Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory

28 June 2020

Papers citing "Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory"

17 / 17 papers shown

Title
Solving Nonlinear PDEs with Sparse Radial Basis Function Networks Zihan Shao Konstantin Pieper Xiaochuan Tian 29 0 0 12 May 2025
Learn Sharp Interface Solution by Homotopy Dynamics Chuqi Chen Yahong Yang Yang Xiang Wenrui Hao ODL 57 1 0 01 Feb 2025
Approximation of Solution Operators for High-dimensional PDEs Nathan Gaby Xiaojing Ye 19 0 0 18 Jan 2024
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 21 6 0 28 May 2022
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent Yiping Lu Jose H. Blanchet Lexing Ying 35 7 0 15 May 2022
Numerical Approximation of Partial Differential Equations by a Variable Projection Method with Artificial Neural Networks S. Dong Jielin Yang 37 17 0 24 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
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yihang Gao Michael K. Ng 35 28 0 30 Aug 2021
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 25 26 0 14 Jun 2021
Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality Lukas Gonon 11 35 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 31 29 0 04 May 2021
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation Q. Du Yiqi Gu Haizhao Yang Chao Zhou 24 20 0 21 Mar 2021
Evolutional Deep Neural Network Yifan Du T. Zaki 16 68 0 18 Mar 2021
Reproducing Activation Function for Deep Learning Senwei Liang Liyao Lyu Chunmei Wang Haizhao Yang 28 21 0 13 Jan 2021
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations Jianfeng Lu Yulong Lu Min Wang 23 37 0 05 Jan 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 30 146 0 22 Dec 2020
Neural Network Approximation: Three Hidden Layers Are Enough Zuowei Shen Haizhao Yang Shijun Zhang 19 115 0 25 Oct 2020