26 citations · 41 across the 5 of their papers we have counts for
16 papers
A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
Jiequn Han, Arnulf Jentzen, Weinan E
High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of t…
Deep Picard Iteration for High-Dimensional Nonlinear PDEs
Jiequn Han, Wei Hu, Jihao Long +1
We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies…
A Machine Learning Enhanced Algorithm for the Optimal Landing Problem
Yaohua Zang, Jihao Long, Xuanxi Zhang +3
We propose a machine learning enhanced algorithm for solving the optimal landing problem. Using Pontryagin's minimum principle, we derive a two-point boundary value problem for the…
A PDE-free, neural network-based eddy viscosity model coupled with RANS equations
Ruiying Xu, Xu-Hui Zhou, Jiequn Han +2
Most turbulence models used in Reynolds-averaged Navier-Stokes (RANS) simulations are partial differential equations (PDE) that describe the transport of turbulent quantities. Such…
Recurrent Neural Networks for Stochastic Control Problems with Delay
Jiequn Han, Ruimeng Hu
Stochastic control problems with delay are challenging due to the path-dependent feature of the system and thus its intrinsic high dimensions. In this paper, we propose and systema…
Optimal Policies for a Pandemic: A Stochastic Game Approach and a Deep Learning Algorithm
Yao Xuan, Robert Balkin, Jiequn Han +2
Game theory has been an effective tool in the control of disease spread and in suggesting optimal policies at both individual and area levels. In this paper, we propose a multi-reg…