Multipole Graph Neural Operator for Parametric Partial Differential Equations

16 June 2020

Zong-Yi Li

Nikola B. Kovachki

Kamyar Azizzadenesheli

Papers citing "Multipole Graph Neural Operator for Parametric Partial Differential Equations"

50 / 225 papers shown

Title
Variationally Mimetic Operator Networks Dhruv V. Patel Deep Ray M. Abdelmalik T. Hughes Assad A. Oberai 52 23 0 26 Sep 2022
Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs Emilia Magnani Nicholas Kramer Runa Eschenhagen Lorenzo Rosasco Philipp Hennig UQCV BDL 13 9 0 02 Aug 2022
Semi-supervised Learning of Partial Differential Operators and Dynamical Flows Michael Rotman A. Dekel R. Ber Lior Wolf Yaron Oz AI4CE 13 4 0 28 Jul 2022
PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers Namgyu Kang Byeonghyeon Lee Youngjoon Hong S. Yun Eunbyung Park PINN AI4CE 22 13 0 26 Jul 2022
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries Zong-Yi Li Daniel Zhengyu Huang Burigede Liu Anima Anandkumar AI4CE 119 251 0 11 Jul 2022
Physics-Informed Deep Neural Operator Networks S. Goswami Aniruddha Bora Yue Yu George Karniadakis PINN AI4CE 31 99 0 08 Jul 2022
Learning to correct spectral methods for simulating turbulent flows Gideon Dresdner Dmitrii Kochkov Peter C. Norgaard Leonardo Zepeda-Núnez Jamie A. Smith M. Brenner Stephan Hoyer AI4CE 12 56 0 01 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 55 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 12 4 0 29 Jun 2022
Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning Thomas O'Leary-Roseberry Peng Chen Umberto Villa Omar Ghattas AI4CE 32 39 0 21 Jun 2022
LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Data Xinquan Huang Wenlei Shi Xiaotian Gao Xinran Wei Jia Zhang Jiang Bian Mao Yang Tie-Yan Liu PINN 27 10 0 19 Jun 2022
Learning to Accelerate Partial Differential Equations via Latent Global Evolution Tailin Wu Takashi Maruyama J. Leskovec AI4CE 31 28 0 15 Jun 2022
Learning to Solve PDE-constrained Inverse Problems with Graph Networks Qingqing Zhao David B. Lindell Gordon Wetzstein AI4CE 36 40 0 01 Jun 2022
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 21 6 0 28 May 2022
Transformer for Partial Differential Equations' Operator Learning Zijie Li Kazem Meidani A. Farimani 42 140 0 26 May 2022
Variable-Input Deep Operator Networks Michael Prasthofer Tim De Ryck Siddhartha Mishra 42 23 0 23 May 2022
Generic bounds on the approximation error for physics-informed (and) operator learning Tim De Ryck Siddhartha Mishra PINN 59 59 0 23 May 2022
Nonparametric learning of kernels in nonlocal operators Fei Lu Qi An Yue Yu 37 18 0 23 May 2022
REMuS-GNN: A Rotation-Equivariant Model for Simulating Continuum Dynamics Mario Lino Stati Fotiadis Anil A. Bharath C. Cantwell AI4CE 19 3 0 05 May 2022
Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networks Mario Lino Stathi Fotiadis Anil A. Bharath C. Cantwell AI4CE 11 12 0 05 May 2022
Graph Anisotropic Diffusion Ahmed A. A. Elhag Gabriele Corso Hannes Stärk Michael M. Bronstein DiffM GNN 17 0 0 30 Apr 2022
Learning Green's functions associated with time-dependent partial differential equations N. Boullé Seick Kim Tianyi Shi Alex Townsend AI4CE 21 25 0 27 Apr 2022
U-NO: U-shaped Neural Operators Md Ashiqur Rahman Zachary E. Ross Kamyar Azizzadenesheli AI4CE 30 132 0 23 Apr 2022
STONet: A Neural-Operator-Driven Spatio-temporal Network Haitao Lin Guojiang Zhao Lirong Wu Stan Z. Li AI4TS AI4CE 11 1 0 18 Apr 2022
Learning time-dependent PDE solver using Message Passing Graph Neural Networks Pourya Pilva A. Zareei AI4CE 27 7 0 15 Apr 2022
Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs Peiyan Hu Qi Meng Bin Chen Shiqi Gong Yue Wang Wei Chen Rongchan Zhu Zhirui Ma Tie-Yan Liu AI4CE 21 11 0 13 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 26 37 0 03 Apr 2022
A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurements Huaiqian You Quinn Zhang Colton J. Ross Chung-Hao Lee M. Hsu Yue Yu AI4CE 17 20 0 01 Apr 2022
Applications of physics informed neural operators S. Rosofsky Hani Al Majed Eliu A. Huerta PINN AI4CE 19 39 0 23 Mar 2022
Can we integrate spatial verification methods into neural-network loss functions for atmospheric science? Ryan Lagerquist I. Ebert‐Uphoff 35 11 0 21 Mar 2022
Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling Huaiqian You Quinn Zhang Colton J. Ross Chung-Hao Lee Yue Yu AI4CE 21 95 0 15 Mar 2022
IAE-Net: Integral Autoencoders for Discretization-Invariant Learning Yong Zheng Ong Zuowei Shen Haizhao Yang 13 15 0 10 Mar 2022
Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems Minglang Yin Enrui Zhang Yue Yu George Karniadakis AI4CE 25 99 0 25 Feb 2022
Message Passing Neural PDE Solvers Johannes Brandstetter Daniel E. Worrall Max Welling AI4CE 27 259 0 07 Feb 2022
Pseudo-Differential Neural Operator: Generalized Fourier Neural Operator for Learning Solution Operators of Partial Differential Equations J. Shin Jae Yong Lee H. Hwang 16 2 0 28 Jan 2022
Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network Huaiqian You Yue Yu M. DÉlia T. Gao Stewart Silling 16 70 0 06 Jan 2022
Learning Operators with Coupled Attention Georgios Kissas Jacob H. Seidman Leonardo Ferreira Guilhoto V. Preciado George J. Pappas P. Perdikaris 24 109 0 04 Jan 2022
Learned Coarse Models for Efficient Turbulence Simulation Kimberly L. Stachenfeld D. Fielding Dmitrii Kochkov M. Cranmer Tobias Pfaff Jonathan Godwin Can Cui S. Ho Peter W. Battaglia Alvaro Sanchez-Gonzalez AI4CE 32 78 0 31 Dec 2021
Frame invariance and scalability of neural operators for partial differential equations M. Zafar Jiequn Han Xueqing Zhou Heng Xiao 16 5 0 28 Dec 2021
Learning High-Dimensional Parametric Maps via Reduced Basis Adaptive Residual Networks Thomas O'Leary-Roseberry Xiaosong Du A. Chaudhuri J. Martins Karen E. Willcox Omar Ghattas 30 22 0 14 Dec 2021
Factorized Fourier Neural Operators Alasdair Tran A. Mathews Lexing Xie Cheng Soon Ong AI4CE 26 141 0 27 Nov 2021
NeuralPDE: Modelling Dynamical Systems from Data Andrzej Dulny Andreas Hotho Anna Krause AI4CE 24 11 0 15 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 62 382 0 06 Nov 2021
FC2T2: The Fast Continuous Convolutional Taylor Transform with Applications in Vision and Graphics Henning Lange J. Nathan Kutz 15 2 0 29 Oct 2021
Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamics C. Salvi M. Lemercier A. Gerasimovičs AI4CE 16 42 0 19 Oct 2021
Beltrami Flow and Neural Diffusion on Graphs B. Chamberlain J. Rowbottom D. Eynard Francesco Di Giovanni Xiaowen Dong M. Bronstein AI4CE 34 79 0 18 Oct 2021
A composable autoencoder-based iterative algorithm for accelerating numerical simulations Rishikesh Ranade C. Hill Haiyang He Amir Maleki Norman Chang Jay Pathak AI4CE 41 6 0 07 Oct 2021
Enhancing Computational Fluid Dynamics with Machine Learning Ricardo Vinuesa Steven L. Brunton AI4CE 111 355 0 05 Oct 2021
Multiwavelet-based Operator Learning for Differential Equations Gaurav Gupta Xiongye Xiao P. Bogdan 126 200 0 28 Sep 2021
Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data Xiaoyu Zhao Zhiqiang Gong Yunyang Zhang Wen Yao Xiaoqian Chen OOD AI4CE 74 91 0 26 Sep 2021