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2101.01708
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A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations
5 January 2021
Jianfeng Lu
Yulong Lu
Min Wang
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Papers citing
"A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations"
16 / 16 papers shown
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks
Neural Networks (Neural Netw.), 2023
Zheyuan Hu
K. Shukla
George Karniadakis
Kenji Kawaguchi
PINN
AI4CE
854
201
0
23 Jul 2023
Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models
Neural Information Processing Systems (NeurIPS), 2023
Anant Raj
Umut Simsekli
Alessandro Rudi
DiffM
446
3
0
30 Mar 2023
Convergence Analysis of the Deep Galerkin Method for Weak Solutions
Yuling Jiao
Yanming Lai
Yang Wang
Haizhao Yang
Yunfei Yang
215
8
0
05 Feb 2023
Convergence analysis of a quasi-Monte Carlo-based deep learning algorithm for solving partial differential equations
Fengjiang Fu
Xiaoqun Wang
123
2
0
28 Oct 2022
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective
International Conference on Machine Learning (ICML), 2022
Tanya Marwah
Zachary Chase Lipton
Jianfeng Lu
Andrej Risteski
324
16
0
21 Oct 2022
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent
Neural Information Processing Systems (NeurIPS), 2022
Yiping Lu
Jose H. Blanchet
Lexing Ying
420
11
0
15 May 2022
IAE-Net: Integral Autoencoders for Discretization-Invariant Learning
Yong Zheng Ong
Zuowei Shen
Haizhao Yang
397
18
0
10 Mar 2022
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces
Journal of machine learning research (JMLR), 2022
Hao Liu
Haizhao Yang
Minshuo Chen
T. Zhao
Wenjing Liao
463
56
0
01 Jan 2022
DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations
Journal of Computational Physics (JCP), 2021
Keju Tang
Xiaoliang Wan
Chao Yang
292
177
0
28 Dec 2021
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
Zheyuan Hu
Ameya Dilip Jagtap
George Karniadakis
Kenji Kawaguchi
AI4CE
PINN
501
127
0
20 Sep 2021
Stationary Density Estimation of Itô Diffusions Using Deep Learning
Yiqi Gu
J. Harlim
Senwei Liang
Haizhao Yang
241
17
0
09 Sep 2021
Generalization Error Analysis of Neural networks with Gradient Based Regularization
Lingfeng Li
X. Tai
Jiang Yang
225
5
0
06 Jul 2021
On the Representation of Solutions to Elliptic PDEs in Barron Spaces
Neural Information Processing Systems (NeurIPS), 2021
Ziang Chen
Jianfeng Lu
Yulong Lu
240
38
0
14 Jun 2021
Solving PDEs on Unknown Manifolds with Machine Learning
Applied and Computational Harmonic Analysis (ACHA), 2021
Senwei Liang
Shixiao W. Jiang
J. Harlim
Haizhao Yang
AI4CE
278
22
0
12 Jun 2021
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems
Communications of the American Mathematical Society (Comm. Amer. Math. Soc.), 2021
Jianfeng Lu
Yulong Lu
314
39
0
04 May 2021
Error Estimates for the Deep Ritz Method with Boundary Penalty
Mathematical and Scientific Machine Learning (MSML), 2021
Johannes Müller
Marius Zeinhofer
589
28
0
01 Mar 2021
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