An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems
Yan, Liang1,2; Zhou, Tao3
AbstractIn 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.
KeywordBayesian inverse problems deep neural networks multi-fidelity surrogate modeling Markov chain Monte Carlo
Indexed BySCI
Funding ProjectNSF 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 Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000591596200006
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Document Type期刊论文
Corresponding AuthorZhou, Tao
Affiliation1.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
Recommended Citation
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.
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