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
A Review of Physics-based Machine Learning in Civil Engineering S. Vadyala S. N. Betgeri J. Matthews Elizabeth Matthews AI4CE 30 152 0 09 Oct 2021
NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs Biswajit Khara Aditya Balu Ameya Joshi S. Sarkar C. Hegde A. Krishnamurthy Baskar Ganapathysubramanian 46 19 0 04 Oct 2021
Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusion S. Basir Inanc Senocak PINN AI4CE 34 68 0 30 Sep 2021
Learning in Sinusoidal Spaces with Physics-Informed Neural Networks Jian Cheng Wong C. Ooi Abhishek Gupta Yew-Soon Ong AI4CE PINN SSL 23 77 0 20 Sep 2021
Learning Density Distribution of Reachable States for Autonomous Systems Yue Meng Dawei Sun Zeng Qiu Md Tawhid Bin Waez Chuchu Fan 79 19 0 14 Sep 2021
Self-adaptive deep neural network: Numerical approximation to functions and PDEs Zhiqiang Cai Jingshuang Chen Min Liu ODL 25 14 0 07 Sep 2021
Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces George Stepaniants 49 15 0 26 Aug 2021
Neural Operator: Learning Maps Between Function Spaces Nikola B. Kovachki Zong-Yi Li Burigede Liu Kamyar Azizzadenesheli K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 57 441 0 19 Aug 2021
A physics-informed variational DeepONet for predicting the crack path in brittle materials S. Goswami Minglang Yin Yue Yu G. Karniadakis AI4CE 33 187 0 16 Aug 2021
MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs Lulu Zhang Yaoyu Zhang Tao Luo Weinan E Z. Xu Zheng Ma AI4CE 27 33 0 08 Jul 2021
PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs Pu Ren Chengping Rao Yang Liu Jianxun Wang Hao Sun DiffM AI4CE 46 193 0 26 Jun 2021
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 38 27 0 14 Jun 2021
Long-time integration of parametric evolution equations with physics-informed DeepONets Sizhuang He P. Perdikaris AI4CE 24 117 0 09 Jun 2021
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs Jérome Darbon P. Dower Tingwei Meng 14 22 0 07 May 2021
Improved Surrogate Modeling of Fluid Dynamics with Physics-Informed Neural Networks Jian Cheng Wong C. Ooi P. Chiu M. Dao PINN AI4CE 32 4 0 05 May 2021
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems Jianfeng Lu Yulong Lu 34 29 0 04 May 2021
Efficient training of physics-informed neural networks via importance sampling M. A. Nabian R. J. Gladstone Hadi Meidani DiffM PINN 71 223 0 26 Apr 2021
Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks N. Sukumar Ankit Srivastava PINN AI4CE 54 241 0 17 Apr 2021
The mixed deep energy method for resolving concentration features in finite strain hyperelasticity J. Fuhg N. Bouklas PINN AI4CE 33 90 0 15 Apr 2021
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces Philipp Grohs F. Voigtlaender 39 34 0 06 Apr 2021
Solving and Learning Nonlinear PDEs with Gaussian Processes Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 32 153 0 24 Mar 2021
Evolutional Deep Neural Network Yifan Du T. Zaki 29 68 0 18 Mar 2021
A Modified Batch Intrinsic Plasticity Method for Pre-training the Random Coefficients of Extreme Learning Machines S. Dong Zongwei Li 30 29 0 14 Mar 2021
Error Estimates for the Deep Ritz Method with Boundary Penalty Johannes Müller Marius Zeinhofer 42 16 0 01 Mar 2021
SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs A. A. Ramabathiran P. Ramachandran PINN AI4CE 29 76 0 25 Feb 2021
A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate Hongwei Guo X. Zhuang Timon Rabczuk AI4CE 27 433 0 04 Feb 2021
Reproducing Activation Function for Deep Learning Senwei Liang Liyao Lyu Chunmei Wang Haizhao Yang 36 21 0 13 Jan 2021
Can Transfer Neuroevolution Tractably Solve Your Differential Equations? Jian Cheng Wong Abhishek Gupta Yew-Soon Ong 28 21 0 06 Jan 2021
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations Jianfeng Lu Yulong Lu Min Wang 36 37 0 05 Jan 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 35 146 0 22 Dec 2020
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning Fan Chen J. Huang Chunmei Wang Haizhao Yang 28 30 0 15 Dec 2020
Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data Ben Adcock Simone Brugiapaglia N. Dexter S. Moraga 41 29 0 11 Dec 2020
Local Extreme Learning Machines and Domain Decomposition for Solving Linear and Nonlinear Partial Differential Equations S. Dong Zongwei Li 36 164 0 04 Dec 2020
A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound A. Stanziola Simon Arridge B. Cox B. Treeby 16 32 0 29 Oct 2020
Deep neural network for solving differential equations motivated by Legendre-Galerkin approximation Bryce Chudomelka Youngjoon Hong Hyunwoo J. Kim Jinyoung Park 32 7 0 24 Oct 2020
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 268 2,315 0 18 Oct 2020
Stochastic analysis of heterogeneous porous material with modified neural architecture search (NAS) based physics-informed neural networks using transfer learning Hongwei Guo X. Zhuang Timon Rabczuk 20 82 0 03 Oct 2020
A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder Youngkyu Kim Youngsoo Choi David Widemann T. Zohdi AI4CE 16 189 0 25 Sep 2020
Discovery of Governing Equations with Recursive Deep Neural Networks Jia Zhao Jarrod Mau PINN 32 6 0 24 Sep 2020
A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks S. Dong Naxian Ni 13 132 0 15 Jul 2020
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions Philipp Grohs L. Herrmann 35 52 0 10 Jul 2020
Expressivity of Deep Neural Networks Ingo Gühring Mones Raslan Gitta Kutyniok 21 51 0 09 Jul 2020
Weak error analysis for stochastic gradient descent optimization algorithms A. Bercher Lukas Gonon Arnulf Jentzen Diyora Salimova 36 4 0 03 Jul 2020
Bayesian Sparse learning with preconditioned stochastic gradient MCMC and its applications Yating Wang Wei Deng Guang Lin 24 13 0 29 Jun 2020
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory Yaoyu Zhang Haizhao Yang 32 74 0 28 Jun 2020
Multipole Graph Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 24 377 0 16 Jun 2020
Learning continuous-time PDEs from sparse data with graph neural networks V. Iakovlev Markus Heinonen Harri Lähdesmäki AI4CE 24 68 0 16 Jun 2020
Physics informed deep learning for computational elastodynamics without labeled data Chengping Rao Hao Sun Yang Liu PINN AI4CE 24 222 0 10 Jun 2020
Space-time deep neural network approximations for high-dimensional partial differential equations F. Hornung Arnulf Jentzen Diyora Salimova AI4CE 34 19 0 03 Jun 2020
Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences Siddhartha Mishra T. Konstantin Rusch 27 49 0 26 May 2020