Physics-Informed Neural Operator for Learning Partial Differential Equations

6 November 2021

Kamyar Azizzadenesheli

Anima Anandkumar

AI4CE

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Papers citing "Physics-Informed Neural Operator for Learning Partial Differential Equations"

47 / 47 papers shown

Title
Operator Learning for Schrödinger Equation: Unitarity, Error Bounds, and Time Generalization Yash Patel Unique Subedi Ambuj Tewari 39 0 0 23 May 2025
Mollifier Layers: Enabling Efficient High-Order Derivatives in Inverse PDE Learning Ananyae Kumar Bhartari Vinayak Vinayak Vivek B Shenoy AI4CE 173 0 0 16 May 2025
Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Abdolmehdi Behroozi Chaopeng Shen and Daniel Kifer AI4CE 75 0 0 13 May 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 85 3 0 14 Mar 2025
Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis Yasamin Jalalian Juan Felipe Osorio Ramirez Alexander W. Hsu Bamdad Hosseini H. Owhadi 144 0 0 02 Mar 2025
DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling Yaohua Zang P. Koutsourelakis AI4CE 84 1 0 10 Feb 2025
Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups Zakhar Shumaylov Peter Zaika James Rowbottom Ferdia Sherry Melanie Weber Carola-Bibiane Schönlieb 66 5 0 03 Oct 2024
Deep Learning Alternatives of the Kolmogorov Superposition Theorem Leonardo Ferreira Guilhoto P. Perdikaris 77 7 0 02 Oct 2024
Generating Physical Dynamics under Priors Zihan Zhou Xiaoxue Wang Tianshu Yu DiffM AI4CE 92 1 0 01 Sep 2024
Active Learning for Neural PDE Solvers Daniel Musekamp Marimuthu Kalimuthu David Holzmüller Makoto Takamoto Carlos Fernandez AI4CE 108 7 0 02 Aug 2024
Linearization Turns Neural Operators into Function-Valued Gaussian Processes Emilia Magnani Marvin Pfortner Tobias Weber Philipp Hennig UQCV 92 1 0 07 Jun 2024
Generalizing Weather Forecast to Fine-grained Temporal Scales via Physics-AI Hybrid Modeling Wanghan Xu Fenghua Ling Wenlong Zhang Tao Han Hao Chen Wanli Ouyang Lei Bai AI4CE 164 5 0 22 May 2024
KAN: Kolmogorov-Arnold Networks Ziming Liu Yixuan Wang Sachin Vaidya Fabian Ruehle James Halverson Marin Soljacic Thomas Y. Hou Max Tegmark 218 538 0 30 Apr 2024
Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere Boris Bonev Thorsten Kurth Christian Hundt Jaideep Pathak Maximilian Baust K. Kashinath Anima Anandkumar AI4Cl AI4CE 48 139 0 06 Jun 2023
Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation Rui Zhang Qi Meng Rongchan Zhu Yue Wang Wenlei Shi Shihua Zhang Zhi-Ming Ma Tie-Yan Liu DiffM AI4CE 110 5 0 10 Feb 2023
Real-time high-resolution CO $_2$ geological storage prediction using nested Fourier neural operators Gege Wen Zong-Yi Li Qirui Long Kamyar Azizzadenesheli Anima Anandkumar Sally Benson AI4CE 55 88 0 31 Oct 2022
Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities S. Lanthaler Roberto Molinaro Patrik Hadorn Siddhartha Mishra 105 24 0 03 Oct 2022
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries Zong-Yi Li Daniel Zhengyu Huang Burigede Liu Anima Anandkumar AI4CE 159 266 0 11 Jul 2022
Generic Lithography Modeling with Dual-band Optics-Inspired Neural Networks Haoyu Yang Zong-Yi Li K. Sastry S. Mukhopadhyay M. Kilgard Anima Anandkumar Brucek Khailany Vivek Singh Haoxing Ren 34 31 0 12 Mar 2022
On the influence of over-parameterization in manifold based surrogates and deep neural operators Katiana Kontolati S. Goswami Michael D. Shields George Karniadakis 43 41 0 09 Mar 2022
FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators Jaideep Pathak Shashank Subramanian P. Harrington S. Raja Ashesh Chattopadhyay ... Zong-Yi Li Kamyar Azizzadenesheli Pedram Hassanzadeh K. Kashinath Anima Anandkumar AI4Cl 213 687 0 22 Feb 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 101 448 0 19 Aug 2021
Data-informed Deep Optimization Lulu Zhang Z. Xu Yaoyu Zhang AI4CE 52 3 0 17 Jul 2021
MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs Lulu Zhang Yaoyu Zhang Yaoyu Zhang Weinan E Z. Xu Zheng Ma AI4CE 45 33 0 08 Jul 2021
Physics-informed neural networks (PINNs) for fluid mechanics: A review Shengze Cai Zhiping Mao Zhicheng Wang Minglang Yin George Karniadakis PINN AI4CE 62 1,183 0 20 May 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 77 697 0 19 Mar 2021
Machine learning accelerated computational fluid dynamics Dmitrii Kochkov Jamie A. Smith Ayya Alieva Qing Wang M. Brenner Stephan Hoyer AI4CE 98 862 0 28 Jan 2021
HypoSVI: Hypocenter inversion with Stein variational inference and Physics Informed Neural Networks Jonathan D. Smith Zachary E. Ross Kamyar Azizzadenesheli J. Muir 46 38 0 09 Jan 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 478 2,397 0 18 Oct 2020
A physics-informed operator regression framework for extracting data-driven continuum models Ravi G. Patel N. Trask M. Wood E. Cyr AI4CE 64 104 0 25 Sep 2020
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism L. McClenny U. Braga-Neto PINN 72 458 0 07 Sep 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 121 906 0 28 Jul 2020
Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers Kiwon Um R. Brand Yun Fei Fei Philipp Holl N. Thürey AI4CE 52 269 0 30 Jun 2020
Multipole Graph 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 198 389 0 16 Jun 2020
The Random Feature Model for Input-Output Maps between Banach Spaces Nicholas H. Nelsen Andrew M. Stuart 66 143 0 20 May 2020
Neural Operator: Graph Kernel Network for Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar 179 732 0 07 Mar 2020
Towards Physics-informed Deep Learning for Turbulent Flow Prediction Rui Wang K. Kashinath M. Mustafa A. Albert Rose Yu PINN AI4CE 39 365 0 20 Nov 2019
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 95 1,525 0 10 Jul 2019
Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equations Vikas Dwivedi Balaji Srinivasan PINN 53 193 0 08 Jul 2019
Machine Learning for Fluid Mechanics Steven Brunton B. R. Noack Petros Koumoutsakos AI4CE PINN 81 2,115 0 27 May 2019
Variational training of neural network approximations of solution maps for physical models Yingzhou Li Jianfeng Lu Anqi Mao GAN 44 35 0 07 May 2019
Learning to Optimize Multigrid PDE Solvers D. Greenfeld Meirav Galun Ron Kimmel I. Yavneh Ronen Basri AI4CE 48 117 0 25 Feb 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 92 867 0 18 Jan 2019
PDE-Net: Learning PDEs from Data Zichao Long Yiping Lu Xianzhong Ma Bin Dong DiffM AI4CE 38 755 0 26 Oct 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 117 1,384 0 30 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 86 2,059 0 24 Aug 2017
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 1.6K 150,006 0 22 Dec 2014