用深度学习解高维非线性偏微分方程，突破传统方法瓶颈
A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
- 用神经网络替代网格法求解高维非线性PDE
- 自2017年起在高维问题中展现有效性和稳定性
- 适合研究高维计算、金融建模或强化学习的读者
高维偏微分方程（PDE）因维数灾难导致传统网格法难以应用。自2017年以来，深度随机微分方程（Deep BSDE）方法引入深度学习技术，成功实现了高维非线性PDE的有效求解。该方法激发了利用神经网络求解高维PDE的广泛研究兴趣，成为当前活跃的研究方向。本文简要梳理Deep BSDE方法的核心思想、后续进展及未来展望。
原文摘要 · Abstract (English)
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.
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