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2103.01007
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Error Estimates for the Deep Ritz Method with Boundary Penalty
Mathematical and Scientific Machine Learning (MSML), 2021
1 March 2021
Johannes Müller
Marius Zeinhofer
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Papers citing
"Error Estimates for the Deep Ritz Method with Boundary Penalty"
13 / 13 papers shown
THINNs: Thermodynamically Informed Neural Networks
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Deep Neural Networks with General Activations: Super-Convergence in Sobolev Norms
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Juncai He
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99
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07 Aug 2025
From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning
Juan Diego Toscano
Vivek Oommen
Alan John Varghese
Zongren Zou
Nazanin Ahmadi Daryakenari
Chenxi Wu
George Karniadakis
PINN
AI4CE
224
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17 Oct 2024
Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditions
Mohan Ren
Zhihao Fang
Keren Li
Anirbit Mukherjee
PINN
AI4CE
223
0
0
30 Jul 2024
Error Analysis of Three-Layer Neural Network Trained with PGD for Deep Ritz Method
IEEE Transactions on Information Theory (IEEE Trans. Inf. Theory), 2024
Yuling Jiao
Yanming Lai
Yang Wang
AI4CE
177
1
0
19 May 2024
Geometry-aware framework for deep energy method: an application to structural mechanics with hyperelastic materials
Computer Physics Communications (CPC), 2024
Thi Nguyen Khoa Nguyen
T. Dairay
Raphael Meunier
Christophe Millet
Mathilde Mougeot
AI4CE
PINN
210
3
0
06 May 2024
Solutions to Elliptic and Parabolic Problems via Finite Difference Based Unsupervised Small Linear Convolutional Neural Networks
Computers and Mathematics with Applications (CMA), 2023
A. Celaya
Keegan L. A. Kirk
David T. Fuentes
Beatrice Riviere
226
1
0
01 Nov 2023
Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives
Neural Information Processing Systems (NeurIPS), 2023
Yahong Yang
Haizhao Yang
Yang Xiang
188
31
0
15 May 2023
Achieving High Accuracy with PINNs via Energy Natural Gradients
International Conference on Machine Learning (ICML), 2023
Johannes Müller
Marius Zeinhofer
287
10
0
25 Feb 2023
Dirichlet-Neumann learning algorithm for solving elliptic interface problems
Qi Sun
Xuejun Xu
Haotian Yi
174
3
0
18 Jan 2023
Convergence analysis of unsupervised Legendre-Galerkin neural networks for linear second-order elliptic PDEs
Seungchan Ko
S. Yun
Youngjoon Hong
184
6
0
16 Nov 2022
Solving Elliptic Problems with Singular Sources using Singularity Splitting Deep Ritz Method
SIAM Journal on Scientific Computing (SISC), 2022
Tianhao Hu
Bangti Jin
Zhi Zhou
337
8
0
07 Sep 2022
NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs
Biswajit Khara
Aditya Balu
Ameya Joshi
Soumik Sarkar
Chinmay Hegde
A. Krishnamurthy
Baskar Ganapathysubramanian
243
24
0
04 Oct 2021
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