Year: 2023
Author: Wanfang Shen, Xiaodong Feng, Yue Qian, Wanfang Shen
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 3 : pp. 769–791
Abstract
We propose Monte Carlo Nonlocal physics-informed neural networks (MC-Nonlocal-PINNs), which are a generalization of MC-fPINNs in L. Guo et al. (Comput. Methods Appl. Mech. Eng. 400 (2022), 115523) for solving general nonlocal models such as integral equations and nonlocal PDEs. Similar to MC-fPINNs, our MC-Nonlocal-PINNs handle nonlocal operators in a Monte Carlo way, resulting in a very stable approach for high dimensional problems. We present a variety of test problems, including high dimensional Volterra type integral equations, hypersingular integral equations and nonlocal PDEs, to demonstrate the effectiveness of our approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0201
Numerical Mathematics: Theory, Methods and Applications, Vol. 16 (2023), Iss. 3 : pp. 769–791
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Nonlocal models PINNs Monte Carlo sampling deep neural networks.