用神经网络求解偏微分方程的三种方法--综述
Three Ways to Solve Partial Differential Equations with Neural Networks -- A Review
摘要：
神经网络越来越多地用于构造偏微分方程的数值解方法。在这篇简要的综述中，我们介绍和对比了最近三种重要的方法，它们的简单性和它们对高维问题的适用性：物理信息神经网络，基于Feynman-Kac公式的方法和基于后向随机微分方程的方法。本文附带了一套笔记本形式的临时软件，其中每一种基本方法都是逐步解释的，允许快速吸收和实验。一个广泛的参考书目总结了最新的技术水平。
英文摘要：
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 methods based on the solution of backward stochastic differential equations. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
