Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and their suitability for high-dimensional problems: physics-informed neural networks, methods based on the Feynman-Kac formula and the Deep BSDE solver. The article is accompanied by a suite of expository software in the form of Jupyter notebooks in which each basic methodology is explained step by step, allowing for a quick assimilation and experimentation. An extensive bibliography summarizes the state of the art.

中文翻译：

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用神经网络求解偏微分方程的三种方法-综述。

神经网络越来越多地用于构造偏微分方程的数值求解方法。在本说明性评论中，我们介绍并对比了三种重要的近期方法，这些方法在其简单性和对高维问题的适用性方面均具有吸引力，它们是物理信息神经网络，基于Feynman-Kac公式的方法和Deep BSDE求解器。本文随附Jupyter笔记本电脑形式的一套说明软件，其中逐步解释了每种基本方法，从而可以快速进行同化和试验。大量的书目总结了最新技术。