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"

35 / 235 papers shown

Title
SciANN: A Keras/Tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks E. Haghighat R. Juanes AI4CE PINN 20 21 0 11 May 2020
Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space Nikolas Nusken Lorenz Richter AI4CE 38 105 0 11 May 2020
Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach Jiequn Han Jianfeng Lu Mo Zhou DiffM 17 83 0 07 Feb 2020
A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks Jihun Han Mihai Nica A. Stinchcombe 30 49 0 17 Jan 2020
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems Pengzhan Jin Zhen Zhang Aiqing Zhu Yifa Tang George Karniadakis 21 21 0 11 Jan 2020
Machine Learning from a Continuous Viewpoint E. Weinan Chao Ma Lei Wu 33 102 0 30 Dec 2019
Accelerating PDE-constrained Inverse Solutions with Deep Learning and Reduced Order Models Sheroze Sheriffdeen J. Ragusa J. Morel M. Adams T. Bui-Thanh AI4CE 36 15 0 17 Dec 2019
Uniform error estimates for artificial neural network approximations for heat equations Lukas Gonon Philipp Grohs Arnulf Jentzen David Kofler David Siska 37 34 0 20 Nov 2019
Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs Z. Cai Jingshuang Chen Min Liu Xinyu Liu 26 88 0 05 Nov 2019
Multi-scale Deep Neural Networks for Solving High Dimensional PDEs Wei Cai Zhi-Qin John Xu AI4CE 22 38 0 25 Oct 2019
Solving Optical Tomography with Deep Learning Yuwei Fan Lexing Ying 24 15 0 10 Oct 2019
D3M: A deep domain decomposition method for partial differential equations Ke Li Keju Tang Tianfan Wu Qifeng Liao AI4CE 22 114 0 24 Sep 2019
A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems Wei Cai Xiaoguang Li Lizuo Liu 25 84 0 23 Sep 2019
A Multi-level procedure for enhancing accuracy of machine learning algorithms K. Lye Siddhartha Mishra Roberto Molinaro 17 32 0 20 Sep 2019
An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications E. Samaniego C. Anitescu S. Goswami Vien Minh Nguyen-Thanh Hongwei Guo Khader M. Hamdia Timon Rabczuk X. Zhuang PINN AI4CE 159 1,344 0 27 Aug 2019
Space-time error estimates for deep neural network approximations for differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philipp Zimmermann 34 33 0 11 Aug 2019
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 52 1,491 0 10 Jul 2019
Deep splitting method for parabolic PDEs C. Beck S. Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld 34 126 0 08 Jul 2019
Meta-learning Pseudo-differential Operators with Deep Neural Networks Jordi Feliu-Fabà Yuwei Fan Lexing Ying 22 39 0 16 Jun 2019
Solving Electrical Impedance Tomography with Deep Learning Yuwei Fan Lexing Ying 28 100 0 06 Jun 2019
A neural network based policy iteration algorithm with global $H^2$ -superlinear convergence for stochastic games on domains Kazufumi Ito C. Reisinger Yufei Zhang 27 27 0 05 Jun 2019
Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning Yufei Wang Ziju Shen Zichao Long Bin Dong AI4CE PINN 13 40 0 27 May 2019
A type of generalization error induced by initialization in deep neural networks Tao Luo Zhi-Qin John Xu Yaoyu Zhang Zheng Ma 9 50 0 19 May 2019
Variational training of neural network approximations of solution maps for physical models Yingzhou Li Jianfeng Lu Anqi Mao GAN 25 35 0 07 May 2019
Data driven approximation of parametrized PDEs by Reduced Basis and Neural Networks N. D. Santo S. Deparis Luca Pegolotti 24 66 0 02 Apr 2019
Deep learning observables in computational fluid dynamics K. Lye Siddhartha Mishra Deep Ray OOD AI4CE 21 158 0 07 Mar 2019
$Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms$ Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms Ingo Gühring Gitta Kutyniok P. Petersen 28 199 0 21 Feb 2019
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks Zhi-Qin John Xu Tao Luo Yaoyu Zhang Yan Xiao Zheng Ma 31 504 0 19 Jan 2019
Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data Yinhao Zhu N. Zabaras P. Koutsourelakis P. Perdikaris PINN AI4CE 46 854 0 18 Jan 2019
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients Arnulf Jentzen Diyora Salimova Timo Welti AI4CE 29 116 0 19 Sep 2018
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philippe von Wurstemberger 21 167 0 07 Sep 2018
Deep Multiscale Model Learning Yating Wang Siu Wun Cheung Eric T. Chung Y. Efendiev Min Wang AI4CE 27 80 0 13 Jun 2018
Solving the Kolmogorov PDE by means of deep learning C. Beck S. Becker Philipp Grohs Nor Jaafari Arnulf Jentzen 24 91 0 01 Jun 2018
Solving for high dimensional committor functions using artificial neural networks Y. Khoo Jianfeng Lu Lexing Ying 31 137 0 28 Feb 2018
A unified deep artificial neural network approach to partial differential equations in complex geometries Jens Berg K. Nystrom AI4CE 29 578 0 17 Nov 2017