Deep Feynman-Kac Methods for High-Dimensional Semilinear Parabolic Equations: Revisit
Abstract
Deep Feynman-Kac method was first introduced to solve parabolic partial differential equations (PDE) by Beck et al. [SIAM J. Sci. Comput., 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
Fields of Study & Subjects
Computational Fluid Dynamics and Aerodynamics
Meteorological Phenomena and Simulations
Advanced Data Storage Technologies
Publication details
- Journal / source
- CSIAM Transactions on Applied Mathematics
- Publisher
- Global Science Press
- Volume
- 7
- Issue
- 6
- Pages
- 1267–1286
- Publication date
- 11 May 2026
- Language
- EN