Neural Operator: Graph Kernel Network for Partial Differential Equations

7 March 2020

Zong-Yi Li

Nikola B. Kovachki

Kamyar Azizzadenesheli

Papers citing "Neural Operator: Graph Kernel Network for Partial Differential Equations"

50 / 160 papers shown

Title
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 52 10 0 21 Oct 2022
Modular Flows: Differential Molecular Generation Yogesh Verma Samuel Kaski Markus Heinonen Vikas K. Garg 34 14 0 12 Oct 2022
A composable machine-learning approach for steady-state simulations on high-resolution grids Rishikesh Ranade C. Hill Lalit Ghule Jay Pathak AI4CE 36 8 0 11 Oct 2022
MAgNet: Mesh Agnostic Neural PDE Solver Oussama Boussif D. Assouline L. Benabbou Yoshua Bengio AI4CE 108 29 0 11 Oct 2022
Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities S. Lanthaler Roberto Molinaro Patrik Hadorn Siddhartha Mishra 64 24 0 03 Oct 2022
Towards Multi-spatiotemporal-scale Generalized PDE Modeling Jayesh K. Gupta Johannes Brandstetter AI4CE 61 120 0 30 Sep 2022
Variationally Mimetic Operator Networks Dhruv V. Patel Deep Ray M. Abdelmalik T. Hughes Assad A. Oberai 60 23 0 26 Sep 2022
NeurOLight: A Physics-Agnostic Neural Operator Enabling Parametric Photonic Device Simulation Jiaqi Gu Zhengqi Gao Chenghao Feng Hanqing Zhu Ray T. Chen Duane S. Boning David Z. Pan 32 17 0 19 Sep 2022
Multi-fidelity wavelet neural operator with application to uncertainty quantification A. Thakur Tapas Tripura S. Chakraborty 38 12 0 11 Aug 2022
Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs Emilia Magnani Nicholas Kramer Runa Eschenhagen Lorenzo Rosasco Philipp Hennig UQCV BDL 21 9 0 02 Aug 2022
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries Zong-Yi Li Daniel Zhengyu Huang Burigede Liu Anima Anandkumar AI4CE 122 256 0 11 Jul 2022
An extensible Benchmarking Graph-Mesh dataset for studying Steady-State Incompressible Navier-Stokes Equations F. Bonnet Jocelyn Ahmed Mazari T. Munzer P. Yser Patrick Gallinari AI4CE 68 10 0 29 Jun 2022
Multi-scale Physical Representations for Approximating PDE Solutions with Graph Neural Operators Léon Migus Yuan Yin Jocelyn Ahmed Mazari Patrick Gallinari AI4CE 23 4 0 29 Jun 2022
Meta Optimal Transport Brandon Amos Samuel N. Cohen Giulia Luise I. Redko OT 45 22 0 10 Jun 2022
NOMAD: Nonlinear Manifold Decoders for Operator Learning Jacob H. Seidman Georgios Kissas P. Perdikaris George J. Pappas AI4CE 31 68 0 07 Jun 2022
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 39 6 0 28 May 2022
Transformer for Partial Differential Equations' Operator Learning Zijie Li Kazem Meidani A. Farimani 47 145 0 26 May 2022
Variable-Input Deep Operator Networks Michael Prasthofer Tim De Ryck Siddhartha Mishra 53 23 0 23 May 2022
Generic bounds on the approximation error for physics-informed (and) operator learning Tim De Ryck Siddhartha Mishra PINN 63 59 0 23 May 2022
Automated differential equation solver based on the parametric approximation optimization A. Hvatov Tatiana Tikhonova 24 4 0 11 May 2022
Wavelet neural operator: a neural operator for parametric partial differential equations Tapas Tripura S. Chakraborty 25 63 0 04 May 2022
Learning Green's functions associated with time-dependent partial differential equations N. Boullé Seick Kim Tianyi Shi Alex Townsend AI4CE 31 25 0 27 Apr 2022
STONet: A Neural-Operator-Driven Spatio-temporal Network Haitao Lin Guojiang Zhao Lirong Wu Stan Z. Li AI4TS AI4CE 23 1 0 18 Apr 2022
Learning time-dependent PDE solver using Message Passing Graph Neural Networks Pourya Pilva A. Zareei AI4CE 34 7 0 15 Apr 2022
Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONets Subhayan De Matthew J. Reynolds M. Hassanaly Ryan N. King Alireza Doostan AI4CE 39 37 0 03 Apr 2022
When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning Chuizheng Meng Sungyong Seo Defu Cao Sam Griesemer Yan Liu PINN AI4CE 56 57 0 31 Mar 2022
Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors Yibo Yang Georgios Kissas P. Perdikaris BDL UQCV 40 40 0 06 Mar 2022
MIONet: Learning multiple-input operators via tensor product Pengzhan Jin Shuai Meng Lu Lu 27 158 0 12 Feb 2022
Towards Empirical Process Theory for Vector-Valued Functions: Metric Entropy of Smooth Function Classes Junhyung Park Krikamol Muandet 27 6 0 09 Feb 2022
Accelerating Part-Scale Simulation in Liquid Metal Jet Additive Manufacturing via Operator Learning S. Taverniers S. Korneev Kyle Pietrzyk M. Behandish AI4CE 16 1 0 02 Feb 2022
Learning Operators with Coupled Attention Georgios Kissas Jacob H. Seidman Leonardo Ferreira Guilhoto V. Preciado George J. Pappas P. Perdikaris 32 110 0 04 Jan 2022
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces Hao Liu Haizhao Yang Minshuo Chen T. Zhao Wenjing Liao 34 36 0 01 Jan 2022
Factorized Fourier Neural Operators Alasdair Tran A. Mathews Lexing Xie Cheng Soon Ong AI4CE 34 143 0 27 Nov 2021
Composing Partial Differential Equations with Physics-Aware Neural Networks Matthias Karlbauer T. Praditia S. Otte S. Oladyshkin Wolfgang Nowak Martin Volker Butz AI4CE 40 18 0 23 Nov 2021
Physics-Informed Neural Operator for Learning Partial Differential Equations Zong-Yi Li Hongkai Zheng Nikola B. Kovachki David Jin Haoxuan Chen Burigede Liu Kamyar Azizzadenesheli Anima Anandkumar AI4CE 62 386 0 06 Nov 2021
A composable autoencoder-based iterative algorithm for accelerating numerical simulations Rishikesh Ranade C. Hill Haiyang He Amir Maleki Norman Chang Jay Pathak AI4CE 45 5 0 07 Oct 2021
Multiwavelet-based Operator Learning for Differential Equations Gaurav Gupta Xiongye Xiao P. Bogdan 126 202 0 28 Sep 2021
PCNN: A physics-constrained neural network for multiphase flows Haoyang Zheng Ziyang Huang Guang Lin PINN 27 8 0 18 Sep 2021
U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow Gege Wen Zong-Yi Li Kamyar Azizzadenesheli Anima Anandkumar S. Benson AI4CE 36 369 0 03 Sep 2021
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yihang Gao Michael K. Ng 38 29 0 30 Aug 2021
Convergence Rates for Learning Linear Operators from Noisy Data Maarten V. de Hoop Nikola B. Kovachki Nicholas H. Nelsen Andrew M. Stuart 26 54 0 27 Aug 2021
Learning Partial Differential Equations in Reproducing Kernel Hilbert Spaces George Stepaniants 51 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 59 442 0 19 Aug 2021
SURFNet: Super-resolution of Turbulent Flows with Transfer Learning using Small Datasets Octavi Obiols-Sales Abhinav Vishnu Nicholas Malaya Aparna Chandramowlishwaran AI4CE 37 24 0 17 Aug 2021
Seismic wave propagation and inversion with Neural Operators Yan Yang Angela F. Gao J. Castellanos Zachary E. Ross Kamyar Azizzadenesheli R. Clayton 19 70 0 11 Aug 2021
Learning the structure of wind: A data-driven nonlocal turbulence model for the atmospheric boundary layer B. Keith U. Khristenko B. Wohlmuth 33 7 0 23 Jul 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
Physics-Guided Deep Learning for Dynamical Systems: A Survey Rui Wang Rose Yu AI4CE PINN 46 65 0 02 Jul 2021
PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs Pu Ren Chengping Rao Yang Liu Jianxun Wang Hao Sun DiffM AI4CE 51 193 0 26 Jun 2021
Choose a Transformer: Fourier or Galerkin Shuhao Cao 42 227 0 31 May 2021