5 papers
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…
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…
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,…
Averaging principle for semilinear slow-fast rough partial differential equations
Miaomiao Li, Yunzhang Li, Bin Pei +1
In this paper, we investigate the averaging principle for a class of semilinear slow-fast partial differential equations driven by finite-dimensional rough multiplicative noise. Sp…
Non-Markovian dynamics: the memory-dependent probability density evolution equations
Bin Pei, Lifang Feng, Yunzhang Li +1
This paper aims to investigate the non-Markovian dynamics. The governing equations are derived for the probability density functions (PDFs) of non-Markovian stochastic responses to…