标题： 高维偏微分方程求解的Deep BSDE方法简要回顾 显示英文标题

标题： A brief review of the Deep BSDE method for solving high-dimensional partial differential equations

摘要： 高维偏微分方程（PDE）由于维度灾难给数值计算带来了重大挑战，这限制了传统基于网格方法的应用。 自 2017 年以来， 深度 BSDE 方法引入了深度学习技术，使得能够有效求解非常高维的非线性 PDE。 这一创新激发了使用神经网络求解高维 PDE 的极大兴趣，使该领域成为研究热点。 在这篇简短的综述中，我们将简要概述深度 BSDE 方法、其后续发展以及该领域的未来方向。 显示英文摘要

摘要： High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of traditional mesh-based methods. Since 2017, the Deep BSDE method has introduced deep learning techniques that enable the effective solution of nonlinear PDEs in very high dimensions. This innovation has sparked considerable interest in using neural networks for high-dimensional PDEs, making it an active area of research. In this short review, we briefly sketch the Deep BSDE method, its subsequent developments, and future directions for the field.