Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 769-791.
Published online: 2023-08
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2022-0201}, url = {http://global-sci.org/intro/article_detail/nmtma/21966.html} }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.