34 citations · 212 across the 40 of their papers we have counts for
4 papers · 1 filter
Solving multiscale steady radiative transfer equation using neural networks with uniform stability
Yulong Lu, Li Wang, Wuzhe Xu
This paper concerns solving the steady radiative transfer equation with diffusive scaling, using the physics informed neural networks (PINNs). The idea of PINNs is to minimize a le…
On the Representation of Solutions to Elliptic PDEs in Barron Spaces
Ziang Chen, Jianfeng Lu, Yulong Lu
Numerical solutions to high-dimensional partial differential equations (PDEs) based on neural networks have seen exciting developments. This paper derives complexity estimates of t…
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems
Jianfeng Lu, Yulong Lu
This paper analyzes the generalization error of two-layer neural networks for computing the ground state of the Schrödinger operator on a -dimensional hypercube. We prove that t…
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations
Jianfeng Lu, Yulong Lu, Min Wang
This paper concerns the a priori generalization analysis of the Deep Ritz Method (DRM) [W. E and B. Yu, 2017], a popular neural-network-based method for solving high dimensional pa…