An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems

doi:10.4208/cicp.OA-2020-0186

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	An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems
	Yan, Liang 1,2; Zhou, Tao 3
	2020-11-01
发表期刊	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN	1815-2406
卷号	28 期号:5 页码:2180-2205
摘要	In Bayesian inverse problems, surrogate models are often constructed to speed up the computational procedure, as the parameter-to-data map can be very expensive to evaluate. However, due to the curse of dimensionality and the nonlinear concentration of the posterior, traditional surrogate approaches (such us the polynomial-based surrogates) are still not feasible for large scale problems. To this end, we present in this work an adaptive multi-fidelity surrogate modeling framework based on deep neural networks (DNNs), motivated by the facts that the DNNs can potentially handle functions with limited regularity and are powerful tools for high dimensional approximations. More precisely, we first construct offline a DNN-based surrogate according to the prior distribution, and then, this prior-based DNN-surrogate will be adaptively & locally refined online using only a few high-fidelity simulations. In particular, in the refine procedure, we construct a new shallow neural network that view the previous constructed surrogate as an input variable - yielding a composite multi-fidelity neural network approach. This makes the online computational procedure rather efficient. Numerical examples are presented to confirm that the proposed approach can obtain accurate posterior information with a limited number of forward simulations.
关键词	Bayesian inverse problems deep neural networks multi-fidelity surrogate modeling Markov chain Monte Carlo
DOI	10.4208/cicp.OA-2020-0186
收录类别	SCI
语种	英语
资助项目	NSF of China[11771081] ; Zhishan Young Scholar Program of SEU ; NSFC[11822111] ; NSFC[11688101] ; NSFC[11731006] ; science challenge project[TZ2018001] ; National Key Basic Research Program[2018YFB0704304] ; youth innovation promotion association (CAS)
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000591596200006
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52477
专题	中国科学院数学与系统科学研究院
通讯作者	Zhou, Tao
作者单位	1.Southeast Univ, Sch Math, Nanjing 210096, Peoples R China 2.Nanjing Ctr Appl Math, Nanjing 211135, Peoples R China 3.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. An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2020,28(5):2180-2205.
APA	Yan, Liang,&Zhou, Tao.(2020).An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,28(5),2180-2205.
MLA	Yan, Liang,et al."An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 28.5(2020):2180-2205.