An adaptive reduced basis ANOVA method forhigh-dimensional Bayesian inverse problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:396

Article

Liao, Qifeng¹  Li, Jinglai² 

[1] ShanghaiTech Univ, Sch Informat Sci & Technol, Shanghai 201210, Peoples R China

[2] Univ Liverpool, Dept Math Sci, Liverpool L69 7XL, Merseyside, England

关键词: ANOVA;    Reduced basis methods;    Bayesian inference;    Markov Chain Monte Carlo;    Inverse problems;   

DOI  :  10.1016/j.jcp.2019.06.059

来源: Elsevier

【 摘 要 】

In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation. However, in many practical problems, the parameter of interest can be of high dimensionality, which renders standard model reduction techniques infeasible. In this paper, we present an approach that employs the ANOVA decomposition method to reduce the model with respect to the unknown parameters, and the reduced basis method to reduce the model with respect to the physical parameters. Moreover, we provide an adaptive scheme within the MCMC iterations, to perform the ANOVA decomposition with respect to the posterior distribution. With numerical examples, we demonstrate that the proposed model reduction method can significantly reduce the computational cost of Bayesian inverse problems, without sacrificing much accuracy. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free