KMS Of Academy of mathematics and systems sciences, CAS
| An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems | |
| Yan, Liang1,2; Zhou, Tao3 | |
| 2020-11-01 | |
| Source Publication | COMMUNICATIONS IN COMPUTATIONAL PHYSICS
 |
| ISSN | 1815-2406 |
| Volume | 28Issue:5Pages:2180-2205 |
| Abstract | 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. |
| Keyword | Bayesian inverse problems deep neural networks multi-fidelity surrogate modeling Markov chain Monte Carlo |
| DOI | 10.4208/cicp.OA-2020-0186 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Physics |
| WOS Subject | Physics, Mathematical |
| WOS ID | WOS:000591596200006 |
| Publisher | GLOBAL SCIENCE PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/52477 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Zhou, Tao |
| Affiliation | 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 |
| 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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