Physics-Informed Graph-Mesh Networks for PDEs: A hybrid approach for complex problems

25 September 2024

Papers citing "Physics-Informed Graph-Mesh Networks for PDEs: A hybrid approach for complex problems"

21 / 21 papers shown

Title
Exact conservation laws for neural network integrators of dynamical systems E. Müller PINN 105 14 0 23 Sep 2022
Finite Element Method-enhanced Neural Network for Forward and Inverse Problems R. Meethal B. Obst Mohamed Khalil A. Ghantasala A. Kodakkal K. Bletzinger R. Wüchner AI4CE 50 33 0 17 May 2022
GRAND: Graph Neural Diffusion B. Chamberlain J. Rowbottom Maria I. Gorinova Stefan Webb Emanuele Rossi M. Bronstein GNN 123 270 0 21 Jun 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 97 707 0 19 Mar 2021
Learning Mesh-Based Simulation with Graph Networks Tobias Pfaff Meire Fortunato Alvaro Sanchez-Gonzalez Peter W. Battaglia AI4CE 82 804 0 07 Oct 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 141 916 0 28 Jul 2020
Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction Filipe de Avila Belbute-Peres T. Economon J. Zico Kolter AI4CE 103 231 0 08 Jul 2020
Learning to Simulate Complex Physics with Graph Networks Alvaro Sanchez-Gonzalez Jonathan Godwin Tobias Pfaff Rex Ying J. Leskovec Peter W. Battaglia PINN AI4CE 145 1,101 0 21 Feb 2020
Lagrangian Duality for Constrained Deep Learning Ferdinando Fioretto Pascal Van Hentenryck Terrence W.K. Mak Cuong Tran Federico Baldo M. Lombardi PINN 47 83 0 26 Jan 2020
PyTorch: An Imperative Style, High-Performance Deep Learning Library Adam Paszke Sam Gross Francisco Massa Adam Lerer James Bradbury ... Sasank Chilamkurthy Benoit Steiner Lu Fang Junjie Bai Soumith Chintala ODL 547 42,591 0 03 Dec 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 215 1,381 0 27 Aug 2019
Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks N. Geneva N. Zabaras AI4CE 69 275 0 13 Jun 2019
Hamiltonian Neural Networks S. Greydanus Misko Dzamba J. Yosinski PINN AI4CE 118 899 0 04 Jun 2019
A Comprehensive Survey on Graph Neural Networks Zonghan Wu Shirui Pan Fengwen Chen Guodong Long Chengqi Zhang Philip S. Yu FaML GNN AI4TS AI4CE 788 8,566 0 03 Jan 2019
Deep Learning on Graphs: A Survey Ziwei Zhang Peng Cui Wenwu Zhu GNN 154 1,336 0 11 Dec 2018
Relational inductive biases, deep learning, and graph networks Peter W. Battaglia Jessica B. Hamrick V. Bapst Alvaro Sanchez-Gonzalez V. Zambaldi ... Pushmeet Kohli M. Botvinick Oriol Vinyals Yujia Li Razvan Pascanu AI4CE NAI 769 3,129 0 04 Jun 2018
A unified deep artificial neural network approach to partial differential equations in complex geometries Jens Berg K. Nystrom AI4CE 65 586 0 17 Nov 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 123 1,389 0 30 Sep 2017
Semi-Supervised Classification with Graph Convolutional Networks Thomas Kipf Max Welling GNN SSL 665 29,156 0 09 Sep 2016
Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering M. Defferrard Xavier Bresson P. Vandergheynst GNN 360 7,671 0 30 Jun 2016
Automatic differentiation in machine learning: a survey A. G. Baydin Barak A. Pearlmutter Alexey Radul J. Siskind PINN AI4CE ODL 172 2,816 0 20 Feb 2015