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"

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Title
LaPON: A Lagrange's-mean-value-theorem-inspired operator network for solving PDEs and its application on NSE Siwen Zhang Xizeng Zhao Zhengzhi Deng Zhaoyuan Huang Gang Tao Nuo Xu Zhouteng Ye 14 0 0 18 May 2025
GeoMaNO: Geometric Mamba Neural Operator for Partial Differential Equations Xi Han Jingwei Zhang Dimitris Samaras Fei Hou Hong Qin AI4CE 7 0 0 17 May 2025
Redefining Neural Operators in $d+1$ Dimensions Haoze Song Zhihao Li Xiaobo Zhang Zecheng Gan Zhilu Lai Wei Wang 14 0 0 17 May 2025
CodePDE: An Inference Framework for LLM-driven PDE Solver Generation Shanda Li Tanya Marwah Junhong Shen W. Sun Andrej Risteski Yiming Yang Ameet Talwalkar AI4CE 46 0 0 13 May 2025
Learning and Transferring Physical Models through Derivatives Alessandro Trenta Andrea Cossu Davide Bacciu AI4CE 43 0 0 02 May 2025
Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions Jihong Wang Xiaochuan Tian Zhongqiang Zhang Stewart Silling S. Jafarzadeh Yue Yu 46 0 0 02 May 2025
Interpretable Spatial-Temporal Fusion Transformers: Multi-Output Prediction for Parametric Dynamical Systems with Time-Varying Inputs Shuwen Sun Lihong Feng P. Benner 49 0 0 01 May 2025
Geometry-Informed Neural Operator Transformer Qibang Liu Vincient Zhong Hadi Meidani Diab Abueidda S. Koric Philippe Geubelle AI4CE 46 1 0 28 Apr 2025
Neural operators struggle to learn complex PDEs in pedestrian mobility: Hughes model case study Prajwal Chauhan Salah Eddine Choutri Mohamed Ghattassi Nader Masmoudi Saif Eddin Jabari 39 0 0 25 Apr 2025
PODNO: Proper Orthogonal Decomposition Neural Operators Zilan Cheng Zhongjian Wang Li-Lian Wang Mejdi Azaiez 36 0 0 25 Apr 2025
EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations Hamidreza Eivazi Jendrik-Alexander Tröger Stefan H. A. Wittek Stefan Hartmann Andreas Rausch AI4CE 48 0 0 27 Mar 2025
Fourier Neural Operator based surrogates for $CO_2$ storage in realistic geologies Anirban Chandra Marius Koch Suraj Pawar Aniruddha Panda Kamyar Azizzadenesheli ... Farah Hariri Clement Etienam Pandu Devarakota Anima Anandkumar Detlef Hohl AI4CE 56 3 0 14 Mar 2025
Sampling-based Distributed Training with Message Passing Neural Network P. Kakka Sheel Nidhan Rishikesh Ranade Jay Pathak J. MacArt GNN 83 3 0 20 Feb 2025
FuncGenFoil: Airfoil Generation and Editing Model in Function Space Jinouwen Zhang Junjie Ren A. Yang Yan Lu Lu Chen Hairun Xie Jing Wang Miao Zhang W. Ouyang Shixiang Tang 240 0 0 15 Feb 2025
DGNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling Yaohua Zang P. Koutsourelakis AI4CE 54 1 0 10 Feb 2025
Graph Neural Preconditioners for Iterative Solutions of Sparse Linear Systems Jie Chen AI4CE 66 2 0 28 Jan 2025
In-Context Operator Learning for Linear Propagator Models Tingwei Meng Moritz Voß Nils Detering Giulio Farolfi Stanley Osher Georg Menz 41 0 0 28 Jan 2025
Image Classification with Deep Reinforcement Active Learning Mingyuan Jiu Xuguang Song H. Sahbi Shupan Li Yan Chen Wei Guo Lihua Guo Mingliang Xu VLM 29 0 0 31 Dec 2024
A physics-informed transformer neural operator for learning generalized solutions of initial boundary value problems Sumanth Kumar Boya Deepak Subramani AI4CE 104 0 0 12 Dec 2024
NeuralDEM -- Real-time Simulation of Industrial Particulate Flows Benedikt Alkin Tobias Kronlachner Samuele Papa Stefan Pirker Thomas Lichtenegger Johannes Brandstetter PINN AI4CE 64 1 1 14 Nov 2024
DeepOSets: Non-Autoregressive In-Context Learning of Supervised Learning Operators Shao-Ting Chiu Junyuan Hong Ulisses Braga-Neto BDL 33 0 0 11 Oct 2024
Mamba Neural Operator: Who Wins? Transformers vs. State-Space Models for PDEs Chun-Wun Cheng Jiahao Huang Yi Zhang Guang Yang Carola-Bibiane Schonlieb Angelica I Aviles-Rivero Mamba AI4CE 93 3 0 03 Oct 2024
Text2PDE: Latent Diffusion Models for Accessible Physics Simulation Anthony Zhou Zijie Li Michael Schneier John R Buchanan Jr Amir Barati Farimani AI4CE DiffM 69 6 0 02 Oct 2024
Physics-Informed Geometry-Aware Neural Operator Weiheng Zhong Hadi Meidani AI4CE 48 4 0 02 Aug 2024
Neural Operator-Based Proxy for Reservoir Simulations Considering Varying Well Settings, Locations, and Permeability Fields Daniel Badawi Eduardo Gildin OOD AI4CE 21 4 0 13 Jul 2024
Accelerating Electron Dynamics Simulations through Machine Learned Time Propagators Karan Shah A. Cangi AI4CE 33 1 0 12 Jul 2024
Reduced-Order Neural Operators: Learning Lagrangian Dynamics on Highly Sparse Graphs Hrishikesh Viswanath Yue Chang Julius Berner Julius Berner Peter Yichen Chen Aniket Bera AI4CE 68 2 0 04 Jul 2024
A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics Tianyu Jin G. Maierhofer Katharina Schratz Yang Xiang 44 1 0 04 Jul 2024
An Advanced Physics-Informed Neural Operator for Comprehensive Design Optimization of Highly-Nonlinear Systems: An Aerospace Composites Processing Case Study Milad Ramezankhani A. Deodhar Rishi Parekh Dagnachew Birru AI4CE 50 3 0 20 Jun 2024
Neural networks in non-metric spaces Luca Galimberti 56 1 0 13 Jun 2024
Linearization Turns Neural Operators into Function-Valued Gaussian Processes Emilia Magnani Marvin Pfortner Tobias Weber Philipp Hennig UQCV 71 1 0 07 Jun 2024
Flexible SE(2) graph neural networks with applications to PDE surrogates Maria Bånkestad Olof Mogren Aleksis Pirinen 61 1 0 30 May 2024
Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media Matthaios Chatzopoulos P. Koutsourelakis AI4CE 41 3 0 29 May 2024
Deep Neural Operator Enabled Digital Twin Modeling for Additive Manufacturing Ning Liu Xuxiao Li M. Rajanna E. Reutzel Brady A Sawyer Prahalada Rao Jim Lua Nam Phan Yue Yu AI4CE 48 8 0 13 May 2024
Efficient and Flexible Method for Reducing Moderate-size Deep Neural Networks with Condensation Tianyi Chen Zhi-Qin John Xu 40 1 0 02 May 2024
Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation Jingmin Sun Yuxuan Liu Zecheng Zhang Hayden Schaeffer AI4CE 30 17 0 18 Apr 2024
Global 4D Ionospheric STEC Prediction based on DeepONet for GNSS Rays Dijia Cai Zenghui Shi Haiyang Fu Huan Liu Hongyi Qian Yun Sui Feng Xu Ya-Qiu Jin 32 2 0 12 Mar 2024
Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations Zijie Li Saurabh Patil Francis Ogoke Dule Shu Wilson Zhen Michael Schneier John R. Buchanan A. Farimani AI4CE 45 5 0 27 Feb 2024
Learning solution operators of PDEs defined on varying domains via MIONet Shanshan Xiao Pengzhan Jin Yifa Tang 55 3 0 23 Feb 2024
Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators Benedikt Alkin Andreas Fürst Simon Schmid Lukas Gruber Markus Holzleitner Johannes Brandstetter PINN AI4CE 53 8 0 19 Feb 2024
Invertible Fourier Neural Operators for Tackling Both Forward and Inverse Problems Da Long Zhitong Xu Qiwei Yuan Yin Yang Shandian Zhe AI4CE 80 5 0 18 Feb 2024
Equivariant Graph Neural Operator for Modeling 3D Dynamics Minkai Xu Jiaqi Han Aaron Lou Jean Kossaifi Arvind Ramanathan Kamyar Azizzadenesheli J. Leskovec Stefano Ermon A. Anandkumar AI4CE 42 17 0 19 Jan 2024
Generalization Error Guaranteed Auto-Encoder-Based Nonlinear Model Reduction for Operator Learning Hao Liu Biraj Dahal Rongjie Lai Wenjing Liao AI4CE 39 5 0 19 Jan 2024
Approximation of Solution Operators for High-dimensional PDEs Nathan Gaby Xiaojing Ye 30 0 0 18 Jan 2024
Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responses S. Jafarzadeh Stewart Silling Ning Liu Zhongqiang Zhang Yue Yu AI4CE 32 16 0 11 Jan 2024
Nonlinear functional regression by functional deep neural network with kernel embedding Zhongjie Shi Jun Fan Linhao Song Ding-Xuan Zhou Johan A. K. Suykens 65 5 0 05 Jan 2024
Generating synthetic data for neural operators Erisa Hasani Rachel A. Ward AI4CE 67 8 0 04 Jan 2024
Operator-learning-inspired Modeling of Neural Ordinary Differential Equations Woojin Cho Seunghyeon Cho Hyundong Jin Jinsung Jeon Kookjin Lee Sanghyun Hong Dongeun Lee Jonghyun Choi Noseong Park AI4TS AI4CE 23 2 0 16 Dec 2023
Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology Qingsong Xu Yilei Shi Jonathan Bamber Ye Tuo Ralf Ludwig Xiao Xiang Zhu AI4CE 37 10 0 08 Oct 2023
LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suite Stefania Costantini Gianluca Galletti Fabian Fritz Stefan Adami Nikolaus A. Adams 42 13 0 28 Sep 2023