1 citations · 2 across the 9 of their papers we have counts for
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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…