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
Neural Stochastic Screened Poisson Reconstruction Silvia Sellán Alec Jacobson 3DV 46 6 0 21 Sep 2023
Latent assimilation with implicit neural representations for unknown dynamics Zhuoyuan Li Bin Dong Pingwen Zhang AI4CE 35 3 0 18 Sep 2023
Multi-Grade Deep Learning for Partial Differential Equations with Applications to the Burgers Equation Yuesheng Xu Taishan Zeng AI4CE 37 4 0 14 Sep 2023
Solving multiscale elliptic problems by sparse radial basis function neural networks Zhiwen Wang Minxin Chen Jingrun Chen 68 15 0 01 Sep 2023
Computing excited states of molecules using normalizing flows Yahya Saleh Álvaro Fernández Corral Emil Vogt Armin Iske J. Küpper A. Yachmenev 43 7 0 31 Aug 2023
Learning Specialized Activation Functions for Physics-informed Neural Networks Honghui Wang Lu Lu Shiji Song Gao Huang PINN AI4CE 26 12 0 08 Aug 2023
Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variables Javier Orera-Echeverria J. Ayensa-Jiménez Manuel Doblaré 30 1 0 07 Aug 2023
Temporal Difference Learning for High-Dimensional PIDEs with Jumps Liwei Lu Hailong Guo Xueqing Yang Yi Zhu AI4CE 33 6 0 06 Jul 2023
Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems Yongcun Song Xiaoming Yuan Hangrui Yue AI4CE 30 2 0 01 Jul 2023
A Finite Expression Method for Solving High-Dimensional Committor Problems Zezheng Song M. Cameron Haizhao Yang 23 6 0 21 Jun 2023
Deep Stochastic Mechanics Elena Orlova Aleksei Ustimenko Ruoxi Jiang Peter Y. Lu Rebecca Willett DiffM 58 0 0 31 May 2023
ParticleWNN: a Novel Neural Networks Framework for Solving Partial Differential Equations Yaohua Zang Gang Bao 48 4 0 21 May 2023
Score Operator Newton transport N. Chandramoorthy F. Schaefer Youssef Marzouk OT 41 1 0 16 May 2023
Theoretical Analysis of Inductive Biases in Deep Convolutional Networks Zihao Wang Lei Wu 28 20 0 15 May 2023
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs Pau Batlle Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 39 17 0 08 May 2023
A Stable and Scalable Method for Solving Initial Value PDEs with Neural Networks Marc Finzi Andres Potapczynski M. Choptuik A. Wilson 28 12 0 28 Apr 2023
Pseudo-Hamiltonian neural networks for learning partial differential equations Sølve Eidnes K. Lye 34 10 0 27 Apr 2023
A Survey on Solving and Discovering Differential Equations Using Deep Neural Networks Hyeonjung Jung Jung Jayant Gupta B. Jayaprakash Matthew J. Eagon Harish Selvam Carl Molnar W. Northrop Shashi Shekhar AI4CE 56 5 0 26 Apr 2023
In-Context Operator Learning with Data Prompts for Differential Equation Problems Liu Yang Siting Liu Tingwei Meng Stanley J. Osher 51 61 0 17 Apr 2023
The R-mAtrIx Net Shailesh Lal Suvajit Majumder E. Sobko 27 5 0 14 Apr 2023
EPINN-NSE: Enhanced Physics-Informed Neural Networks for Solving Navier-Stokes Equations Ayoub Farkane Mounir Ghogho M. Oudani M. Boutayeb PINN 39 5 0 07 Apr 2023
$Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion$ Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion Xiongbin Yan Zhi-Qin John Xu Zheng Ma 37 2 0 03 Apr 2023
Multilevel CNNs for Parametric PDEs Cosmas Heiß Ingo Gühring Martin Eigel AI4CE 37 8 0 01 Apr 2023
Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models Anant Raj Umut Simsekli Alessandro Rudi DiffM 48 1 0 30 Mar 2023
GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs Yuling Jiao Dingwei Li Xiliang Lu J. Yang Cheng Yuan 47 9 0 28 Mar 2023
GNN-based physics solver for time-independent PDEs R. J. Gladstone H. Rahmani V. Suryakumar Hadi Meidani M. DÉlia A. Zareei AI4CE 30 15 0 28 Mar 2023
GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs Yanlai Chen Shawn Koohy PINN AI4CE 42 24 0 27 Mar 2023
Error Analysis of Physics-Informed Neural Networks for Approximating Dynamic PDEs of Second Order in Time Y. Qian Yongchao Zhang Yuanfei Huang S. Dong PINN 31 1 0 22 Mar 2023
Achieving High Accuracy with PINNs via Energy Natural Gradients Johannes Müller Marius Zeinhofer 35 5 0 25 Feb 2023
Minimax Instrumental Variable Regression and $L_2$ Convergence Guarantees without Identification or Closedness Andrew Bennett Nathan Kallus Xiaojie Mao Whitney Newey Vasilis Syrgkanis Masatoshi Uehara 43 14 0 10 Feb 2023
Failure-informed adaptive sampling for PINNs, Part II: combining with re-sampling and subset simulation Zhi-Hao Gao Tao Tang Liang Yan Tao Zhou 56 18 0 03 Feb 2023
Sharp Lower Bounds on Interpolation by Deep ReLU Neural Networks at Irregularly Spaced Data Jonathan W. Siegel 21 2 0 02 Feb 2023
Experimental observation on a low-rank tensor model for eigenvalue problems Jun Hu Pengzhan Jin 27 2 0 01 Feb 2023
Koopman neural operator as a mesh-free solver of non-linear partial differential equations Wei Xiong Xiaomeng Huang Ziyang Zhang Ruixuan Deng Pei Sun Yang Tian AI4CE 29 32 0 24 Jan 2023
KoopmanLab: machine learning for solving complex physics equations Wei Xiong Muyuan Ma Xiaomeng Huang Ziyang Zhang Pei Sun Yang Tian AI4CE 39 14 0 03 Jan 2023
MC-Nonlocal-PINNs: handling nonlocal operators in PINNs via Monte Carlo sampling Xiaodong Feng Yue Qian W. Shen 30 3 0 26 Dec 2022
Guiding continuous operator learning through Physics-based boundary constraints Nadim Saad Gaurav Gupta S. Alizadeh Danielle C. Maddix AI4CE 48 20 0 14 Dec 2022
Non-equispaced Fourier Neural Solvers for PDEs Haitao Lin Lirong Wu Yongjie Xu Yufei Huang Siyuan Li Guojiang Zhao Z. Stan 27 7 0 09 Dec 2022
Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations Wuzhe Xu Yulong Lu Li Wang 37 34 0 09 Dec 2022
Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equations Yemo Li Yiwen Pang Bin Shan AI4CE 36 3 0 08 Dec 2022
Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems Derick Nganyu Tanyu Jianfeng Ning Tom Freudenberg Nick Heilenkötter A. Rademacher U. Iben Peter Maass AI4CE 28 34 0 06 Dec 2022
Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators Ha Maust Zong-Yi Li Yixuan Wang Daniel Leibovici O. Bruno T. Hou Anima Anandkumar AI4CE 29 11 0 29 Nov 2022
Bayesian Inversion with Neural Operator (BINO) for Modeling Subdiffusion: Forward and Inverse Problems Xiongbin Yan Z. Xu Zheng Ma 23 2 0 22 Nov 2022
Neural tangent kernel analysis of PINN for advection-diffusion equation M. Saadat B. Gjorgiev L. Das G. Sansavini 40 0 0 21 Nov 2022
Convergence analysis of unsupervised Legendre-Galerkin neural networks for linear second-order elliptic PDEs Seungchan Ko S. Yun Youngjoon Hong 40 5 0 16 Nov 2022
Gradient-enhanced deep neural network approximations Xiaodong Feng Li Zeng UQCV 41 5 0 08 Nov 2022
A Deep Double Ritz Method (D $^2$ RM) for solving Partial Differential Equations using Neural Networks C. Uriarte David Pardo I. Muga J. Muñoz‐Matute 54 18 0 07 Nov 2022
An optimal control perspective on diffusion-based generative modeling Julius Berner Lorenz Richter Karen Ullrich DiffM 73 82 0 02 Nov 2022
Convergence analysis of a quasi-Monte Carlo-based deep learning algorithm for solving partial differential equations Fengjiang Fu Xiaoqun Wang 29 2 0 28 Oct 2022
Neuro-symbolic partial differential equation solver Pouria A. Mistani Samira Pakravan Rajesh Ilango S. Choudhry Frédéric Gibou 41 1 0 25 Oct 2022