model is applied to several scenarios for the natural gas market that cover the formation of a cartel by the members of the Gas Exporting Countries Forum, a low availability of unconventional gas in the United States, and cost reductions in long-distance gas transportation. 1 The results provide insights in how different regions are affected by various developments, in terms of production, consumption, traded volumes, prices and profits of market participants. The stochastic MCP is developed and applied to a global natural gas market problem with four scenarios for a time horizon until 2050 with nineteen regions and containing 78,768 variables. The scenarios vary in the possibility of a gas market cartel formation and varying depletion rates of gas reserves in the major gas importing regions. Outcomes for hedging decisions of market participants show some significant shifts in the timing and location of infrastructure investments, thereby affecting local market situations. A first application of Benders decomposition (BD) is presented to solve a large-scale stochastic MCP for the global gas market with many hundreds of first-stage capacity expansion variables and market players exerting various levels of market power. The largest problem solved successfully using BD contained 47,373 variables of which 763 first-stage variables, however using BD did not result in shorter solution times relative to solving the extensive-forms. Larger problems, up to 117,481 variables, were solved in extensive-form, but not when applying BD due to numerical issues. It is discussed how BD could significantly reduce the solution time of large-scale stochastic models, but various challenges remain and more research is needed to assess the potential of Benders decomposition for solving large-scale stochastic MCP. 1 www.gecforum.org

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

DOE PAGES

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

2017-10-26

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

A self-adaptive memeplexes robust search scheme for solving stochastic demands vehicle routing problem

NASA Astrophysics Data System (ADS)

Chen, Xianshun; Feng, Liang; Ong, Yew Soon

2012-07-01

In this article, we proposed a self-adaptive memeplex robust search (SAMRS) for finding robust and reliable solutions that are less sensitive to stochastic behaviours of customer demands and have low probability of route failures, respectively, in vehicle routing problem with stochastic demands (VRPSD). In particular, the contribution of this article is three-fold. First, the proposed SAMRS employs the robust solution search scheme (RS 3) as an approximation of the computationally intensive Monte Carlo simulation, thus reducing the computation cost of fitness evaluation in VRPSD, while directing the search towards robust and reliable solutions. Furthermore, a self-adaptive individual learning based on the conceptual modelling of memeplex is introduced in the SAMRS. Finally, SAMRS incorporates a gene-meme co-evolution model with genetic and memetic representation to effectively manage the search for solutions in VRPSD. Extensive experimental results are then presented for benchmark problems to demonstrate that the proposed SAMRS serves as an efficable means of generating high-quality robust and reliable solutions in VRPSD.

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

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

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

Stochastic optimization model for order acceptance with multiple demand classes and uncertain demand/supply

NASA Astrophysics Data System (ADS)

Yang, Wen; Fung, Richard Y. K.

2014-06-01

This article considers an order acceptance problem in a make-to-stock manufacturing system with multiple demand classes in a finite time horizon. Demands in different periods are random variables and are independent of one another, and replenishments of inventory deviate from the scheduled quantities. The objective of this work is to maximize the expected net profit over the planning horizon by deciding the fraction of the demand that is going to be fulfilled. This article presents a stochastic order acceptance optimization model and analyses the existence of the optimal promising policies. An example of a discrete problem is used to illustrate the policies by applying the dynamic programming method. In order to solve the continuous problems, a heuristic algorithm based on stochastic approximation (HASA) is developed. Finally, the computational results of a case example illustrate the effectiveness and efficiency of the HASA approach, and make the application of the proposed model readily acceptable.

An inventory-theory-based interval-parameter two-stage stochastic programming model for water resources management

NASA Astrophysics Data System (ADS)

Suo, M. Q.; Li, Y. P.; Huang, G. H.

2011-09-01

In this study, an inventory-theory-based interval-parameter two-stage stochastic programming (IB-ITSP) model is proposed through integrating inventory theory into an interval-parameter two-stage stochastic optimization framework. This method can not only address system uncertainties with complex presentation but also reflect transferring batch (the transferring quantity at once) and period (the corresponding cycle time) in decision making problems. A case of water allocation problems in water resources management planning is studied to demonstrate the applicability of this method. Under different flow levels, different transferring measures are generated by this method when the promised water cannot be met. Moreover, interval solutions associated with different transferring costs also have been provided. They can be used for generating decision alternatives and thus help water resources managers to identify desired policies. Compared with the ITSP method, the IB-ITSP model can provide a positive measure for solving water shortage problems and afford useful information for decision makers under uncertainty.

Control Improvement for Jump-Diffusion Processes with Applications to Finance

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

Baeuerle, Nicole, E-mail: nicole.baeuerle@kit.edu; Rieder, Ulrich, E-mail: ulrich.rieder@uni-ulm.de

2012-02-15

We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control {pi}, a new control with a better value. If no improvement is possible, then {pi} is optimal. Such an algorithm is well-known for discrete-time Markov Decision Problems under the name Howard's policy improvement algorithm. The idea can be traced back to Bellman. Here we show with the help of martingale techniques that such an algorithm can also be formulated for stochastic control problems with jump-diffusion processes. As an application we derive some interesting results in financial portfolio optimization.

Walking the Filament of Feasibility: Global Optimization of Highly-Constrained, Multi-Modal Interplanetary Trajectories Using a Novel Stochastic Search Technique

NASA Technical Reports Server (NTRS)

Englander, Arnold C.; Englander, Jacob A.

2017-01-01

Interplanetary trajectory optimization problems are highly complex and are characterized by a large number of decision variables and equality and inequality constraints as well as many locally optimal solutions. Stochastic global search techniques, coupled with a large-scale NLP solver, have been shown to solve such problems but are inadequately robust when the problem constraints become very complex. In this work, we present a novel search algorithm that takes advantage of the fact that equality constraints effectively collapse the solution space to lower dimensionality. This new approach walks the filament'' of feasibility to efficiently find the global optimal solution.

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.

Space-time-modulated stochastic processes

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

Coevolution Maintains Diversity in the Stochastic "Kill the Winner" Model

NASA Astrophysics Data System (ADS)

Xue, Chi; Goldenfeld, Nigel

2017-12-01

The "kill the winner" hypothesis is an attempt to address the problem of diversity in biology. It argues that host-specific predators control the population of each prey, preventing a winner from emerging and thus maintaining the coexistence of all species in the system. We develop a stochastic model for the kill the winner paradigm and show that the stable coexistence state of the deterministic kill the winner model is destroyed by demographic stochasticity, through a cascade of extinction events. We formulate an individual-level stochastic model in which predator-prey coevolution promotes the high diversity of the ecosystem by generating a persistent population flux of species.

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

DOE PAGES

Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M.; ...

2016-04-02

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. In conclusion, we report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.

Analytical pricing formulas for hybrid variance swaps with regime-switching

NASA Astrophysics Data System (ADS)

Roslan, Teh Raihana Nazirah; Cao, Jiling; Zhang, Wenjun

2017-11-01

The problem of pricing discretely-sampled variance swaps under stochastic volatility, stochastic interest rate and regime-switching is being considered in this paper. An extension of the Heston stochastic volatility model structure is done by adding the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. In addition, the parameters of the model are permitted to have transitions following a Markov chain process which is continuous and discoverable. This hybrid model can be used to illustrate certain macroeconomic conditions, for example the changing phases of business stages. The outcome of our regime-switching hybrid model is presented in terms of analytical pricing formulas for variance swaps.

Robust synthetic biology design: stochastic game theory approach.

PubMed

Chen, Bor-Sen; Chang, Chia-Hung; Lee, Hsiao-Ching

2009-07-15

Synthetic biology is to engineer artificial biological systems to investigate natural biological phenomena and for a variety of applications. However, the development of synthetic gene networks is still difficult and most newly created gene networks are non-functioning due to uncertain initial conditions and disturbances of extra-cellular environments on the host cell. At present, how to design a robust synthetic gene network to work properly under these uncertain factors is the most important topic of synthetic biology. A robust regulation design is proposed for a stochastic synthetic gene network to achieve the prescribed steady states under these uncertain factors from the minimax regulation perspective. This minimax regulation design problem can be transformed to an equivalent stochastic game problem. Since it is not easy to solve the robust regulation design problem of synthetic gene networks by non-linear stochastic game method directly, the Takagi-Sugeno (T-S) fuzzy model is proposed to approximate the non-linear synthetic gene network via the linear matrix inequality (LMI) technique through the Robust Control Toolbox in Matlab. Finally, an in silico example is given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed robust gene design method. http://www.ee.nthu.edu.tw/bschen/SyntheticBioDesign_supplement.pdf.

Random variable transformation for generalized stochastic radiative transfer in finite participating slab media

NASA Astrophysics Data System (ADS)

El-Wakil, S. A.; Sallah, M.; El-Hanbaly, A. M.

2015-10-01

The stochastic radiative transfer problem is studied in a participating planar finite continuously fluctuating medium. The problem is considered for specular- and diffusly-reflecting boundaries with linear anisotropic scattering. Random variable transformation (RVT) technique is used to get the complete average for the solution functions, that are represented by the probability-density function (PDF) of the solution process. In the RVT algorithm, a simple integral transformation to the input stochastic process (the extinction function of the medium) is applied. This linear transformation enables us to rewrite the stochastic transport equations in terms of the optical random variable (x) and the optical random thickness (L). Then the transport equation is solved deterministically to get a closed form for the solution as a function of x and L. So, the solution is used to obtain the PDF of the solution functions applying the RVT technique among the input random variable (L) and the output process (the solution functions). The obtained averages of the solution functions are used to get the complete analytical averages for some interesting physical quantities, namely, reflectivity and transmissivity at the medium boundaries. In terms of the average reflectivity and transmissivity, the average of the partial heat fluxes for the generalized problem with internal source of radiation are obtained and represented graphically.

Strategic planning for disaster recovery with stochastic last mile distribution

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

Bent, Russell Whitford; Van Hentenryck, Pascal; Coffrin, Carleton

2010-01-01

This paper considers the single commodity allocation problem (SCAP) for disaster recovery, a fundamental problem faced by all populated areas. SCAPs are complex stochastic optimization problems that combine resource allocation, warehouse routing, and parallel fleet routing. Moreover, these problems must be solved under tight runtime constraints to be practical in real-world disaster situations. This paper formalizes the specification of SCAPs and introduces a novel multi-stage hybrid-optimization algorithm that utilizes the strengths of mixed integer programming, constraint programming, and large neighborhood search. The algorithm was validated on hurricane disaster scenarios generated by Los Alamos National Laboratory using state-of-the-art disaster simulation toolsmore » and is deployed to aid federal organizations in the US.« less

Inference of multi-Gaussian property fields by probabilistic inversion of crosshole ground penetrating radar data using an improved dimensionality reduction

NASA Astrophysics Data System (ADS)

Hunziker, Jürg; Laloy, Eric; Linde, Niklas

2016-04-01

Deterministic inversion procedures can often explain field data, but they only deliver one final subsurface model that depends on the initial model and regularization constraints. This leads to poor insights about the uncertainties associated with the inferred model properties. In contrast, probabilistic inversions can provide an ensemble of model realizations that accurately span the range of possible models that honor the available calibration data and prior information allowing a quantitative description of model uncertainties. We reconsider the problem of inferring the dielectric permittivity (directly related to radar velocity) structure of the subsurface by inversion of first-arrival travel times from crosshole ground penetrating radar (GPR) measurements. We rely on the DREAM_(ZS) algorithm that is a state-of-the-art Markov chain Monte Carlo (MCMC) algorithm. Such algorithms need several orders of magnitude more forward simulations than deterministic algorithms and often become infeasible in high parameter dimensions. To enable high-resolution imaging with MCMC, we use a recently proposed dimensionality reduction approach that allows reproducing 2D multi-Gaussian fields with far fewer parameters than a classical grid discretization. We consider herein a dimensionality reduction from 5000 to 257 unknowns. The first 250 parameters correspond to a spectral representation of random and uncorrelated spatial fluctuations while the remaining seven geostatistical parameters are (1) the standard deviation of the data error, (2) the mean and (3) the variance of the relative electric permittivity, (4) the integral scale along the major axis of anisotropy, (5) the anisotropy angle, (6) the ratio of the integral scale along the minor axis of anisotropy to the integral scale along the major axis of anisotropy and (7) the shape parameter of the Matérn function. The latter essentially defines the type of covariance function (e.g., exponential, Whittle, Gaussian). We present an improved formulation of the dimensionality reduction, and numerically show how it reduces artifacts in the generated models and provides better posterior estimation of the subsurface geostatistical structure. We next show that the results of the method compare very favorably against previous deterministic and stochastic inversion results obtained at the South Oyster Bacterial Transport Site in Virginia, USA. The long-term goal of this work is to enable MCMC-based full waveform inversion of crosshole GPR data.

Inverse gravity modeling for depth varying density structures through genetic algorithm, triangulated facet representation, and switching routines

NASA Astrophysics Data System (ADS)

King, Thomas Steven

A hybrid gravity modeling method is developed to investigate the structure of sedimentary mass bodies. The method incorporates as constraints surficial basement/sediment contacts and topography of a mass target with a quadratically varying density distribution. The inverse modeling utilizes a genetic algorithm (GA) to scan a wide range of the solution space to determine initial models and the Marquardt-Levenberg (ML) nonlinear inversion to determine final models that meet pre-assigned misfit criteria, thus providing an estimate of model variability and uncertainty. The surface modeling technique modifies Delaunay triangulation by allowing individual facets to be manually constructed and non-convex boundaries to be incorporated into the triangulation scheme. The sedimentary body is represented by a set of uneven prisms and edge elements, comprised of tetrahedrons, capped by polyhedrons. Each underlying prism and edge element's top surface is located by determining its point of tangency with the overlying terrain. The remaining overlying mass is gravitationally evaluated and subtracted from the observation points. Inversion then proceeds in the usual sense, but on an irregular tiered surface with each element's density defined relative to their top surface. Efficiency is particularly important due to the large number of facets evaluated for surface representations and the many repeated element evaluations of the stochastic GA. The gravitation of prisms, triangular faceted polygons, and tetrahedrons can be formulated in different ways, either mathematically or by physical approximations, each having distinct characteristics, such as evaluation time, accuracy over various spatial ranges, and computational singularities. A decision tree or switching routine is constructed for each element by combining these characteristics into a single cohesive package that optimizes the computation for accuracy and speed while avoiding singularities. The GA incorporates a subspace technique and parameter dependency to maintain model smoothness during development, thus minimizing creating nonphysical models. The stochastic GA explores the solution space, producing a broad range of unbiased initial models, while the ML inversion is deterministic and thus quickly converges to the final model. The combination allows many solution models to be determined from the same observed data.

Topology optimization under stochastic stiffness

NASA Astrophysics Data System (ADS)

Asadpoure, Alireza

Topology optimization is a systematic computational tool for optimizing the layout of materials within a domain for engineering design problems. It allows variation of structural boundaries and connectivities. This freedom in the design space often enables discovery of new, high performance designs. However, solutions obtained by performing the optimization in a deterministic setting may be impractical or suboptimal when considering real-world engineering conditions with inherent variabilities including (for example) variabilities in fabrication processes and operating conditions. The aim of this work is to provide a computational methodology for topology optimization in the presence of uncertainties associated with structural stiffness, such as uncertain material properties and/or structural geometry. Existing methods for topology optimization under deterministic conditions are first reviewed. Modifications are then proposed to improve the numerical performance of the so-called Heaviside Projection Method (HPM) in continuum domains. Next, two approaches, perturbation and Polynomial Chaos Expansion (PCE), are proposed to account for uncertainties in the optimization procedure. These approaches are intrusive, allowing tight and efficient coupling of the uncertainty quantification with the optimization sensitivity analysis. The work herein develops a robust topology optimization framework aimed at reducing the sensitivity of optimized solutions to uncertainties. The perturbation-based approach combines deterministic topology optimization with a perturbation method for the quantification of uncertainties. The use of perturbation transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. The PCE approach combines the spectral stochastic approach for the representation and propagation of uncertainties with an existing deterministic topology optimization technique. The resulting compact representations for the response quantities allow for efficient and accurate calculation of sensitivities of response statistics with respect to the design variables. The proposed methods are shown to be successful at generating robust optimal topologies. Examples from topology optimization in continuum and discrete domains (truss structures) under uncertainty are presented. It is also shown that proposed methods lead to significant computational savings when compared to Monte Carlo-based optimization which involve multiple formations and inversions of the global stiffness matrix and that results obtained from the proposed method are in excellent agreement with those obtained from a Monte Carlo-based optimization algorithm.

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.

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.

Evaluation of hybrid inverse planning and optimization (HIPO) algorithm for optimization in real-time, high-dose-rate (HDR) brachytherapy for prostate.

PubMed

Pokharel, Shyam; Rana, Suresh; Blikenstaff, Joseph; Sadeghi, Amir; Prestidge, Bradley

2013-07-08

The purpose of this study is to investigate the effectiveness of the HIPO planning and optimization algorithm for real-time prostate HDR brachytherapy. This study consists of 20 patients who underwent ultrasound-based real-time HDR brachytherapy of the prostate using the treatment planning system called Oncentra Prostate (SWIFT version 3.0). The treatment plans for all patients were optimized using inverse dose-volume histogram-based optimization followed by graphical optimization (GRO) in real time. The GRO is manual manipulation of isodose lines slice by slice. The quality of the plan heavily depends on planner expertise and experience. The data for all patients were retrieved later, and treatment plans were created and optimized using HIPO algorithm with the same set of dose constraints, number of catheters, and set of contours as in the real-time optimization algorithm. The HIPO algorithm is a hybrid because it combines both stochastic and deterministic algorithms. The stochastic algorithm, called simulated annealing, searches the optimal catheter distributions for a given set of dose objectives. The deterministic algorithm, called dose-volume histogram-based optimization (DVHO), optimizes three-dimensional dose distribution quickly by moving straight downhill once it is in the advantageous region of the search space given by the stochastic algorithm. The PTV receiving 100% of the prescription dose (V100) was 97.56% and 95.38% with GRO and HIPO, respectively. The mean dose (D(mean)) and minimum dose to 10% volume (D10) for the urethra, rectum, and bladder were all statistically lower with HIPO compared to GRO using the student pair t-test at 5% significance level. HIPO can provide treatment plans with comparable target coverage to that of GRO with a reduction in dose to the critical structures.

A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media

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

Liao, Qinzhuo, E-mail: liaoqz@pku.edu.cn; Zhang, Dongxiao; Tchelepi, Hamdi

A new computational method is proposed for efficient uncertainty quantification of multiphase flow in porous media with stochastic permeability. For pressure estimation, it combines the dimension-adaptive stochastic collocation method on Smolyak sparse grids and the Kronrod–Patterson–Hermite nested quadrature formulas. For saturation estimation, an additional stage is developed, in which the pressure and velocity samples are first generated by the sparse grid interpolation and then substituted into the transport equation to solve for the saturation samples, to address the low regularity problem of the saturation. Numerical examples are presented for multiphase flow with stochastic permeability fields to demonstrate accuracy and efficiencymore » of the proposed two-stage adaptive stochastic collocation method on nested sparse grids.« less

Stochastic sensitivity analysis of the variability of dynamics and transition to chaos in the business cycles model

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev; Ryazanova, Tatyana

2018-01-01

A problem of mathematical modeling of complex stochastic processes in macroeconomics is discussed. For the description of dynamics of income and capital stock, the well-known Kaldor model of business cycles is used as a basic example. The aim of the paper is to give an overview of the variety of stochastic phenomena which occur in Kaldor model forced by additive and parametric random noise. We study a generation of small- and large-amplitude stochastic oscillations, and their mixed-mode intermittency. To analyze these phenomena, we suggest a constructive approach combining the study of the peculiarities of deterministic phase portrait, and stochastic sensitivity of attractors. We show how parametric noise can stabilize the unstable equilibrium and transform dynamics of Kaldor system from order to chaos.

Resonance Properties of Class I and Class II Neurons Differentially Modulated by Channel Noise

NASA Astrophysics Data System (ADS)

Wang, Lei

2018-01-01

Resonance properties of two different neuron types (Class I and Class II) induced by channel noise are investigated in this study. It is found that for Class I neuron, spiking activity is enhanced when certain noise intensity is presented, especially under weak current stimuli -- a typical phenomenon of stochastic resonance (SR); while for Class II neuron, in addition to perform the SR, certain noise intensity would inhibit neuronal activity under some current stimuli -- a typical phenomenon of inverse stochastic resonance (ISR). Moreover, we show that only sodium channel noise or potassium channel noise variation can achieve the similar phenomena. Consequently, the model results suggest that channel noise may exert differential roles in modulating the resonance properties of Class I and Class II neurons.

Total-variation based velocity inversion with Bregmanized operator splitting algorithm

NASA Astrophysics Data System (ADS)

Zand, Toktam; Gholami, Ali

2018-04-01

Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numerical methods for solving such problems in this paper. In order to tackle the ill-conditioning of the problem we use blockiness as a prior information of the subsurface parameters and formulate the problem as a constrained total variation (TV) regularization. The Bregmanized operator splitting (BOS) algorithm as a combination of the Bregman iteration and the proximal forward backward operator splitting method is developed to solve the arranged problem. Two main advantages of this new algorithm are that no matrix inversion is required and that a discrepancy stopping criterion is used to stop the iterations, which allow efficient solution of large-scale problems. The high performance of the proposed TV regularization method is demonstrated using two different experiments: 1) velocity inversion from (synthetic) seismic data which is based on Born approximation, 2) computing interval velocities from RMS velocities via Dix formula. Numerical examples are presented to verify the feasibility of the proposed method for high-resolution velocity inversion.

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

PubMed Central

Zatsiorsky, Vladimir M.

2011-01-01

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem. PMID:21311907

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.

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

Quantum learning of classical stochastic processes: The completely positive realization problem

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

Monràs, Alex; Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543; Winter, Andreas

2016-01-15

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece inmore » the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print http://arxiv.org/abs/1303.3771 (2013)].« less

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.

Assessing the causal effect of policies: an example using stochastic interventions.

PubMed

Díaz, Iván; van der Laan, Mark J

2013-11-19

Assessing the causal effect of an exposure often involves the definition of counterfactual outcomes in a hypothetical world in which the stochastic nature of the exposure is modified. Although stochastic interventions are a powerful tool to measure the causal effect of a realistic intervention that intends to alter the population distribution of an exposure, their importance to answer questions about plausible policy interventions has been obscured by the generalized use of deterministic interventions. In this article, we follow the approach described in Díaz and van der Laan (2012) to define and estimate the effect of an intervention that is expected to cause a truncation in the population distribution of the exposure. The observed data parameter that identifies the causal parameter of interest is established, as well as its efficient influence function under the non-parametric model. Inverse probability of treatment weighted (IPTW), augmented IPTW and targeted minimum loss-based estimators (TMLE) are proposed, their consistency and efficiency properties are determined. An extension to longitudinal data structures is presented and its use is demonstrated with a real data example.

Model reduction method using variable-separation for stochastic saddle point problems

NASA Astrophysics Data System (ADS)

Jiang, Lijian; Li, Qiuqi

2018-02-01

In this paper, we consider a variable-separation (VS) method to solve the stochastic saddle point (SSP) problems. The VS method is applied to obtain the solution in tensor product structure for stochastic partial differential equations (SPDEs) in a mixed formulation. The aim of such a technique is to construct a reduced basis approximation of the solution of the SSP problems. The VS method attempts to get a low rank separated representation of the solution for SSP in a systematic enrichment manner. No iteration is performed at each enrichment step. In order to satisfy the inf-sup condition in the mixed formulation, we enrich the separated terms for the primal system variable at each enrichment step. For the SSP problems by regularization or penalty, we propose a more efficient variable-separation (VS) method, i.e., the variable-separation by penalty method. This can avoid further enrichment of the separated terms in the original mixed formulation. The computation of the variable-separation method decomposes into offline phase and online phase. Sparse low rank tensor approximation method is used to significantly improve the online computation efficiency when the number of separated terms is large. For the applications of SSP problems, we present three numerical examples to illustrate the performance of the proposed methods.

Multiband infrared inversion for low-concentration methane monitoring in a confined dust-polluted atmosphere.

PubMed

Wang, Wenzheng; Wang, Yanming; Song, Wujun; Li, Xueqin

2017-03-20

A multiband infrared diagnostic (MBID) method for methane emission monitoring in limited underground environments was presented considering the strong optical background of gas/solid attenuation. Based on spatial distribution of aerosols and complex refractive index of dust particles, forward calculations were carried out with/without methane to obtain the spectral transmittance through the participating atmosphere in a mine roadway. Considering the concurrent attenuation and absorption behavior of dust and gases, four infrared wavebands were selected to retrieve the methane concentration combined with a stochastic particle swarm optimization (SPSO) algorithm. Inversion results prove that the presented MBID method is robust and effective in identifying methane at concentrations of 0.1% or even lower with inversed relative error within 10%. Further analyses illustrate that the four selected wavebands are indispensable, and the MBID method is still valid with transmission signal disturbance in a conventional dust-polluted atmosphere under mechanized mining condition. However, the effective detection distance should be limited within 50 m to ensure inversed relative error less than 5% at 1% methane concentration.

O the Derivation of the Schroedinger Equation from Stochastic Mechanics.

NASA Astrophysics Data System (ADS)

Wallstrom, Timothy Clarke

The thesis is divided into four largely independent chapters. The first three chapters treat mathematical problems in the theory of stochastic mechanics. The fourth chapter deals with stochastic mechanisms as a physical theory and shows that the Schrodinger equation cannot be derived from existing formulations of stochastic mechanics, as had previously been believed. Since the drift coefficients of stochastic mechanical diffusions are undefined on the nodes, or zeros of the density, an important problem has been to show that the sample paths stay away from the nodes. In Chapter 1, it is shown that for a smooth wavefunction, the closest approach to the nodes can be bounded solely in terms of the time -integrated energy. The ergodic properties of stochastic mechanical diffusions are greatly complicated by the tendency of the particles to avoid the nodes. In Chapter 2, it is shown that a sufficient condition for a stationary process to be ergodic is that there exist positive t and c such that for all x and y, p^{t} (x,y) > cp(y), and this result is applied to show that the set of spin-1over2 diffusions is uniformly ergodic. In stochastic mechanics, the Bopp-Haag-Dankel diffusions on IR^3times SO(3) are used to represent particles with spin. Nelson has conjectured that in the limit as the particle's moment of inertia I goes to zero, the projections of the Bopp -Haag-Dankel diffusions onto IR^3 converge to a Markovian limit process. This conjecture is proved for the spin-1over2 case in Chapter 3, and the limit process identified as the diffusion naturally associated with the solution to the regular Pauli equation. In Chapter 4 it is shown that the general solution of the stochastic Newton equation does not correspond to a solution of the Schrodinger equation, and that there are solutions to the Schrodinger equation which do not satisfy the Guerra-Morato Lagrangian variational principle. These observations are shown to apply equally to other existing formulations of stochastic mechanics, and it is argued that these difficulties represent fundamental inadequacies in the physical foundation of stochastic mechanics.

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.

Periodic measure for the stochastic equation of the barotropic viscous gas in a discretized one-dimensional domain

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

Benseghir, Rym, E-mail: benseghirrym@ymail.com, E-mail: benseghirrym@ymail.com; Benchettah, Azzedine, E-mail: abenchettah@hotmail.com; Raynaud de Fitte, Paul, E-mail: prf@univ-rouen.fr

2015-11-30

A stochastic equation system corresponding to the description of the motion of a barotropic viscous gas in a discretized one-dimensional domain with a weight regularizing the density is considered. In [2], the existence of an invariant measure was established for this discretized problem in the stationary case. In this paper, applying a slightly modified version of Khas’minskii’s theorem [5], we generalize this result in the periodic case by proving the existence of a periodic measure for this problem.

Effect of multiplicative noise on stationary stochastic process

NASA Astrophysics Data System (ADS)

Kargovsky, A. V.; Chikishev, A. Yu.; Chichigina, O. A.

2018-03-01

An open system that can be analyzed using the Langevin equation with multiplicative noise is considered. The stationary state of the system results from a balance of deterministic damping and random pumping simulated as noise with controlled periodicity. The dependence of statistical moments of the variable that characterizes the system on parameters of the problem is studied. A nontrivial decrease in the mean value of the main variable with an increase in noise stochasticity is revealed. Applications of the results in several physical, chemical, biological, and technical problems of natural and humanitarian sciences are discussed.

Output regulation control for switched stochastic delay systems with dissipative property under error-dependent switching

NASA Astrophysics Data System (ADS)

Li, L. L.; Jin, C. L.; Ge, X.

2018-01-01

In this paper, the output regulation problem with dissipative property for a class of switched stochastic delay systems is investigated, based on an error-dependent switching law. Under the assumption that none subsystem is solvable for the problem, a sufficient condition is derived by structuring multiple Lyapunov-Krasovskii functionals with respect to multiple supply rates, via designing error feedback regulators. The condition is also established when dissipative property reduces to passive property. Finally, two numerical examples are given to demonstrate the feasibility and efficiency of the present method.

Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets

NASA Astrophysics Data System (ADS)

Gontis, V.; Kononovicius, A.

2017-10-01

We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic differential equations. In this contribution we address this problem by analyzing empirical return and trading activity time series from the Forex. From the empirical time series we obtain probability density functions of burst and inter-burst duration. Our analysis reveals that the power-law exponents of the obtained probability density functions are close to 3 / 2, which is a characteristic feature of the one-dimensional stochastic processes. This is in a good agreement with earlier proposed model of absolute return based on the non-linear stochastic differential equations derived from the agent-based herding model.

Stochastic Multi-Commodity Facility Location Based on a New Scenario Generation Technique

NASA Astrophysics Data System (ADS)

Mahootchi, M.; Fattahi, M.; Khakbazan, E.

2011-11-01

This paper extends two models for stochastic multi-commodity facility location problem. The problem is formulated as two-stage stochastic programming. As a main point of this study, a new algorithm is applied to efficiently generate scenarios for uncertain correlated customers' demands. This algorithm uses Latin Hypercube Sampling (LHS) and a scenario reduction approach. The relation between customer satisfaction level and cost are considered in model I. The risk measure using Conditional Value-at-Risk (CVaR) is embedded into the optimization model II. Here, the structure of the network contains three facility layers including plants, distribution centers, and retailers. The first stage decisions are the number, locations, and the capacity of distribution centers. In the second stage, the decisions are the amount of productions, the volume of transportation between plants and customers.

Bi-Objective Flexible Job-Shop Scheduling Problem Considering Energy Consumption under Stochastic Processing Times.

PubMed

Yang, Xin; Zeng, Zhenxiang; Wang, Ruidong; Sun, Xueshan

2016-01-01

This paper presents a novel method on the optimization of bi-objective Flexible Job-shop Scheduling Problem (FJSP) under stochastic processing times. The robust counterpart model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to solve the bi-objective FJSP with consideration of the completion time and the total energy consumption under stochastic processing times. The case study on GM Corporation verifies that the NSGA-II used in this paper is effective and has advantages to solve the proposed model comparing with HPSO and PSO+SA. The idea and method of the paper can be generalized widely in the manufacturing industry, because it can reduce the energy consumption of the energy-intensive manufacturing enterprise with less investment when the new approach is applied in existing systems.

Bi-Objective Flexible Job-Shop Scheduling Problem Considering Energy Consumption under Stochastic Processing Times

PubMed Central

Zeng, Zhenxiang; Wang, Ruidong; Sun, Xueshan

2016-01-01

This paper presents a novel method on the optimization of bi-objective Flexible Job-shop Scheduling Problem (FJSP) under stochastic processing times. The robust counterpart model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to solve the bi-objective FJSP with consideration of the completion time and the total energy consumption under stochastic processing times. The case study on GM Corporation verifies that the NSGA-II used in this paper is effective and has advantages to solve the proposed model comparing with HPSO and PSO+SA. The idea and method of the paper can be generalized widely in the manufacturing industry, because it can reduce the energy consumption of the energy-intensive manufacturing enterprise with less investment when the new approach is applied in existing systems. PMID:27907163

Integration of Monte-Carlo ray tracing with a stochastic optimisation method: application to the design of solar receiver geometry.

PubMed

Asselineau, Charles-Alexis; Zapata, Jose; Pye, John

2015-06-01

A stochastic optimisation method adapted to illumination and radiative heat transfer problems involving Monte-Carlo ray-tracing is presented. A solar receiver shape optimisation case study illustrates the advantages of the method and its potential: efficient receivers are identified using a moderate computational cost.

Fault detection and diagnosis for non-Gaussian stochastic distribution systems with time delays via RBF neural networks.

PubMed

Yi, Qu; Zhan-ming, Li; Er-chao, Li

2012-11-01

A new fault detection and diagnosis (FDD) problem via the output probability density functions (PDFs) for non-gausian stochastic distribution systems (SDSs) is investigated. The PDFs can be approximated by radial basis functions (RBFs) neural networks. Different from conventional FDD problems, the measured information for FDD is the output stochastic distributions and the stochastic variables involved are not confined to Gaussian ones. A (RBFs) neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighings of the RBFs neural network. In this work, a nonlinear adaptive observer-based fault detection and diagnosis algorithm is presented by introducing the tuning parameter so that the residual is as sensitive as possible to the fault. Stability and Convergency analysis is performed in fault detection and fault diagnosis analysis for the error dynamic system. At last, an illustrated example is given to demonstrate the efficiency of the proposed algorithm, and satisfactory results have been obtained. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Calculating the Malliavin derivative of some stochastic mechanics problems

PubMed Central

Hauseux, Paul; Hale, Jack S.

2017-01-01

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. PMID:29261776

Efficient sampling of parsimonious inversion histories with application to genome rearrangement in Yersinia.

PubMed

Miklós, István; Darling, Aaron E

2009-06-22

Inversions are among the most common mutations acting on the order and orientation of genes in a genome, and polynomial-time algorithms exist to obtain a minimal length series of inversions that transform one genome arrangement to another. However, the minimum length series of inversions (the optimal sorting path) is often not unique as many such optimal sorting paths exist. If we assume that all optimal sorting paths are equally likely, then statistical inference on genome arrangement history must account for all such sorting paths and not just a single estimate. No deterministic polynomial algorithm is known to count the number of optimal sorting paths nor sample from the uniform distribution of optimal sorting paths. Here, we propose a stochastic method that uniformly samples the set of all optimal sorting paths. Our method uses a novel formulation of parallel Markov chain Monte Carlo. In practice, our method can quickly estimate the total number of optimal sorting paths. We introduce a variant of our approach in which short inversions are modeled to be more likely, and we show how the method can be used to estimate the distribution of inversion lengths and breakpoint usage in pathogenic Yersinia pestis. The proposed method has been implemented in a program called "MC4Inversion." We draw comparison of MC4Inversion to the sampler implemented in BADGER and a previously described importance sampling (IS) technique. We find that on high-divergence data sets, MC4Inversion finds more optimal sorting paths per second than BADGER and the IS technique and simultaneously avoids bias inherent in the IS technique.

Model-based image analysis of a tethered Brownian fibre for shear stress sensing

PubMed Central

2017-01-01

The measurement of fluid dynamic shear stress acting on a biologically relevant surface is a challenging problem, particularly in the complex environment of, for example, the vasculature. While an experimental method for the direct detection of wall shear stress via the imaging of a synthetic biology nanorod has recently been developed, the data interpretation so far has been limited to phenomenological random walk modelling, small-angle approximation, and image analysis techniques which do not take into account the production of an image from a three-dimensional subject. In this report, we develop a mathematical and statistical framework to estimate shear stress from rapid imaging sequences based firstly on stochastic modelling of the dynamics of a tethered Brownian fibre in shear flow, and secondly on a novel model-based image analysis, which reconstructs fibre positions by solving the inverse problem of image formation. This framework is tested on experimental data, providing the first mechanistically rational analysis of the novel assay. What follows further develops the established theory for an untethered particle in a semi-dilute suspension, which is of relevance to, for example, the study of Brownian nanowires without flow, and presents new ideas in the field of multi-disciplinary image analysis. PMID:29212755

Stochastic optimization for the detection of changes in maternal heart rate kinetics during pregnancy

NASA Astrophysics Data System (ADS)

Zakynthinaki, M. S.; Barakat, R. O.; Cordente Martínez, C. A.; Sampedro Molinuevo, J.

2011-03-01

The stochastic optimization method ALOPEX IV has been successfully applied to the problem of detecting possible changes in the maternal heart rate kinetics during pregnancy. For this reason, maternal heart rate data were recorded before, during and after gestation, during sessions of exercises of constant mild intensity; ALOPEX IV stochastic optimization was used to calculate the parameter values that optimally fit a dynamical systems model to the experimental data. The results not only demonstrate the effectiveness of ALOPEX IV stochastic optimization, but also have important implications in the area of exercise physiology, as they reveal important changes in the maternal cardiovascular dynamics, as a result of pregnancy.

Doubly stochastic radial basis function methods

NASA Astrophysics Data System (ADS)

Yang, Fenglian; Yan, Liang; Ling, Leevan

2018-06-01

We propose a doubly stochastic radial basis function (DSRBF) method for function recoveries. Instead of a constant, we treat the RBF shape parameters as stochastic variables whose distribution were determined by a stochastic leave-one-out cross validation (LOOCV) estimation. A careful operation count is provided in order to determine the ranges of all the parameters in our methods. The overhead cost for setting up the proposed DSRBF method is O (n2) for function recovery problems with n basis. Numerical experiments confirm that the proposed method not only outperforms constant shape parameter formulation (in terms of accuracy with comparable computational cost) but also the optimal LOOCV formulation (in terms of both accuracy and computational cost).

Frnakenstein: multiple target inverse RNA folding.

PubMed

Lyngsø, Rune B; Anderson, James W J; Sizikova, Elena; Badugu, Amarendra; Hyland, Tomas; Hein, Jotun

2012-10-09

RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein.

Frnakenstein: multiple target inverse RNA folding

PubMed Central

2012-01-01

Background RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. Results In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Conclusions Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein. PMID:23043260

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations

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

Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C., E-mail: waymire@math.oregonstate.edu

2015-07-15

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturallymore » arise as a result of this investigation.« less

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations.

PubMed

Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C

2015-07-01

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.

Kalman filters for fractional discrete-time stochastic systems along with time-delay in the observation signal

NASA Astrophysics Data System (ADS)

Torabi, H.; Pariz, N.; Karimpour, A.

2016-02-01

This paper investigates fractional Kalman filters when time-delay is entered in the observation signal in the discrete-time stochastic fractional order state-space representation. After investigating the common fractional Kalman filter, we try to derive a fractional Kalman filter for time-delay fractional systems. A detailed derivation is given. Fractional Kalman filters will be used to estimate recursively the states of fractional order state-space systems based on minimizing the cost function when there is a constant time delay (d) in the observation signal. The problem will be solved by converting the filtering problem to a usual d-step prediction problem for delay-free fractional systems.

Stochastic correlative firing for figure-ground segregation.

PubMed

Chen, Zhe

2005-03-01

Segregation of sensory inputs into separate objects is a central aspect of perception and arises in all sensory modalities. The figure-ground segregation problem requires identifying an object of interest in a complex scene, in many cases given binaural auditory or binocular visual observations. The computations required for visual and auditory figure-ground segregation share many common features and can be cast within a unified framework. Sensory perception can be viewed as a problem of optimizing information transmission. Here we suggest a stochastic correlative firing mechanism and an associative learning rule for figure-ground segregation in several classic sensory perception tasks, including the cocktail party problem in binaural hearing, binocular fusion of stereo images, and Gestalt grouping in motion perception.

Supercomputer optimizations for stochastic optimal control applications

NASA Technical Reports Server (NTRS)

Chung, Siu-Leung; Hanson, Floyd B.; Xu, Huihuang

1991-01-01

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.

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.

Mean-square state and parameter estimation for stochastic linear systems with Gaussian and Poisson noises

NASA Astrophysics Data System (ADS)

Basin, M.; Maldonado, J. J.; Zendejo, O.

2016-07-01

This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.

First-principles theory of anharmonicity and the inverse isotope effect in superconducting palladium-hydride compounds.

PubMed

Errea, Ion; Calandra, Matteo; Mauri, Francesco

2013-10-25

Palladium hydrides display the largest isotope effect anomaly known in the literature. Replacement of hydrogen with the heavier isotopes leads to higher superconducting temperatures, a behavior inconsistent with harmonic theory. Solving the self-consistent harmonic approximation by a stochastic approach, we obtain the anharmonic free energy, the thermal expansion, and the superconducting properties fully ab initio. We find that the phonon spectra are strongly renormalized by anharmonicity far beyond the perturbative regime. Superconductivity is phonon mediated, but the harmonic approximation largely overestimates the superconducting critical temperatures. We explain the inverse isotope effect, obtaining a -0.38 value for the isotope coefficient in good agreement with experiments, hydrogen anharmonicity being mainly responsible for the isotope anomaly.

Silicon-carbon bond inversions driven by 60-keV electrons in graphene.

PubMed

Susi, Toma; Kotakoski, Jani; Kepaptsoglou, Demie; Mangler, Clemens; Lovejoy, Tracy C; Krivanek, Ondrej L; Zan, Recep; Bangert, Ursel; Ayala, Paola; Meyer, Jannik C; Ramasse, Quentin

2014-09-12

We demonstrate that 60-keV electron irradiation drives the diffusion of threefold-coordinated Si dopants in graphene by one lattice site at a time. First principles simulations reveal that each step is caused by an electron impact on a C atom next to the dopant. Although the atomic motion happens below our experimental time resolution, stochastic analysis of 38 such lattice jumps reveals a probability for their occurrence in a good agreement with the simulations. Conversions from three- to fourfold coordinated dopant structures and the subsequent reverse process are significantly less likely than the direct bond inversion. Our results thus provide a model of nondestructive and atomically precise structural modification and detection for two-dimensional materials.

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

Minimum Action Path Theory Reveals the Details of Stochastic Transitions Out of Oscillatory States

NASA Astrophysics Data System (ADS)

de la Cruz, Roberto; Perez-Carrasco, Ruben; Guerrero, Pilar; Alarcon, Tomas; Page, Karen M.

2018-03-01

Cell state determination is the outcome of intrinsically stochastic biochemical reactions. Transitions between such states are studied as noise-driven escape problems in the chemical species space. Escape can occur via multiple possible multidimensional paths, with probabilities depending nonlocally on the noise. Here we characterize the escape from an oscillatory biochemical state by minimizing the Freidlin-Wentzell action, deriving from it the stochastic spiral exit path from the limit cycle. We also use the minimized action to infer the escape time probability density function.

? filtering for stochastic systems driven by Poisson processes

NASA Astrophysics Data System (ADS)

Song, Bo; Wu, Zheng-Guang; Park, Ju H.; Shi, Guodong; Zhang, Ya

2015-01-01

This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

Minimum Action Path Theory Reveals the Details of Stochastic Transitions Out of Oscillatory States.

PubMed

de la Cruz, Roberto; Perez-Carrasco, Ruben; Guerrero, Pilar; Alarcon, Tomas; Page, Karen M

2018-03-23

Cell state determination is the outcome of intrinsically stochastic biochemical reactions. Transitions between such states are studied as noise-driven escape problems in the chemical species space. Escape can occur via multiple possible multidimensional paths, with probabilities depending nonlocally on the noise. Here we characterize the escape from an oscillatory biochemical state by minimizing the Freidlin-Wentzell action, deriving from it the stochastic spiral exit path from the limit cycle. We also use the minimized action to infer the escape time probability density function.

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.

Analytical Assessment for Transient Stability Under Stochastic Continuous Disturbances

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

Ju, Ping; Li, Hongyu; Gan, Chun

Here, with the growing integration of renewable power generation, plug-in electric vehicles, and other sources of uncertainty, increasing stochastic continuous disturbances are brought to power systems. The impact of stochastic continuous disturbances on power system transient stability attracts significant attention. To address this problem, this paper proposes an analytical assessment method for transient stability of multi-machine power systems under stochastic continuous disturbances. In the proposed method, a probability measure of transient stability is presented and analytically solved by stochastic averaging. Compared with the conventional method (Monte Carlo simulation), the proposed method is many orders of magnitude faster, which makes itmore » very attractive in practice when many plans for transient stability must be compared or when transient stability must be analyzed quickly. Also, it is found that the evolution of system energy over time is almost a simple diffusion process by the proposed method, which explains the impact mechanism of stochastic continuous disturbances on transient stability in theory.« less

Stochastic Spiking Neural Networks Enabled by Magnetic Tunnel Junctions: From Nontelegraphic to Telegraphic Switching Regimes

NASA Astrophysics Data System (ADS)

Liyanagedera, Chamika M.; Sengupta, Abhronil; Jaiswal, Akhilesh; Roy, Kaushik

2017-12-01

Stochastic spiking neural networks based on nanoelectronic spin devices can be a possible pathway to achieving "brainlike" compact and energy-efficient cognitive intelligence. The computational model attempt to exploit the intrinsic device stochasticity of nanoelectronic synaptic or neural components to perform learning or inference. However, there has been limited analysis on the scaling effect of stochastic spin devices and its impact on the operation of such stochastic networks at the system level. This work attempts to explore the design space and analyze the performance of nanomagnet-based stochastic neuromorphic computing architectures for magnets with different barrier heights. We illustrate how the underlying network architecture must be modified to account for the random telegraphic switching behavior displayed by magnets with low barrier heights as they are scaled into the superparamagnetic regime. We perform a device-to-system-level analysis on a deep neural-network architecture for a digit-recognition problem on the MNIST data set.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low-dimensional input stochastic models to represent thermal diffusivity in two-phase microstructures. This model is used in analyzing the effect of topological variations of two-phase microstructures on the evolution of temperature in heat conduction processes.

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

Randomly Sampled-Data Control Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Han, Kuoruey

1990-01-01

The purpose is to solve the Linear Quadratic Regulator (LQR) problem with random time sampling. Such a sampling scheme may arise from imperfect instrumentation as in the case of sampling jitter. It can also model the stochastic information exchange among decentralized controllers to name just a few. A practical suboptimal controller is proposed with the nice property of mean square stability. The proposed controller is suboptimal in the sense that the control structure is limited to be linear. Because of i. i. d. assumption, this does not seem unreasonable. Once the control structure is fixed, the stochastic discrete optimal control problem is transformed into an equivalent deterministic optimal control problem with dynamics described by the matrix difference equation. The N-horizon control problem is solved using the Lagrange's multiplier method. The infinite horizon control problem is formulated as a classical minimization problem. Assuming existence of solution to the minimization problem, the total system is shown to be mean square stable under certain observability conditions. Computer simulations are performed to illustrate these conditions.

Physically-based parameterization of spatially variable soil and vegetation using satellite multispectral data

NASA Technical Reports Server (NTRS)

Jasinski, Michael F.; Eagleson, Peter S.

1989-01-01

A stochastic-geometric landsurface reflectance model is formulated and tested for the parameterization of spatially variable vegetation and soil at subpixel scales using satellite multispectral images without ground truth. Landscapes are conceptualized as 3-D Lambertian reflecting surfaces consisting of plant canopies, represented by solid geometric figures, superposed on a flat soil background. A computer simulation program is developed to investigate image characteristics at various spatial aggregations representative of satellite observational scales, or pixels. The evolution of the shape and structure of the red-infrared space, or scattergram, of typical semivegetated scenes is investigated by sequentially introducing model variables into the simulation. The analytical moments of the total pixel reflectance, including the mean, variance, spatial covariance, and cross-spectral covariance, are derived in terms of the moments of the individual fractional cover and reflectance components. The moments are applied to the solution of the inverse problem: The estimation of subpixel landscape properties on a pixel-by-pixel basis, given only one multispectral image and limited assumptions on the structure of the landscape. The landsurface reflectance model and inversion technique are tested using actual aerial radiometric data collected over regularly spaced pecan trees, and using both aerial and LANDSAT Thematic Mapper data obtained over discontinuous, randomly spaced conifer canopies in a natural forested watershed. Different amounts of solar backscattered diffuse radiation are assumed and the sensitivity of the estimated landsurface parameters to those amounts is examined.

Ultimate open pit stochastic optimization

NASA Astrophysics Data System (ADS)

Marcotte, Denis; Caron, Josiane

2013-02-01

Classical open pit optimization (maximum closure problem) is made on block estimates, without directly considering the block grades uncertainty. We propose an alternative approach of stochastic optimization. The stochastic optimization is taken as the optimal pit computed on the block expected profits, rather than expected grades, computed from a series of conditional simulations. The stochastic optimization generates, by construction, larger ore and waste tonnages than the classical optimization. Contrary to the classical approach, the stochastic optimization is conditionally unbiased for the realized profit given the predicted profit. A series of simulated deposits with different variograms are used to compare the stochastic approach, the classical approach and the simulated approach that maximizes expected profit among simulated designs. Profits obtained with the stochastic optimization are generally larger than the classical or simulated pit. The main factor controlling the relative gain of stochastic optimization compared to classical approach and simulated pit is shown to be the information level as measured by the boreholes spacing/range ratio. The relative gains of the stochastic approach over the classical approach increase with the treatment costs but decrease with mining costs. The relative gains of the stochastic approach over the simulated pit approach increase both with the treatment and mining costs. At early stages of an open pit project, when uncertainty is large, the stochastic optimization approach appears preferable to the classical approach or the simulated pit approach for fair comparison of the values of alternative projects and for the initial design and planning of the open pit.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« 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

Time-domain full waveform inversion using instantaneous phase information with damping

NASA Astrophysics Data System (ADS)

Luo, Jingrui; Wu, Ru-Shan; Gao, Fuchun

2018-06-01

In time domain, the instantaneous phase can be obtained from the complex seismic trace using Hilbert transform. The instantaneous phase information has great potential in overcoming the local minima problem and improving the result of full waveform inversion. However, the phase wrapping problem, which comes from numerical calculation, prevents its application. In order to avoid the phase wrapping problem, we choose to use the exponential phase combined with the damping method, which gives instantaneous phase-based multi-stage inversion. We construct the objective functions based on the exponential instantaneous phase, and also derive the corresponding gradient operators. Conventional full waveform inversion and the instantaneous phase-based inversion are compared with numerical examples, which indicates that in the case without low frequency information in seismic data, our method is an effective and efficient approach for initial model construction for full waveform inversion.

Asymmetric and Stochastic Behavior in Magnetic Vortices Studied by Soft X-ray Microscopy

NASA Astrophysics Data System (ADS)

Im, Mi-Young

Asymmetry and stochasticity in spin processes are not only long-standing fundamental issues but also highly relevant to technological applications of nanomagnetic structures to memory and storage nanodevices. Those nontrivial phenomena have been studied by direct imaging of spin structures in magnetic vortices utilizing magnetic transmission soft x-ray microscopy (BL6.1.2 at ALS). Magnetic vortices have attracted enormous scientific interests due to their fascinating spin structures consisting of circularity rotating clockwise (c = + 1) or counter-clockwise (c = -1) and polarity pointing either up (p = + 1) or down (p = -1). We observed a symmetry breaking in the formation process of vortex structures in circular permalloy (Ni80Fe20) disks. The generation rates of two different vortex groups with the signature of cp = + 1 and cp =-1 are completely asymmetric. The asymmetric nature was interpreted to be triggered by ``intrinsic'' Dzyaloshinskii-Moriya interaction (DMI) arising from the spin-orbit coupling due to the lack of inversion symmetry near the disk surface and ``extrinsic'' factors such as roughness and defects. We also investigated the stochastic behavior of vortex creation in the arrays of asymmetric disks. The stochasticity was found to be very sensitive to the geometry of disk arrays, particularly interdisk distance. The experimentally observed phenomenon couldn't be explained by thermal fluctuation effect, which has been considered as a main reason for the stochastic behavior in spin processes. We demonstrated for the first time that the ultrafast dynamics at the early stage of vortex creation, which has a character of classical chaos significantly affects the stochastic nature observed at the steady state in asymmetric disks. This work provided the new perspective of dynamics as a critical factor contributing to the stochasticity in spin processes and also the possibility for the control of the intrinsic stochastic nature by optimizing the design of asymmetric disk arrays. This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, by Leading Foreign Research Institute Recruitment Program through the NRF.

Low-complexity stochastic modeling of wall-bounded shear flows

NASA Astrophysics Data System (ADS)

Zare, Armin

Turbulent flows are ubiquitous in nature and they appear in many engineering applications. Transition to turbulence, in general, increases skin-friction drag in air/water vehicles compromising their fuel-efficiency and reduces the efficiency and longevity of wind turbines. While traditional flow control techniques combine physical intuition with costly experiments, their effectiveness can be significantly enhanced by control design based on low-complexity models and optimization. In this dissertation, we develop a theoretical and computational framework for the low-complexity stochastic modeling of wall-bounded shear flows. Part I of the dissertation is devoted to the development of a modeling framework which incorporates data-driven techniques to refine physics-based models. We consider the problem of completing partially known sample statistics in a way that is consistent with underlying stochastically driven linear dynamics. Neither the statistics nor the dynamics are precisely known. Thus, our objective is to reconcile the two in a parsimonious manner. To this end, we formulate optimization problems to identify the dynamics and directionality of input excitation in order to explain and complete available covariance data. For problem sizes that general-purpose solvers cannot handle, we develop customized optimization algorithms based on alternating direction methods. The solution to the optimization problem provides information about critical directions that have maximal effect in bringing model and statistics in agreement. In Part II, we employ our modeling framework to account for statistical signatures of turbulent channel flow using low-complexity stochastic dynamical models. We demonstrate that white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics and develop models for colored-in-time forcing of the linearized Navier-Stokes equations. We also examine the efficacy of stochastically forced linearized NS equations and their parabolized equivalents in the receptivity analysis of velocity fluctuations to external sources of excitation as well as capturing the effect of the slowly-varying base flow on streamwise streaks and Tollmien-Schlichting waves. In Part III, we develop a model-based approach to design surface actuation of turbulent channel flow in the form of streamwise traveling waves. This approach is capable of identifying the drag reducing trends of traveling waves in a simulation-free manner. We also use the stochastically forced linearized NS equations to examine the Reynolds number independent effects of spanwise wall oscillations on drag reduction in turbulent channel flows. This allows us to extend the predictive capability of our simulation-free approach to high Reynolds numbers.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Opanchuk, B.; Drummond, P. D.

2013-04-01

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.

Stochastic Inversion of 2D Magnetotelluric Data

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

Chen, Jinsong

2010-07-01

The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function is explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, itmore » provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows« less

Extreme wave formation in unidirectional sea due to stochastic wave phase dynamics

NASA Astrophysics Data System (ADS)

Wang, Rui; Balachandran, Balakumar

2018-07-01

The authors consider a stochastic model based on the interaction and phase coupling amongst wave components that are modified envelope soliton solutions to the nonlinear Schrödinger equation. A probabilistic study is carried out and the resulting findings are compared with ocean wave field observations and laboratory experimental results. The wave height probability distribution obtained from the model is found to match well with prior data in the large wave height region. From the eigenvalue spectrum obtained through the Inverse Scattering Transform, it is revealed that the deep-water wave groups move at a speed different from the linear group speed, which justifies the inclusion of phase correction to the envelope solitary wave components. It is determined that phase synchronization amongst elementary solitary wave components can be critical for the formation of extreme waves in unidirectional sea states.

Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

NASA Astrophysics Data System (ADS)

Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun

2015-12-01

This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.

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.

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

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration

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

Berezhkovskii, Alexander M.; Shvartsman, Stanislav Y.

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and themore » perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.« less

Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem.

PubMed

Pandiselvi, S; Raja, R; Cao, Jinde; Rajchakit, G; Ahmad, Bashir

2018-01-01

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.

Asynchronous Incremental Stochastic Dual Descent Algorithm for Network Resource Allocation

NASA Astrophysics Data System (ADS)

Bedi, Amrit Singh; Rajawat, Ketan

2018-05-01

Stochastic network optimization problems entail finding resource allocation policies that are optimum on an average but must be designed in an online fashion. Such problems are ubiquitous in communication networks, where resources such as energy and bandwidth are divided among nodes to satisfy certain long-term objectives. This paper proposes an asynchronous incremental dual decent resource allocation algorithm that utilizes delayed stochastic {gradients} for carrying out its updates. The proposed algorithm is well-suited to heterogeneous networks as it allows the computationally-challenged or energy-starved nodes to, at times, postpone the updates. The asymptotic analysis of the proposed algorithm is carried out, establishing dual convergence under both, constant and diminishing step sizes. It is also shown that with constant step size, the proposed resource allocation policy is asymptotically near-optimal. An application involving multi-cell coordinated beamforming is detailed, demonstrating the usefulness of the proposed algorithm.

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

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

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Lu, Hanqing, E-mail: hanqing@math.wisc.edu

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (inmore » the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.« less

Resilient filtering for time-varying stochastic coupling networks under the event-triggering scheduling

NASA Astrophysics Data System (ADS)

Wang, Fan; Liang, Jinling; Dobaie, Abdullah M.

2018-07-01

The resilient filtering problem is considered for a class of time-varying networks with stochastic coupling strengths. An event-triggered strategy is adopted to save the network resources by scheduling the signal transmission from the sensors to the filters based on certain prescribed rules. Moreover, the filter parameters to be designed are subject to gain perturbations. The primary aim of the addressed problem is to determine a resilient filter that ensures an acceptable filtering performance for the considered network with event-triggering scheduling. To handle such an issue, an upper bound on the estimation error variance is established for each node according to the stochastic analysis. Subsequently, the resilient filter is designed by locally minimizing the derived upper bound at each iteration. Moreover, rigorous analysis shows the monotonicity of the minimal upper bound regarding the triggering threshold. Finally, a simulation example is presented to show effectiveness of the established filter scheme.

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration.

PubMed

Berezhkovskii, Alexander M; Shvartsman, Stanislav Y

2016-05-28

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.

Data-driven monitoring for stochastic systems and its application on batch process

NASA Astrophysics Data System (ADS)

Yin, Shen; Ding, Steven X.; Haghani Abandan Sari, Adel; Hao, Haiyang

2013-07-01

Batch processes are characterised by a prescribed processing of raw materials into final products for a finite duration and play an important role in many industrial sectors due to the low-volume and high-value products. Process dynamics and stochastic disturbances are inherent characteristics of batch processes, which cause monitoring of batch processes a challenging problem in practice. To solve this problem, a subspace-aided data-driven approach is presented in this article for batch process monitoring. The advantages of the proposed approach lie in its simple form and its abilities to deal with stochastic disturbances and process dynamics existing in the process. The kernel density estimation, which serves as a non-parametric way of estimating the probability density function, is utilised for threshold calculation. An industrial benchmark of fed-batch penicillin production is finally utilised to verify the effectiveness of the proposed approach.

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.