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 / 252 papers shown

Title
JAX-DIPS: Neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuities Pouria A. Mistani Samira Pakravan Rajesh Ilango Frédéric Gibou 26 8 0 25 Oct 2022
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 57 10 0 21 Oct 2022
$r-$ Adaptive Deep Learning Method for Solving Partial Differential Equations Ángel J. Omella David Pardo AI4CE 36 4 0 19 Oct 2022
A cusp-capturing PINN for elliptic interface problems Yu-Hau Tseng Te-Sheng Lin Wei-Fan Hu M. Lai 21 33 0 16 Oct 2022
A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs Songming Liu Zhongkai Hao Chengyang Ying Hang Su Jun Zhu Ze Cheng AI4CE 42 17 0 06 Oct 2022
Limitations of neural network training due to numerical instability of backpropagation Clemens Karner V. Kazeev P. Petersen 45 3 0 03 Oct 2022
Failure-informed adaptive sampling for PINNs Zhiwei Gao Liang Yan Tao Zhou 41 79 0 01 Oct 2022
Scaling transformation of the multimode nonlinear Schrödinger equation for physics-informed neural networks I. Chuprov D. Efremenko Jiexing Gao P. Anisimov V. Zemlyakov 34 0 0 29 Sep 2022
Minimax Optimal Kernel Operator Learning via Multilevel Training Jikai Jin Yiping Lu Jose H. Blanchet Lexing Ying 38 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 38 21 0 20 Sep 2022
Residual-Quantile Adjustment for Adaptive Training of Physics-informed Neural Network Jiayue Han Zhiqiang Cai Zhiyou Wu Xiang Zhou 70 7 0 09 Sep 2022
Solving Elliptic Problems with Singular Sources using Singularity Splitting Deep Ritz Method Tianhao Hu Bangti Jin Zhi Zhou 57 6 0 07 Sep 2022
Semi-analytic PINN methods for singularly perturbed boundary value problems G. Gie Youngjoon Hong Chang-Yeol Jung PINN 20 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 48 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 29 5 0 03 Jul 2022
Anisotropic, Sparse and Interpretable Physics-Informed Neural Networks for PDEs A. A. Ramabathiran P. Ramachandran AI4CE 24 0 0 01 Jul 2022
Finite Expression Method for Solving High-Dimensional Partial Differential Equations Senwei Liang Haizhao Yang 40 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 41 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 47 6 0 28 May 2022
Transformer for Partial Differential Equations' Operator Learning Zijie Li Kazem Meidani A. Farimani 59 145 0 26 May 2022
Generic bounds on the approximation error for physics-informed (and) operator learning Tim De Ryck Siddhartha Mishra PINN 77 59 0 23 May 2022
Towards Size-Independent Generalization Bounds for Deep Operator Nets Pulkit Gopalani Sayar Karmakar Dibyakanti Kumar Anirbit Mukherjee AI4CE 37 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 24 12 0 18 May 2022
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent Yiping Lu Jose H. Blanchet Lexing Ying 55 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 41 20 0 28 Apr 2022
Numerical Computation of Partial Differential Equations by Hidden-Layer Concatenated Extreme Learning Machine Naxian Ni S. Dong 34 20 0 24 Apr 2022
STONet: A Neural-Operator-Driven Spatio-temporal Network Haitao Lin Guojiang Zhao Lirong Wu Stan Z. Li AI4TS AI4CE 28 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 31 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 37 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 39 23 0 03 Mar 2022
Learning Neural Hamiltonian Dynamics: A Methodological Overview Zhijie Chen Mingquan Feng Junchi Yan H. Zha AI4CE 41 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 33 161 0 12 Feb 2022
Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning Chengping Rao Pu Ren Yang Liu Hao Sun AI4CE 56 28 0 28 Jan 2022
Born-Infeld (BI) for AI: Energy-Conserving Descent (ECD) for Optimization G. Luca E. Silverstein 48 10 0 26 Jan 2022
Numerical Approximation of Partial Differential Equations by a Variable Projection Method with Artificial Neural Networks S. Dong Jielin Yang 50 17 0 24 Jan 2022
Overview frequency principle/spectral bias in deep learning Z. Xu Yaoyu Zhang Yaoyu Zhang FaML 46 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 36 1,200 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 34 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 32 109 0 28 Dec 2021
Solving time dependent Fokker-Planck equations via temporal normalizing flow Xiaodong Feng Li Zeng Tao Zhou AI4CE 41 25 0 28 Dec 2021