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"

13 / 13 papers shown

Title
Space-Time Approximation with Shallow Neural Networks in Fourier Lebesgue spaces Ahmed Abdeljawad Thomas Dittrich 26 2 0 13 Dec 2023
Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms Yahong Yang Yulong Lu 37 3 0 08 Nov 2023
Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks Jonathan W. Siegel 45 7 0 28 Jul 2023
Embedding Inequalities for Barron-type Spaces Lei Wu 16 0 0 30 May 2023
Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models Anant Raj Umut Simsekli Alessandro Rudi DiffM 20 1 0 30 Mar 2023
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 47 10 0 21 Oct 2022
$A Regularity Theory for Static Schrödinger Equations on $\mathbb{R}^d$ in Spectral Barron Spaces$ A Regularity Theory for Static Schrödinger Equations on $\mathbb{R}^d$ in Spectral Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu Sheng-Wei Zhou 21 0 0 25 Jan 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
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems Nikolas Nusken Lorenz Richter PINN DiffM 31 27 0 07 Dec 2021
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 25 26 0 14 Jun 2021
Solving PDEs on Unknown Manifolds with Machine Learning Senwei Liang Shixiao W. Jiang J. Harlim Haizhao Yang AI4CE 34 16 0 12 Jun 2021
Deep neural network solution of the electronic Schrödinger equation J. Hermann Zeno Schätzle Frank Noé 149 446 0 16 Sep 2019
$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 127 142 0 26 Jul 2016