Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems

doi:10.1016/j.jcp.2018.12.025

	Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems
	Yan, Liang 1; Zhou, Tao2
	2019-03-15
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	381 页码:110-128
摘要	The polynomial chaos (PC) expansion has been widely used as a surrogate model in the Bayesian inference to speed up the Markov chain Monte Carlo (MCMC) calculations. However, the use of a PC surrogate introduces the modeling error, that may severely distort the estimate of the posterior distribution. This error can be corrected by increasing the order of the PC expansion, but the cost for building the surrogate may increase dramatically. In this work, we seek to address this challenge by proposing an adaptive procedure to construct a multi-fidelity PC surrogate. This new strategy combines (a large number of) low-fidelity surrogate model evaluations and (a small number of) high-fidelity model evaluations, yielding a locally adaptive multi-fidelity approach. Here the low-fidelity surrogate is chosen as the prior-based PC surrogate, while the high-fidelity model refers to the true forward model. The key idea is to construct and refine the multi-fidelity approach over a sequence of samples adaptively determined from data so that the approximation can eventually concentrate on the posterior distribution. We illustrate the performance of the proposed strategy through two nonlinear inverse problems. It is shown that the proposed adaptive multi-fidelity approach can improve significantly the accuracy, yet without a dramatic increase in computational complexity. The numerical results also indicate that our new algorithm can enhance the efficiency by several orders of magnitude compared to a standard MCMC approach using only the true forward model. (C) 2019 Elsevier Inc. All rights reserved.
关键词	Bayesian inverse problems Multi-fidelity polynomial chaos Surrogate modeling Markov chain Monte Carlo
DOI	10.1016/j.jcp.2018.12.025
语种	英语
资助项目	NSFC[11822111] ; NSFC[11688101] ; NSFC[91630203] ; NSFC[11571351] ; NSFC[11731006] ; NSFC[11771081] ; Qing Lan project of Jiangsu Province ; Southeast UniversityZhishan Young Scholars Program ; science challenge project[TZ2018001] ; NCMIS ; youth innovation promotion association (CAS)
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000458147100007
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32447
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Tao
作者单位	1.Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Yan, Liang,Zhou, Tao. Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2019,381:110-128.
APA	Yan, Liang,&Zhou, Tao.(2019).Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems.JOURNAL OF COMPUTATIONAL PHYSICS,381,110-128.
MLA	Yan, Liang,et al."Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems".JOURNAL OF COMPUTATIONAL PHYSICS 381(2019):110-128.