Open AccessAccelerating the Bayesian inference of inverse problems by using data-driven compressive sensing method based on proper orthogonal decomposition
Author(s) -
Meixin Xiong,
Liuhong Chen,
Ming Ju,
Jeeyoung Shin
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021044
Subject(s) - polynomial chaos , mathematics , inverse problem , markov chain monte carlo , bayesian probability , bayesian inference , inverse , algorithm , inference , collocation (remote sensing) , polynomial , mathematical optimization , compressed sensing , computer science , monte carlo method , statistics , artificial intelligence , mathematical analysis , geometry , machine learning
In Bayesian inverse problems, using the Markov Chain Monte Carlo method to sample from the posterior space of unknown parameters is a formidable challenge due to the requirement of evaluating the forward model a large number of times. For the purpose of accelerating the inference of the Bayesian inverse problems, in this work, we present a proper orthogonal decomposition (POD) based data-driven compressive sensing (DCS) method and construct a low dimensional approximation to the stochastic surrogate model on the prior support. Specifically, we first use POD to generate a reduced order model. Then we construct a compressed polynomial approximation by using a stochastic collocation method based on the generalized polynomial chaos expansion and solving an \begin{document}$ l_1 $\end{document} -minimization problem. Rigorous error analysis and coefficient estimation was provided. Numerical experiments on stochastic elliptic inverse problem were performed to verify the effectiveness of our POD-DCS method.