Solve High-Dimensional Reflected Partial Differential Equations by Neural Network Method

Reflected partial differential equations (PDEs) have important applications in financial mathematics, stochastic control, physics, and engineering. This paper aims to present a numerical method for solving high-dimensional reflected PDEs. In fact, overcoming the “dimensional curse” approximating reflection term are challenges. Some algorithms based on neural networks developed recently fail To solve these problems, firstly, PDEs transformed into backward (BSDEs) using Feyman–Kac formula. Secondly, of BSDEs is approximated penalization method. Next, discretized strategy that combines Euler Crank–Nicolson schemes. Finally, deep network model employed simulate solution BSDEs. The effectiveness proposed tested by two experiments, shows high stability accuracy up 100 dimensions.