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

TL;DR

This paper reviews the Deep BSDE method, a deep learning approach that effectively solves high-dimensional nonlinear PDEs, overcoming traditional computational limitations and inspiring ongoing research.

Contribution

It provides a concise overview of the Deep BSDE method, its developments, and future research directions in high-dimensional PDE solving.

Findings

Deep BSDE enables solving high-dimensional PDEs efficiently.

The method has spurred active research and development.

Future directions include improving accuracy and computational efficiency.

Abstract

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.