11 citations · 37 across the 9 of their papers we have counts for
9 papers
Predictive Moving Sample Method for Physics-Informed Neural Solvers of Time-Dependent PDEs
Beining Xu, Bocheng Zhang, Haijun Yu +2
Time-dependent partial differential equations (PDEs) often develop sharp fronts, localized peaks, and other moving structures that occupy only a small portion of the space--time do…
Moving sample method for solving time-dependent partial differential equations
Beining Xu, Haijun Yu, Jiayu Zhai +2
Solving time-dependent partial differential equations (PDEs) that exhibit sharp gradients or local singularities is computationally demanding, as traditional physics-informed neura…
Deep adaptive sampling for surrogate modeling without labeled data
Xili Wang, Kejun Tang, Jiayu Zhai +2
Surrogate modeling is of great practical significance for parametric differential equation systems. In contrast to classical numerical methods, using physics-informed deep learning…
Bregman Graph Neural Network
Jiayu Zhai, Lequan Lin, Dai Shi +1
Numerous recent research on graph neural networks (GNNs) has focused on formulating GNN architectures as an optimization problem with the smoothness assumption. However, in node cl…
Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs
Kejun Tang, Jiayu Zhai, Xiaoliang Wan +1
Solving partial differential equations (PDEs) is a central task in scientific computing. Recently, neural network approximation of PDEs has received increasing attention due to its…
A deep learning method for solving Fokker-Planck equations
Jiayu Zhai, Matthew Dobson, Yao Li
The time evolution of the probability distribution of a stochastic differential equation follows the Fokker-Planck equation, which usually has an unbounded, high-dimensional domain…
Using coupling methods to estimate sample quality for stochastic differential equations
Matthew Dobson, Jiayu Zhai, Yao Li
A probabilistic approach for estimating sample qualities for stochastic differential equations is introduced in this paper. The aim is to provide a quantitative upper bound of the…
An efficient data-driven solver for Fokker-Planck equations: algorithm and analysis
Matthew Dobson, Yao Li, Jiayu Zhai
Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key pro…
Convergence analysis of a finite element approximation of minimum action methods
Xiaoliang Wan, Haijun Yu, Jiayu Zhai
In this work, we address the convergence of a finite element approximation of the minimizer of the Freidlin-Wentzell (F-W) action functional for non-gradient dynamical systems pert…