Learning time-dependent PDE via graph neural networks and deep operator
network for robust accuracy on irregular grids

Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids

13 February 2024

Papers citing "Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids"

19 / 19 papers shown

Title
Non-equispaced Fourier Neural Solvers for PDEs Haitao Lin Lirong Wu Yongjie Xu Yufei Huang Siyuan Li Guojiang Zhao Z. Stan 52 8 0 09 Dec 2022
PDEBENCH: An Extensive Benchmark for Scientific Machine Learning M. Takamoto T. Praditia Raphael Leiteritz Dan MacKinlay Francesco Alesiani Dirk Pflüger Mathias Niepert AI4CE 67 230 0 13 Oct 2022
FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators Thorsten Kurth Shashank Subramanian P. Harrington Jaideep Pathak Morteza Mardani D. Hall Andrea Miele K. Kashinath Anima Anandkumar AI4Cl 81 187 0 08 Aug 2022
Transformer for Partial Differential Equations' Operator Learning Zijie Li Kazem Meidani A. Farimani 102 166 0 26 May 2022
Physics-Embedded Neural Networks: Graph Neural PDE Solvers with Mixed Boundary Conditions Masanobu Horie Naoto Mitsume PINN AI4CE 85 27 0 24 May 2022
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 117 449 0 19 Aug 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 97 699 0 19 Mar 2021
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 497 2,414 0 18 Oct 2020
Learning Mesh-Based Simulation with Graph Networks Tobias Pfaff Meire Fortunato Alvaro Sanchez-Gonzalez Peter W. Battaglia AI4CE 82 790 0 07 Oct 2020
Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction Filipe de Avila Belbute-Peres T. Economon J. Zico Kolter AI4CE 95 231 0 08 Jul 2020
Learning continuous-time PDEs from sparse data with graph neural networks V. Iakovlev Markus Heinonen Harri Lähdesmäki AI4CE 79 70 0 16 Jun 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 139 1,091 0 21 Feb 2020
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 245 2,131 0 08 Oct 2019
Graph Matching Networks for Learning the Similarity of Graph Structured Objects Yujia Li Chenjie Gu T. Dullien Oriol Vinyals Pushmeet Kohli 102 530 0 29 Apr 2019
Fast Graph Representation Learning with PyTorch Geometric Matthias Fey J. E. Lenssen 3DH GNN 3DPC 226 4,341 0 06 Mar 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 106 867 0 18 Jan 2019
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 758 3,121 0 04 Jun 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 121 1,387 0 30 Sep 2017
Neural Message Passing for Quantum Chemistry Justin Gilmer S. Schoenholz Patrick F. Riley Oriol Vinyals George E. Dahl 593 7,455 0 04 Apr 2017