On the Representation of Solutions to Elliptic PDEs in Barron Spaces

14 June 2021

Papers citing "On the Representation of Solutions to Elliptic PDEs in Barron Spaces"

19 / 19 papers shown

Title
Solving partial differential equations with sampled neural networks Chinmay Datar Taniya Kapoor Abhishek Chandra Qing Sun Iryna Burak Erik Lien Bolager Anna Veselovska Massimo Fornasier Felix Dietrich 35 1 0 31 May 2024
Error analysis for finite element operator learning methods for solving parametric second-order elliptic PDEs Youngjoon Hong Seungchan Ko Jae Yong Lee 20 1 0 27 Apr 2024
Space-Time Approximation with Shallow Neural Networks in Fourier Lebesgue spaces Ahmed Abdeljawad Thomas Dittrich 20 2 0 13 Dec 2023
Statistical Spatially Inhomogeneous Diffusion Inference Yinuo Ren Yiping Lu Lexing Ying Grant M. Rotskoff 10 2 0 10 Dec 2023
Deep Equilibrium Based Neural Operators for Steady-State PDEs Tanya Marwah Ashwini Pokle J. Zico Kolter Zachary Chase Lipton Jianfeng Lu Andrej Risteski 20 8 0 30 Nov 2023
Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms Yahong Yang Yulong Lu 29 3 0 08 Nov 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 10 1 0 30 Mar 2023
Operator learning with PCA-Net: upper and lower complexity bounds S. Lanthaler 21 25 0 28 Mar 2023
Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems Derick Nganyu Tanyu Jianfeng Ning Tom Freudenberg Nick Heilenkötter A. Rademacher U. Iben Peter Maass AI4CE 18 34 0 06 Dec 2022
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 41 10 0 21 Oct 2022
DeepMed: Semiparametric Causal Mediation Analysis with Debiased Deep Learning Siqi Xu Lin Liu Zhong Liu CML MedIm 26 8 0 10 Oct 2022
Generic bounds on the approximation error for physics-informed (and) operator learning Tim De Ryck Siddhartha Mishra PINN 59 59 0 23 May 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 15 0 0 25 Jan 2022
Stationary Density Estimation of Itô Diffusions Using Deep Learning Yiqi Gu J. Harlim Senwei Liang Haizhao Yang 15 12 0 09 Sep 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
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 203 2,282 0 18 Oct 2020
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 122 142 0 26 Jul 2016