A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations

5 January 2021

Papers citing "A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations"

7 / 7 papers shown

Title
Convergence analysis of a quasi-Monte Carlo-based deep learning algorithm for solving partial differential equations Fengjiang Fu Xiaoqun Wang 21 2 0 28 Oct 2022
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 39 10 0 21 Oct 2022
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent Yiping Lu Jose H. Blanchet Lexing Ying 30 7 0 15 May 2022
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces Hao Liu Haizhao Yang Minshuo Chen T. Zhao Wenjing Liao 32 36 0 01 Jan 2022
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 17 26 0 14 Jun 2021
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems Jianfeng Lu Yulong Lu 29 29 0 04 May 2021
$Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with $ \ell^1 $ and $ \ell^0 $ Controls$ Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with $\ell^1$ and $\ell^0$ Controls Jason M. Klusowski Andrew R. Barron 122 142 0 26 Jul 2016