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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Data-driven discovery of Green's functions with human-understandable deep learning Nicolas Boullé Christopher Earls Alex Townsend PINN AI4CE 17 55 0 01 May 2021
Inductive biases and Self Supervised Learning in modelling a physical heating system C. Vicas AI4CE 13 0 0 23 Apr 2021
Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains Hengjie Wang R. Planas Aparna Chandramowlishwaran Ramin Bostanabad AI4CE 50 61 0 22 Apr 2021
On the approximation of functions by tanh neural networks Tim De Ryck S. Lanthaler Siddhartha Mishra 21 137 0 18 Apr 2021
Applications of physics-informed scientific machine learning in subsurface science: A survey A. Sun H. Yoon C. Shih Zhi Zhong AI4CE 26 9 0 10 Apr 2021
One-shot learning for solution operators of partial differential equations Priya Kasimbeg Haiyang He Rishikesh Ranade Jay Pathak Lu Lu AI4CE 21 11 0 06 Apr 2021
Deep Learning of Conjugate Mappings J. Bramburger S. Patterson J. Nathan Kutz 26 15 0 01 Apr 2021
Latent Space Data Assimilation by using Deep Learning Mathis Peyron Anthony Fillion S. Gürol Victor Marchais Serge Gratton Pierre Boudier G. Goret AI4CE 26 44 0 01 Apr 2021
Rethinking Neural Operations for Diverse Tasks Nicholas Roberts M. Khodak Tri Dao Liam Li Christopher Ré Ameet Talwalkar AI4CE 36 22 0 29 Mar 2021
Elvet -- a neural network-based differential equation and variational problem solver Jack Y. Araz J. C. Criado M. Spannowsky 21 13 0 26 Mar 2021
Solving and Learning Nonlinear PDEs with Gaussian Processes Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 22 153 0 24 Mar 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 40 667 0 19 Mar 2021
Evolutional Deep Neural Network Yifan Du T. Zaki 29 68 0 18 Mar 2021
Frame-independent vector-cloud neural network for nonlocal constitutive modeling on arbitrary grids Xueqing Zhou Jiequn Han Heng Xiao 8 30 0 11 Mar 2021
Parametric Complexity Bounds for Approximating PDEs with Neural Networks Tanya Marwah Zachary Chase Lipton Andrej Risteski 28 19 0 03 Mar 2021
Uncertainty Quantification by Ensemble Learning for Computational Optical Form Measurements L. Hoffmann I. Fortmeier Clemens Elster UQCV 25 28 0 01 Mar 2021
Error Estimates for the Deep Ritz Method with Boundary Penalty Johannes Müller Marius Zeinhofer 37 16 0 01 Mar 2021
Meta-Learning Dynamics Forecasting Using Task Inference Rui Wang Robin G. Walters Rose Yu OOD AI4TS AI4CE 27 31 0 20 Feb 2021
Deep learning approaches to surrogates for solving the diffusion equation for mechanistic real-world simulations J. Q. Toledo-Marín Geoffrey C. Fox J. Sluka J. Glazier MedIm AI4CE 21 8 0 10 Feb 2021
Novel Deep neural networks for solving Bayesian statistical inverse Harbir Antil H. Elman Akwum Onwunta Deepanshu Verma BDL 19 17 0 08 Feb 2021
Learning elliptic partial differential equations with randomized linear algebra Nicolas Boullé Alex Townsend 11 40 0 31 Jan 2021
Reduced operator inference for nonlinear partial differential equations E. Qian Ionut-Gabriel Farcas Karen E. Willcox AI4CE 19 38 0 29 Jan 2021
Recurrent Localization Networks applied to the Lippmann-Schwinger Equation Conlain Kelly S. Kalidindi AI4CE 12 9 0 29 Jan 2021
Convolutional conditional neural processes for local climate downscaling Anna Vaughan Will Tebbutt J. S. Hosking Richard Turner BDL 16 47 0 20 Jan 2021
Hybrid FEM-NN models: Combining artificial neural networks with the finite element method Sebastian K. Mitusch S. Funke M. Kuchta AI4CE 31 93 0 04 Jan 2021
DeepGreen: Deep Learning of Green's Functions for Nonlinear Boundary Value Problems Craig Gin D. Shea Steven L. Brunton J. Nathan Kutz 10 87 0 31 Dec 2020
Neural Network Approximations for Calabi-Yau Metrics Vishnu Jejjala D. M. Peña Challenger Mishra 29 52 0 31 Dec 2020
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 30 146 0 22 Dec 2020
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks Sizhuang He Hanwen Wang P. Perdikaris 131 438 0 18 Dec 2020
Algebraically-Informed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic Structures Mustafa Hajij Ghada Zamzmi Matthew Dawson G. Muller 14 3 0 02 Dec 2020
Importance Weight Estimation and Generalization in Domain Adaptation under Label Shift Kamyar Azizzadenesheli OOD 29 13 0 29 Nov 2020
Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks Matthew T.C. Li L. Demanet Leonardo Zepeda-Núnez 35 8 0 24 Nov 2020
Discovering Hidden Physics Behind Transport Dynamics Peirong Liu Lin Tian Yubo Zhang S. Aylward Yueh Z. Lee Marc Niethammer DiffM MedIm 28 8 0 24 Nov 2020
Data Assimilation Networks Pierre Boudier Anthony Fillion Serge Gratton S. Gürol Sixin Zhang AI4CE 22 10 0 19 Oct 2020
Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference Ricardo Baptista Bamdad Hosseini Nikola B. Kovachki Youssef Marzouk OT GAN 38 24 0 11 Jun 2020
The Random Feature Model for Input-Output Maps between Banach Spaces Nicholas H. Nelsen Andrew M. Stuart 21 140 0 20 May 2020
MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework C. Jiang S. Esmaeilzadeh Kamyar Azizzadenesheli K. Kashinath Mustafa A. Mustafa H. Tchelepi P. Marcus P. Prabhat Anima Anandkumar AI4CE 187 141 0 01 May 2020
Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems J. Willard X. Jia Shaoming Xu M. Steinbach Vipin Kumar AI4CE 91 387 0 10 Mar 2020
Hamiltonian neural networks for solving equations of motion M. Mattheakis David Sondak Akshunna S. Dogra P. Protopapas 27 56 0 29 Jan 2020