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MC-Nonlocal-PINNs: handling nonlocal operators in PINNs via Monte Carlo sampling

Xiaodong FengYue QianWanfang Shen
Dec 2022
摘要
We propose, Monte Carlo Nonlocal physics-informed neural networks(MC-Nonlocal-PINNs), which is a generalization of MC-fPINNs in\cite{guo2022monte}, for solving general nonlocal models such as integralequations and nonlocal PDEs. Similar as in MC-fPINNs, our MC-Nonlocal-PINNshandle the nonlocal operators in a Monte Carlo way, resulting in a very stableapproach for high dimensional problems. We present a variety of test problems,including high dimensional Volterra type integral equations, hypersingularintegral equations and nonlocal PDEs, to demonstrate the effectiveness of ourapproach.
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