Related papers: Solving inverse problems by combination of maximum…
We present a procedure for the determination of the interaction potential from the knowledge of the radial pair distribution function. The method, realized inside an inverse Monte Carlo simulation scheme, is based on the application of the…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
Indentation test is used with growing popularity for the characterization of various materials on different scales. Developed methods are combining the test with computer simulation and inverse analyses to assess material parameters…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
We propose a suitable analytical framework to perform numerical analysis of problems arising in compressible fluid models with uncertain data. We discuss both weak and strong stochastic approach, where the former is based on the knowledge…
Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop a novel approach to reduce this…
We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we…
A first-order, Monte Carlo ensemble method has been recently introduced for solving parabolic equations with random coefficients in [26], which is a natural synthesis of the ensemble-based, Monte Carlo sampling algorithm and the…
This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…
Recently it has been shown that using diffusion models for inverse problems can lead to remarkable results. However, these approaches require a closed-form expression of the degradation model and can not support complex degradations. To…
The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a suitable deterministic…
We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching…
Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given…
In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the…
The following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from global EM scattering measurements, at various incidences and wave frequencies.…
Markov Chain Monte Carlo algorithms, the method of choice to sample from generic high-dimensional distributions, are rarely used for continuous one-dimensional distributions, for which more effective approaches are usually available (e.g.…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…