@Article{NMTMA-16-769,
author = {Feng , XiaodongQian , Yue and Shen , Wanfang},
title = {MC-Nonlocal-PINNs: Handling Nonlocal Operators in PINNs via Monte Carlo Sampling},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2023},
volume = {16},
number = {3},
pages = {769--791},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2022-0201},
url = {http://global-sci.org/intro/article_detail/nmtma/21966.html}
}