论文标题
MC-Nonlocal-Pinns：通过Monte Carlo采样在PINNS中处理非本地操作员
MC-Nonlocal-PINNs: handling nonlocal operators in PINNs via Monte Carlo sampling
论文作者
论文摘要
我们提出了Monte Carlo非局部物理知识的神经网络（MC-Nonlocal-Pinns），该网络是\ cite {Guo20222monte}中MC-FPINN的概括，用于求解一般的非局部模型，例如积分方程和非局部PDES。与MC-Fpinn相似，我们的MC-Nonlocal-Pinns以蒙特卡洛的方式处理非局部运算符，从而导致了非常稳定的高维问题的方法。我们提出了各种测试问题，包括高维伏尔泰型积分方程，超源积分方程和非局部PDE，以证明我们方法的有效性。
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 integral equations and nonlocal PDEs. Similar as in MC-fPINNs, our MC-Nonlocal-PINNs handle the 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.
