Deep Feynman-Kac Methods for High-dimensional Semilinear Parabolic Equations: Revisit
Computational Engineering, Finance, and Science
2025-03-21 v1
Abstract
Deep Feynman-Kac method was first introduced to solve parabolic partial differential equations(PDE) by Beck et al. (SISC, V.43, 2021), named Deep Splitting method since they trained the Neural Networks step by step in the time direction. In this paper, we propose a new training approach with two different features. Firstly, neural networks are trained at all time steps globally, instead of step by step. Secondly, the training data are generated in a new way, in which the method is consistent with a direct Monte Carlo scheme when dealing with a linear parabolic PDE. Numerical examples show that our method has significant improvement both in efficiency and accuracy.
Cite
@article{arxiv.2503.16407,
title = {Deep Feynman-Kac Methods for High-dimensional Semilinear Parabolic Equations: Revisit},
author = {Xiaotao Zheng and Xingye Yue and Jiyang Shi},
journal= {arXiv preprint arXiv:2503.16407},
year = {2025}
}