A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems

4 May 2021

Papers citing "A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems"

19 / 19 papers shown

Title
Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks Jonathan W. Siegel 279 7 0 28 Jul 2023
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 65 29 0 14 Jun 2021
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations Jianfeng Lu Yulong Lu Min Wang 59 37 0 05 Jan 2021
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning Fan Chen J. Huang Chunmei Wang Haizhao Yang 60 33 0 15 Dec 2020
Neural network approximation and estimation of classifiers with classification boundary in a Barron class A. Caragea P. Petersen F. Voigtlaender 58 36 0 18 Nov 2020
Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't E. Weinan Chao Ma Stephan Wojtowytsch Lei Wu AI4CE 88 134 0 22 Sep 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs Siddhartha Mishra Roberto Molinaro PINN 82 266 0 29 Jun 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs Siddhartha Mishra Roberto Molinaro PINN 77 175 0 29 Jun 2020
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory Yaoyu Zhang Haizhao Yang 57 75 0 28 Jun 2020
Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach Jiequn Han Jianfeng Lu Mo Zhou DiffM 77 87 0 07 Feb 2020
Deep neural network solution of the electronic Schrödinger equation J. Hermann Zeno Schätzle Frank Noé 217 456 0 16 Sep 2019
Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks David Pfau J. Spencer A. G. Matthews W. Foulkes 84 465 0 05 Sep 2019
The Barron Space and the Flow-induced Function Spaces for Neural Network Models E. Weinan Chao Ma Lei Wu 71 110 0 18 Jun 2019
Solving for high dimensional committor functions using artificial neural networks Y. Khoo Jianfeng Lu Lexing Ying 67 137 0 28 Feb 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 123 1,389 0 30 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 93 2,067 0 24 Aug 2017
$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 264 143 0 26 Jul 2016
Breaking the Curse of Dimensionality with Convex Neural Networks Francis R. Bach 184 706 0 30 Dec 2014
Deep Learning in Neural Networks: An Overview Jürgen Schmidhuber HAI 246 16,377 0 30 Apr 2014