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Friedrichs Learning: Weak Solutions of Partial Differential Equations
  via Deep Learning
v1v2v3 (latest)

Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning

SIAM Journal on Scientific Computing (SIAM J. Sci. Comput.), 2020
15 December 2020
Fan Chen
J. Huang
Chunmei Wang
Haizhao Yang
ArXiv (abs)PDFHTML

Papers citing "Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning"

16 / 16 papers shown
Learning Singularity-Encoded Green's Functions with Application to Iterative Methods
Learning Singularity-Encoded Green's Functions with Application to Iterative Methods
Qi Sun
Shengyan Li
Bowen Zheng
Lili Ju
Xuejun Xu
303
4
0
15 Sep 2025
Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks
Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks
Bangti Jin
Longjun Wu
183
1
0
29 Aug 2025
Error analysis for the deep Kolmogorov method
Error analysis for the deep Kolmogorov method
Iulian Cîmpean
Thang Do
Lukas Gonon
Arnulf Jentzen
Ionel Popescu
224
0
0
23 Aug 2025
A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
Jiequn Han
Arnulf Jentzen
Weinan E
AI4CE
318
6
0
07 May 2025
Beyond Derivative Pathology of PINNs: Variable Splitting Strategy with
  Convergence Analysis
Beyond Derivative Pathology of PINNs: Variable Splitting Strategy with Convergence Analysis
Yesom Park
Changhoon Song
Myungjoo Kang
317
4
0
30 Sep 2024
Astral: training physics-informed neural networks with error majorants
Astral: training physics-informed neural networks with error majorants
V. Fanaskov
Tianchi Yu
Alexander Rudikov
Ivan Oseledets
310
1
0
04 Jun 2024
Error Analysis of Three-Layer Neural Network Trained with PGD for Deep
  Ritz Method
Error Analysis of Three-Layer Neural Network Trained with PGD for Deep Ritz MethodIEEE Transactions on Information Theory (IEEE Trans. Inf. Theory), 2024
Yuling Jiao
Yanming Lai
Yang Wang
AI4CE
209
1
0
19 May 2024
On Continuity of Robust and Accurate Classifiers
On Continuity of Robust and Accurate Classifiers
Ramin Barati
Reza Safabakhsh
Mohammad Rahmati
AAML
433
1
0
29 Sep 2023
Energy stable neural network for gradient flow equations
Energy stable neural network for gradient flow equations
Gang-Han Fan
Tianyu Jin
Yuan Lan
Yang Xiang
Luchan Zhang
221
0
0
17 Sep 2023
A Finite Expression Method for Solving High-Dimensional Committor Problems
A Finite Expression Method for Solving High-Dimensional Committor ProblemsSIAM Journal on Scientific Computing (SISC), 2023
Zezheng Song
M. Cameron
Haizhao Yang
247
8
0
21 Jun 2023
Convergence Analysis of the Deep Galerkin Method for Weak Solutions
Convergence Analysis of the Deep Galerkin Method for Weak Solutions
Yuling Jiao
Yanming Lai
Yang Wang
Haizhao Yang
Yunfei Yang
221
8
0
05 Feb 2023
EgPDE-Net: Building Continuous Neural Networks for Time Series
  Prediction with Exogenous Variables
EgPDE-Net: Building Continuous Neural Networks for Time Series Prediction with Exogenous VariablesIEEE Transactions on Cybernetics (IEEE Trans. Cybern.), 2022
Penglei Gao
Xi Yang
Rui Zhang
Ping Guo
John Y. Goulermas
Kaizhu Huang
AI4TS
359
10
0
03 Aug 2022
Finite Expression Method for Solving High-Dimensional Partial Differential Equations
Finite Expression Method for Solving High-Dimensional Partial Differential Equations
Senwei Liang
Haizhao Yang
497
22
0
21 Jun 2022
On the Representation of Solutions to Elliptic PDEs in Barron Spaces
On the Representation of Solutions to Elliptic PDEs in Barron SpacesNeural Information Processing Systems (NeurIPS), 2021
Ziang Chen
Jianfeng Lu
Yulong Lu
243
38
0
14 Jun 2021
A Priori Generalization Error Analysis of Two-Layer Neural Networks for
  Solving High Dimensional Schrödinger Eigenvalue Problems
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue ProblemsCommunications of the American Mathematical Society (Comm. Amer. Math. Soc.), 2021
Jianfeng Lu
Yulong Lu
314
39
0
04 May 2021
Bayesian neural networks for weak solution of PDEs with uncertainty
  quantification
Bayesian neural networks for weak solution of PDEs with uncertainty quantification
Xiaoxuan Zhang
K. Garikipati
AI4CE
259
15
0
13 Jan 2021
1
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