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math.NA2026
Deep Truncated FBSDE Method for High-Dimensional Nonlinear PDEs and Fully Coupled FBSDEs
Xinyu Cheng, Yunzhang Li, Weiran Xiong
In this paper, we introduce a deep truncated forward-backward stochastic differential equation (FBSDE) method for high-dimensional partial differential equations (PDEs) and fully c…
math.NA2026
High-Moment Stability and Error Analysis of a Fully Discrete LDG-IMEX Method for High Dimensional Nonlinear Stochastic Convection-Diffusion Equations
Yiming Chen, Yunzhang Li, Yulong Xing
A fully discrete local discontinuous Galerkin (LDG) method coupled with an implicit-explicit (IMEX) Euler time discretization is presented and analyzed for a class of high dimensio…
math.NA2026
A deep backward regression-based scheme for high-dimensional nonlinear partial differential equations
Qiang Han, Shaolin Ji, Yunzhang Li
We propose a deep backward regression-based (DBR) scheme for solving high-dimensional nonlinear parabolic partial differential equations. Building on the DBDP method of Huré, Pham,…