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
Computing excited states of molecules using normalizing flows Yahya Saleh Álvaro Fernández Corral Emil Vogt Armin Iske J. Küpper A. Yachmenev 38 7 0 31 Aug 2023
Learning Specialized Activation Functions for Physics-informed Neural Networks Honghui Wang Lu Lu Shiji Song Gao Huang PINN AI4CE 21 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 27 1 0 07 Aug 2023
Temporal Difference Learning for High-Dimensional PIDEs with Jumps Liwei Lu Hailong Guo Xueqing Yang Yi Zhu AI4CE 28 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 19 2 0 01 Jul 2023
A Finite Expression Method for Solving High-Dimensional Committor Problems Zezheng Song M. Cameron Haizhao Yang 20 6 0 21 Jun 2023
Deep Stochastic Mechanics Elena Orlova Aleksei Ustimenko Ruoxi Jiang Peter Y. Lu Rebecca Willett DiffM 51 0 0 31 May 2023
ParticleWNN: a Novel Neural Networks Framework for Solving Partial Differential Equations Yaohua Zang Gang Bao 37 4 0 21 May 2023
Score Operator Newton transport N. Chandramoorthy F. Schaefer Youssef Marzouk OT 25 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 34 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 26 12 0 28 Apr 2023
Pseudo-Hamiltonian neural networks for learning partial differential equations Sølve Eidnes K. Lye 28 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 45 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 40 60 0 17 Apr 2023
The R-mAtrIx Net Shailesh Lal Suvajit Majumder E. Sobko 24 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 28 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 32 2 0 03 Apr 2023
Multilevel CNNs for Parametric PDEs Cosmas Heiß Ingo Gühring Martin Eigel AI4CE 30 8 0 01 Apr 2023
Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models Anant Raj Umut Simsekli Alessandro Rudi DiffM 31 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 36 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 25 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 37 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 26 1 0 22 Mar 2023
Achieving High Accuracy with PINNs via Energy Natural Gradients Johannes Müller Marius Zeinhofer 18 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 36 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 37 18 0 03 Feb 2023
Sharp Lower Bounds on Interpolation by Deep ReLU Neural Networks at Irregularly Spaced Data Jonathan W. Siegel 19 2 0 02 Feb 2023
Experimental observation on a low-rank tensor model for eigenvalue problems Jun Hu Pengzhan Jin 19 2 0 01 Feb 2023
KoopmanLab: machine learning for solving complex physics equations Wei Xiong Muyuan Ma Xiaomeng Huang Ziyang Zhang Pei Sun Yang Tian AI4CE 26 13 0 03 Jan 2023
Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations Wuzhe Xu Yulong Lu Li Wang 32 33 0 09 Dec 2022
Physics-guided Data Augmentation for Learning the Solution Operator of Linear Differential Equations Yemo Li Yiwen Pang Bin Shan AI4CE 31 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 23 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 14 2 0 22 Nov 2022
Neural tangent kernel analysis of PINN for advection-diffusion equation M. Saadat B. Gjorgiev L. Das G. Sansavini 35 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 30 5 0 16 Nov 2022
Gradient-enhanced deep neural network approximations Xiaodong Feng Li Zeng UQCV 34 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 49 18 0 07 Nov 2022
An optimal control perspective on diffusion-based generative modeling Julius Berner Lorenz Richter Karen Ullrich DiffM 44 81 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 36 1 0 25 Oct 2022
JAX-DIPS: Neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuities Pouria A. Mistani Samira Pakravan Rajesh Ilango Frédéric Gibou 21 8 0 25 Oct 2022
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 52 10 0 21 Oct 2022
$r-$ Adaptive Deep Learning Method for Solving Partial Differential Equations Ángel J. Omella David Pardo AI4CE 31 4 0 19 Oct 2022
A cusp-capturing PINN for elliptic interface problems Yu-Hau Tseng Te-Sheng Lin Wei-Fan Hu M. Lai 16 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 23 17 0 06 Oct 2022
Limitations of neural network training due to numerical instability of backpropagation Clemens Karner V. Kazeev P. Petersen 40 3 0 03 Oct 2022
Failure-informed adaptive sampling for PINNs Zhiwei Gao Liang Yan Tao Zhou 18 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 29 0 0 29 Sep 2022