DGM: A deep learning algorithm for solving partial differential equations

24 August 2017

Papers citing "DGM: A deep learning algorithm for solving partial differential equations"

50 / 315 papers shown

Title
Efficient training of physics-informed neural networks via importance sampling M. A. Nabian R. J. Gladstone Hadi Meidani DiffM PINN 71 225 0 26 Apr 2021
Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks N. Sukumar Ankit Srivastava PINN AI4CE 57 241 0 17 Apr 2021
Rethinking Neural Operations for Diverse Tasks Nicholas Roberts M. Khodak Tri Dao Liam Li Christopher Ré Ameet Talwalkar AI4CE 43 22 0 29 Mar 2021
Elvet -- a neural network-based differential equation and variational problem solver Jack Y. Araz J. C. Criado M. Spannowsky 26 13 0 26 Mar 2021
Solving and Learning Nonlinear PDEs with Gaussian Processes Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 32 153 0 24 Mar 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 45 671 0 19 Mar 2021
Transferable Model for Shape Optimization subject to Physical Constraints Lukas Harsch Johannes Burgbacher S. Riedelbauch AI4CE 24 1 0 19 Mar 2021
dNNsolve: an efficient NN-based PDE solver V. Guidetti F. Muia Y. Welling A. Westphal 27 6 0 15 Mar 2021
Physics-Informed Neural Network Method for Solving One-Dimensional Advection Equation Using PyTorch S. Vadyala S. N. Betgeri PINN 29 26 0 15 Mar 2021
A Modified Batch Intrinsic Plasticity Method for Pre-training the Random Coefficients of Extreme Learning Machines S. Dong Zongwei Li 33 29 0 14 Mar 2021
Parametric Complexity Bounds for Approximating PDEs with Neural Networks Tanya Marwah Zachary Chase Lipton Andrej Risteski 33 19 0 03 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
Learning optimal multigrid smoothers via neural networks Ru Huang Ruipeng Li Yuanzhe Xi AI4CE 18 27 0 24 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
Bayesian neural networks for weak solution of PDEs with uncertainty quantification Xiaoxuan Zhang K. Garikipati AI4CE 46 11 0 13 Jan 2021
Reproducing Activation Function for Deep Learning Senwei Liang Liyao Lyu Chunmei Wang Haizhao Yang 36 21 0 13 Jan 2021
Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning Li Wang Zhenya Yan 84 47 0 12 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
Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D Nils Wandel Michael Weinmann Reinhard Klein AI4CE 31 50 0 22 Dec 2020
Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning Li Wang Zhenya Yan 27 80 0 18 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
Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes Raffaele Marino N. Macris 29 16 0 09 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 Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data Priyabrata Saha Saibal Mukhopadhyay AI4CE 29 4 0 30 Nov 2020
Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture S. Niaki E. Haghighat Trevor Campbell Xinglong Li R. Vaziri AI4CE 18 203 0 27 Nov 2020
Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems Rui Wang Danielle C. Maddix Christos Faloutsos Bernie Wang Rose Yu OOD AI4CE 27 51 0 20 Nov 2020
DeepReach: A Deep Learning Approach to High-Dimensional Reachability Somil Bansal Claire Tomlin 23 153 0 04 Nov 2020
Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets Christian Soize R. Ghanem AI4CE 9 26 0 27 Oct 2020
Data-driven Identification of 2D Partial Differential Equations using extracted physical features Kazem Meidani A. Farimani 21 17 0 20 Oct 2020
Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting Yuan Yin Vincent Le Guen Jérémie Donà Emmanuel de Bézenac Ibrahim Ayed Nicolas Thome Patrick Gallinari AI4CE PINN 33 132 0 09 Oct 2020
Analysis of three dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis Hongwei Guo X. Zhuang Pengwan Chen N. Alajlan Timon Rabczuk 27 58 0 03 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
POMDPs in Continuous Time and Discrete Spaces Bastian Alt M. Schultheis Heinz Koeppl 19 9 0 02 Oct 2020
A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications N. Zobeiry K. D. Humfeld AI4CE 25 265 0 28 Sep 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 Qualitative Study of the Dynamic Behavior for Adaptive Gradient Algorithms Chao Ma Lei Wu E. Weinan ODL 19 23 0 14 Sep 2020
Convergence of Deep Fictitious Play for Stochastic Differential Games Jiequn Han Ruimeng Hu Jihao Long 29 19 0 12 Aug 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 33 881 0 28 Jul 2020
Deep Learning Gauss-Manin Connections K. Heal Avinash Kulkarni E. Sertöz 34 8 0 27 Jul 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
Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks Colby Wight Jia Zhao 20 219 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
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory Yaoyu Zhang Haizhao Yang 32 74 0 28 Jun 2020
Implicit Neural Representations with Periodic Activation Functions Vincent Sitzmann Julien N. P. Martel Alexander W. Bergman David B. Lindell Gordon Wetzstein AI4TS 47 2,490 0 17 Jun 2020
Solving Differential Equations Using Neural Network Solution Bundles Cedric Wen Flamant P. Protopapas David Sondak 20 29 0 17 Jun 2020