Fourier Neural Operator for Parametric Partial Differential Equations

18 October 2020

Zong-Yi Li

Nikola B. Kovachki

Kamyar Azizzadenesheli

Papers citing "Fourier Neural Operator for Parametric Partial Differential Equations"

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Title
Unsupervised Legendre-Galerkin Neural Network for Singularly Perturbed Partial Differential Equations Junho Choi N. Kim Youngjoon Hong AI4CE 24 0 0 21 Jul 2022
Learning differentiable solvers for systems with hard constraints Geoffrey Negiar Michael W. Mahoney Aditi S. Krishnapriyan 34 28 0 18 Jul 2022
wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws Tim De Ryck Siddhartha Mishra Roberto Molinaro PINN 32 29 0 18 Jul 2022
Error analysis for deep neural network approximations of parametric hyperbolic conservation laws Tim De Ryck Siddhartha Mishra PINN 15 10 0 15 Jul 2022
Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach Dimitrios G. Patsatzis Lucia Russo Ioannis G. Kevrekidis Constantinos Siettos 19 15 0 12 Jul 2022
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries Zong-Yi Li Daniel Zhengyu Huang Burigede Liu Anima Anandkumar AI4CE 119 254 0 11 Jul 2022
Neural and spectral operator surrogates: unified construction and expression rate bounds L. Herrmann Christoph Schwab Jakob Zech 51 10 0 11 Jul 2022
Large Scale Mask Optimization Via Convolutional Fourier Neural Operator and Litho-Guided Self Training Haoyu Yang Zong-Yi Li K. Sastry S. Mukhopadhyay Anima Anandkumar Brucek Khailany Vivek Singh Haoxing Ren 17 8 0 08 Jul 2022
Physics-Informed Deep Neural Operator Networks S. Goswami Aniruddha Bora Yue Yu George Karniadakis PINN AI4CE 31 99 0 08 Jul 2022
Complementing Brightness Constancy with Deep Networks for Optical Flow Prediction Vincent Le Guen Clément Rambour Nicolas Thome 30 1 0 08 Jul 2022
Neural Implicit Dictionary via Mixture-of-Expert Training Peihao Wang Zhiwen Fan Tianlong Chen Zhangyang Wang 25 12 0 08 Jul 2022
The Deep Ritz Method for Parametric $p$ -Dirichlet Problems A. Kaltenbach Marius Zeinhofer 22 3 0 05 Jul 2022
opPINN: Physics-Informed Neural Network with operator learning to approximate solutions to the Fokker-Planck-Landau equation Jae Yong Lee J. Jang H. Hwang 14 9 0 05 Jul 2022
Learning to correct spectral methods for simulating turbulent flows Gideon Dresdner Dmitrii Kochkov Peter C. Norgaard Leonardo Zepeda-Núñez Jamie A. Smith M. Brenner Stephan Hoyer AI4CE 23 56 0 01 Jul 2022
Learning the Solution Operator of Boundary Value Problems using Graph Neural Networks Winfried Lotzsch Simon Ohler Johannes Otterbach AI4CE 24 18 0 28 Jun 2022
Continual Learning of Dynamical Systems with Competitive Federated Reservoir Computing Leonard Bereska E. Gavves 32 6 0 27 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
Principled Acceleration of Iterative Numerical Methods Using Machine Learning S. Arisaka Qianxiao Li 27 5 0 17 Jun 2022
Noisy Learning for Neural ODEs Acts as a Robustness Locus Widening Martin Gonzalez H. Hajri Loic Cantat Mihaly Petreczky 34 1 0 16 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
Residual-based physics-informed transfer learning: A hybrid method for accelerating long-term CFD simulations via deep learning J. Jeon Juhyeong Lee Ricardo Vinuesa S. J. Kim AI4CE 8 25 0 14 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
Variational Monte Carlo Approach to Partial Differential Equations with Neural Networks M. Reh M. Gärttner 27 8 0 04 Jun 2022
Discretization Invariant Networks for Learning Maps between Neural Fields Clinton Jia Wang Polina Golland 33 0 0 02 Jun 2022
Learning to Solve PDE-constrained Inverse Problems with Graph Networks Qingqing Zhao David B. Lindell Gordon Wetzstein AI4CE 39 40 0 01 Jun 2022
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 29 6 0 28 May 2022
Transformer for Partial Differential Equations' Operator Learning Zijie Li Kazem Meidani A. Farimani 42 144 0 26 May 2022
Faster Optimization on Sparse Graphs via Neural Reparametrization Nima Dehmamy C. Both J. Long Rose Yu 13 0 0 26 May 2022
PREF: Phasorial Embedding Fields for Compact Neural Representations Binbin Huang Xinhao Yan Anpei Chen Shenghua Gao Jingyi Yu 31 14 0 26 May 2022
Variable-Input Deep Operator Networks Michael Prasthofer Tim De Ryck Siddhartha Mishra 48 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
Towards Size-Independent Generalization Bounds for Deep Operator Nets Pulkit Gopalani Sayar Karmakar Dibyakanti Kumar Anirbit Mukherjee AI4CE 24 5 0 23 May 2022
Nonparametric learning of kernels in nonlocal operators Fei Lu Qi An Yue Yu 37 18 0 23 May 2022
Learning Interface Conditions in Domain Decomposition Solvers Ali Taghibakhshi Nicolas Nytko Tareq Uz Zaman S. MacLachlan Luke N. Olson Matthew West AI4CE 38 11 0 19 May 2022
Uncertainty Quantification for Transport in Porous media using Parameterized Physics Informed neural Networks Cedric Fraces Gasmi H. Tchelepi 17 5 0 19 May 2022
FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting Tian Zhou Ziqing Ma Xue Wang Qingsong Wen Liang Sun Tao Yao Wotao Yin Rong Jin AI4TS 121 170 0 18 May 2022
Unraveling Attention via Convex Duality: Analysis and Interpretations of Vision Transformers Arda Sahiner Tolga Ergen Batu Mehmet Ozturkler John M. Pauly Morteza Mardani Mert Pilanci 40 33 0 17 May 2022
Automated differential equation solver based on the parametric approximation optimization A. Hvatov Tatiana Tikhonova 18 4 0 11 May 2022
Inferring electrochemical performance and parameters of Li-ion batteries based on deep operator networks Qi Zheng Xiaoguang Yin Dongxiao Zhang 14 10 0 06 May 2022
Generative Adversarial Neural Operators Md Ashiqur Rahman Manuel A. Florez Anima Anandkumar Zachary E. Ross Kamyar Azizzadenesheli GAN 25 34 0 06 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
Demystifying the Data Need of ML-surrogates for CFD Simulations Tongtao Zhang Biswadip Dey Krishna Veeraraghavan Harshad Kulkarni Amit Chakraborty AI4CE 25 5 0 05 May 2022
Wavelet neural operator: a neural operator for parametric partial differential equations Tapas Tripura S. Chakraborty 17 63 0 04 May 2022
Accelerating phase-field-based simulation via machine learning Iman Peivaste N. Siboni G. Alahyarizadeh R. Ghaderi Bob Svendsen Dierk Raabe J. Mianroodi AI4CE 14 3 0 04 May 2022
Graph Anisotropic Diffusion Ahmed A. A. Elhag Gabriele Corso Hannes Stärk Michael M. Bronstein DiffM GNN 25 0 0 30 Apr 2022
BI-GreenNet: Learning Green's functions by boundary integral network Guochang Lin Fu-jun Chen Pipi Hu Xiang Chen Junqing Chen Jun Wang Zuoqiang Shi 34 20 0 28 Apr 2022
Evolving Generalizable Multigrid-Based Helmholtz Preconditioners with Grammar-Guided Genetic Programming J. Schmitt Harald Kostler AI4CE 27 0 0 27 Apr 2022
Learning Green's functions associated with time-dependent partial differential equations N. Boullé Seick Kim Tianyi Shi Alex Townsend AI4CE 29 25 0 27 Apr 2022
SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability Simone Venturi T. Casey 23 37 0 27 Apr 2022