Year: 2021
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 6 : pp. 848–864
Abstract
Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO can be computationally intensive for complexity problems due to repetitive evaluations of the expensive forward model and its gradient. In this work, we present a novel goal-oriented deep neural networks (DNN) surrogate approach to substantially reduce the computation burden of RTO. In particular, we propose to draw the training points for the DNN-surrogate from a local approximated posterior distribution — yielding a flexible and efficient sampling algorithm that converges to the direct RTO approach. We present a Bayesian inverse problem governed by elliptic PDEs to demonstrate the computational accuracy and efficiency of our DNN-RTO approach, which shows that DNN-RTO can significantly outperform the traditional RTO.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2102-m2020-0339
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 6 : pp. 848–864
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Bayesian inverse problems Deep neural network Markov chain Monte Carlo.
Author Details
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Surrogate modeling for Bayesian inverse problems based on physics-informed neural networks
Li, Yongchao
Wang, Yanyan
Yan, Liang
Journal of Computational Physics, Vol. 475 (2023), Iss. P.111841
https://doi.org/10.1016/j.jcp.2022.111841 [Citations: 13]