The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems

30 September 2017

Papers citing "The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems"

50 / 235 papers shown

Title
Minimax Optimal Kernel Operator Learning via Multilevel Training Jikai Jin Yiping Lu Jose H. Blanchet Lexing Ying 31 12 0 28 Sep 2022
Deep learning for gradient flows using the Brezis-Ekeland principle Laura Carini Max Jensen R. Nürnberg 28 0 0 28 Sep 2022
Neural Networks Based on Power Method and Inverse Power Method for Solving Linear Eigenvalue Problems Qihong Yang Yangtao Deng Yu Yang Qiaolin He Shiquan Zhang 24 13 0 22 Sep 2022
Investigating and Mitigating Failure Modes in Physics-informed Neural Networks (PINNs) S. Basir PINN AI4CE 31 21 0 20 Sep 2022
Solving Elliptic Problems with Singular Sources using Singularity Splitting Deep Ritz Method Tianhao Hu Bangti Jin Zhi Zhou 36 6 0 07 Sep 2022
Semi-analytic PINN methods for singularly perturbed boundary value problems G. Gie Youngjoon Hong Chang-Yeol Jung PINN 13 5 0 19 Aug 2022
Physics-Informed Neural Networks for Shell Structures Jan-Hendrik Bastek D. Kochmann AI4CE 29 51 0 26 Jul 2022
Learning Relaxation for Multigrid Dmitry Kuznichov AI4CE 24 1 0 25 Jul 2022
Unsupervised Legendre-Galerkin Neural Network for Singularly Perturbed Partial Differential Equations Junho Choi N. Kim Youngjoon Hong AI4CE 29 0 0 21 Jul 2022
The Deep Ritz Method for Parametric $p$ -Dirichlet Problems A. Kaltenbach Marius Zeinhofer 27 3 0 05 Jul 2022
Evaluating Error Bound for Physics-Informed Neural Networks on Linear Dynamical Systems Shuheng Liu Xiyue Huang P. Protopapas PINN 24 5 0 03 Jul 2022
Anisotropic, Sparse and Interpretable Physics-Informed Neural Networks for PDEs A. A. Ramabathiran P. Ramachandran AI4CE 19 0 0 01 Jul 2022
Finite Expression Method for Solving High-Dimensional Partial Differential Equations Senwei Liang Haizhao Yang 34 18 0 21 Jun 2022
Critical Investigation of Failure Modes in Physics-informed Neural Networks S. Basir Inanc Senocak PINN AI4CE 12 18 0 20 Jun 2022
Unsupervised Learning of the Total Variation Flow T. G. Grossmann Sören Dittmer Yury Korolev Carola-Bibiane Schönlieb 33 3 0 09 Jun 2022
A Neural Network Approach for Homogenization of Multiscale Problems Jihun Han Yoonsang Lee 35 13 0 04 Jun 2022
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 36 6 0 28 May 2022
Transformer for Partial Differential Equations' Operator Learning Zijie Li Kazem Meidani A. Farimani 47 145 0 26 May 2022
Towards Size-Independent Generalization Bounds for Deep Operator Nets Pulkit Gopalani Sayar Karmakar Dibyakanti Kumar Anirbit Mukherjee AI4CE 24 5 0 23 May 2022
Revisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Method Wensheng Li Chao Zhang Chuncheng Wang Hanting Guan Dacheng Tao DiffM PINN 18 12 0 18 May 2022
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent Yiping Lu Jose H. Blanchet Lexing Ying 38 7 0 15 May 2022
BI-GreenNet: Learning Green's functions by boundary integral network Guochang Lin Fu-jun Chen Pipi Hu Xiang Chen Junqing Chen Jun Wang Zuoqiang Shi 34 20 0 28 Apr 2022
Numerical Computation of Partial Differential Equations by Hidden-Layer Concatenated Extreme Learning Machine Naxian Ni S. Dong 29 20 0 24 Apr 2022
STONet: A Neural-Operator-Driven Spatio-temporal Network Haitao Lin Guojiang Zhao Lirong Wu Stan Z. Li AI4TS AI4CE 21 1 0 18 Apr 2022
Learning time-dependent PDE solver using Message Passing Graph Neural Networks Pourya Pilva A. Zareei AI4CE 34 7 0 15 Apr 2022
The Mathematics of Artificial Intelligence Gitta Kutyniok 24 0 0 16 Mar 2022
$Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations$ Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations Ling Guo Hao Wu Xiao-Jun Yu Tao Zhou PINN AI4CE 32 58 0 16 Mar 2022
Physics-informed neural network solution of thermo-hydro-mechanical (THM) processes in porous media Daniel Amini E. Haghighat R. Juanes PINN AI4CE 36 23 0 03 Mar 2022
Learning Neural Hamiltonian Dynamics: A Methodological Overview Zhijie Chen Mingquan Feng Junchi Yan H. Zha AI4CE 28 15 0 28 Feb 2022
Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations Benwei Wu O. Hennigh Jan Kautz S. Choudhry Wonmin Byeon MLAU AI4CE 14 11 0 24 Feb 2022
MIONet: Learning multiple-input operators via tensor product Pengzhan Jin Shuai Meng Lu Lu 25 158 0 12 Feb 2022
Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning Chengping Rao Pu Ren Yang Liu Hao Sun AI4CE 45 28 0 28 Jan 2022
Numerical Approximation of Partial Differential Equations by a Variable Projection Method with Artificial Neural Networks S. Dong Jielin Yang 47 17 0 24 Jan 2022
Overview frequency principle/spectral bias in deep learning Z. Xu Tao Luo Yaoyu Zhang FaML 35 66 0 19 Jan 2022
Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next S. Cuomo Vincenzo Schiano Di Cola F. Giampaolo G. Rozza Maizar Raissi F. Piccialli PINN 31 1,190 0 14 Jan 2022
De Rham compatible Deep Neural Network FEM M. Longo J. Opschoor Nico Disch Christoph Schwab Jakob Zech 38 8 0 14 Jan 2022
Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network Huaiqian You Yue Yu M. DÉlia T. Gao Stewart Silling 29 70 0 06 Jan 2022
DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations Keju Tang Xiaoliang Wan Chao Yang 32 107 0 28 Dec 2021
Solving time dependent Fokker-Planck equations via temporal normalizing flow Xiaodong Feng Li Zeng Tao Zhou AI4CE 36 25 0 28 Dec 2021
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations C. Marcati Christoph Schwab 27 38 0 15 Dec 2021
Subspace Decomposition based DNN algorithm for elliptic type multi-scale PDEs Xi-An Li Z. Xu Lei Zhang 27 27 0 10 Dec 2021
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems Nikolas Nusken Lorenz Richter PINN DiffM 38 27 0 07 Dec 2021
A coarse space acceleration of deep-DDM Valentin Mercier Serge Gratton Pierre Boudier AI4CE 33 10 0 07 Dec 2021
Hierarchical Learning to Solve Partial Differential Equations Using Physics-Informed Neural Networks Jihun Han Yoonsang Lee AI4CE 24 10 0 02 Dec 2021
Physics-Informed Neural Operator for Learning Partial Differential Equations Zong-Yi Li Hongkai Zheng Nikola B. Kovachki David Jin Haoxuan Chen Burigede Liu Kamyar Azizzadenesheli Anima Anandkumar AI4CE 62 386 0 06 Nov 2021
Solving Partial Differential Equations with Point Source Based on Physics-Informed Neural Networks Xiang Huang Hongsheng Liu Beiji Shi Zidong Wang Kan Yang ... Jing Zhou Fan Yu Bei Hua Lei Chen Bin Dong 19 20 0 02 Nov 2021
DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method Zhongjian Wang Jack Xin Zhiwen Zhang 39 15 0 02 Nov 2021
Polynomial-Spline Neural Networks with Exact Integrals Jonas A. Actor Andrew Huang N. Trask 33 1 0 26 Oct 2021
Computing the Invariant Distribution of Randomly Perturbed Dynamical Systems Using Deep Learning Bo Lin Qianxiao Li W. Ren 29 8 0 22 Oct 2021
Solving Image PDEs with a Shallow Network Pascal Getreuer P. Milanfar Xiyang Luo 39 1 0 15 Oct 2021