Journal ArticleDOI
Stochastic spectral methods for efficient Bayesian solution of inverse problems
Reads0
Chats0
TLDR
This work presents a reformulation of the Bayesian approach to inverse problems, that seeks to accelerate Bayesian inference by using polynomial chaos expansions to represent random variables, and evaluates the utility of this technique on a transient diffusion problem arising in contaminant source inversion.About:
This article is published in Journal of Computational Physics.The article was published on 2007-06-01. It has received 484 citations till now. The article focuses on the topics: Bayesian inference & Polynomial chaos.read more
Citations
More filters
Journal ArticleDOI
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
TL;DR: Model reduction aims to reduce the computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior as mentioned in this paper. But model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books.
Journal ArticleDOI
Physics-informed machine learning
TL;DR: Some of the prevailing trends in embedding physics into machine learning are reviewed, some of the current capabilities and limitations are presented and diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems are discussed.
Journal Article
Fast numerical methods for stochastic computations: A review
TL;DR: This paper presents a review of the current state-of-the-art of numerical methods for stochastic computations, with a particular emphasis on those based on generalized polynomial chaos (gPC) methodology.
Journal ArticleDOI
Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces
TL;DR: This work presents a method to first detect the directions of the strongest variability using evaluations of the gradient and subsequently exploit these directions to construct a response surface on a low-dimensional subspace---i.e., the active subspace ---of the inputs.
Journal ArticleDOI
A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
TL;DR: This work addresses the solution of large-scale statistical inverse problems in the framework of Bayesian inference with a so-called Stochastic Monte Carlo method.
References
More filters
BookDOI
Markov Chain Monte Carlo in Practice
TL;DR: The Markov Chain Monte Carlo Implementation Results Summary and Discussion MEDICAL MONITORING Introduction Modelling Medical Monitoring Computing Posterior Distributions Forecasting Model Criticism Illustrative Application Discussion MCMC for NONLINEAR HIERARCHICAL MODELS.
Journal ArticleDOI
Sampling-Based Approaches to Calculating Marginal Densities
TL;DR: In this paper, three sampling-based approaches, namely stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm, are compared and contrasted in relation to various joint probability structures frequently encountered in applications.
Journal Article
Sampling-based approaches to calculating marginal densities
TL;DR: Stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm can be viewed as three alternative sampling- (or Monte Carlo-) based approaches to the calculation of numerical estimates of marginal probability distributions.
Book
Stochastic Finite Elements: A Spectral Approach
Roger Ghanem,Pol D. Spanos +1 more
TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.