Deep Feynman-Kac Methods for High-Dimensional Semilinear Parabolic Equations: Revisit

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