47 citations · 123 across the 13 of their papers we have counts for
12 papers · 1 filter
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…
Manifold Learning and Nonlinear Homogenization
Shi Chen, Qin Li, Jianfeng Lu +1
We describe an efficient domain decomposition-based framework for nonlinear multiscale PDE problems. The framework is inspired by manifold learning techniques and exploits the tang…
Fast localization of eigenfunctions via smoothed potentials
Jianfeng Lu, Cody Murphey, Stefan Steinerberger
We study the problem of predicting highly localized low-lying eigenfunctions in bounded domains for rapidly varying potentials . Filoche &…
A Proximal-Gradient Algorithm for Crystal Surface Evolution
Katy Craig, Jian-Guo Liu, Jianfeng Lu +2
As a counterpoint to recent numerical methods for crystal surface evolution, which agree well with microscopic dynamics but suffer from significant stiffness that prevents simulati…