1 citations · 2 across the 9 of their papers we have counts for
9 papers
Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse Problem
Yang Zhao, Junxiong Jia, Tao Zhou
This paper addresses infinite-dimensional Bayesian inference for inverse problem of partial differential equations with model parameters in infinite-dimensional Hilbert space. To e…
Deep Policy Iteration for High-Dimensional Mean-Field Games with Regenerative Reformulation
Shuixin Fang, Shupeng Wang, Zhen Wu +2
This paper develops a deep policy iteration method for high-dimensional finite-horizon mean-field games (MFG). We reformulate the game as a regenerative problem with deterministic…
A derivative-free localized stochastic method for very high-dimensional semilinear parabolic PDEs
Shuixin Fang, Changtao Sheng, Bihao Su +1
We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs. The efficiency of the proposed…
Explicit Runge-Kutta schemes for Backward Stochastic Differential Equations
Shuixin Fang, Yue Qiu, Weidong Zhao
The Butcher theory provides a powerful tool for analyzing order conditions of Runge-Kutta schemes for ordinary differential equations (ODEs); however, such a theory has not yet bee…
Deep random difference method for high-dimensional quasilinear parabolic partial differential equations
Wei Cai, Shuixin Fang, Tao Zhou
Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for aut…
Adaptive neural network basis methods for partial differential equations with low-regular solutions
Jianguo Huang, Haohao Wu, Tao Zhou
This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions i…
Functional normalizing flow for statistical inverse problems of partial differential equations
Yang Zhao, Haoyu Lu, Junxiong Jia +1
Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem…
Martingale deep neural network for very high-dimensional stochastic optimal controls
Wei Cai, Shuixin Fang, Wenzhong Zhang +1
We propose a martingale deep learning method for very high-dimensional stochastic optimal control problems (SOCPs) via their associated Hamilton--Jacobi--Bellman equations and the…
SOC-MartNet: A Martingale Neural Network for the Hamilton-Jacobi-Bellman Equation without Explicit inf H in Stochastic Optimal Controls
Wei Cai, Shuixin Fang, Tao Zhou
In this paper, we propose a martingale-based neural network, SOC-MartNet, for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) equations where no explicit expression is neede…