Year: 2024
Author: Wenbin Liu, Liang Yan, Tao Zhou, Yuancheng Zhou
CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 3 : pp. 636–670
Abstract
In this paper, we present a novel adaptive sampling strategy for enhancing the performance of physics-informed neural networks (PINNs) in addressing inverse problems with low regularity and high dimensionality. The framework is based on failure-informed PINNs, which was recently developed in [Gao et al., SIAM J. Sci. Comput., 45(4), 2023]. Specifically, we employ a truncated Gaussian mixture model to estimate the failure probability; this model additionally serves as an error indicator in our adaptive strategy. New samples for further computation are also produced using the truncated Gaussian mixture model. To describe the new framework, we consider two important classes of inverse problems: the inverse conductivity problem in electrical impedance tomography and the inverse source problem in a parabolic system. The effectiveness of our method is demonstrated through a series of numerical examples.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2023-0059
CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 3 : pp. 636–670
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Inverse problem FI-PINNs Gaussian mixture model.
Author Details
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Adaptive Operator Learning for Infinite-Dimensional Bayesian Inverse Problems
Gao, Zhiwei
Yan, Liang
Zhou, Tao
SIAM/ASA Journal on Uncertainty Quantification, Vol. 12 (2024), Iss. 4 P.1389
https://doi.org/10.1137/24M1643815 [Citations: 0]