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Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences.
Dedalus: A flexible framework for numerical simulations with spectral methods
Keaton J. Burns, Geoffrey M. Vasil, Jeffrey S. Oishi, Daniel Lecoanet, and Benjamin P. Brown · 1905
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On a numerical method for integration of the hydrodynamical equations with a spectral representation of the horizontal fields
Erik Eliasen, Bennert Machenhauer, and Erik Rasmussen · 1970
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Transform Method for the Calculation of Vector-Coupled Sums: Application to the Spectral Form of the Vorticity Equation
Steven A Orszag · 1970
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On the elimination of aliasing in finite-difference schemes by filtering high-wavenumber components
Steven A. Orszag · 1971
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The pseudospectral approximation applied to the shallow water equations on a sphere
Philip E. Merilees · 1973
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Fourier Series on Spheres
Steven A Orszag · 1974
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A standard test set for numerical approximations to the shallow water equations in spherical geometry
David L. Williamson, John B. Drake, James J. Hack, Rüdiger Jakob, and Paul N. Swarztrauber · 1992
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Computing Fourier Transforms and Convolutions on the 2-Sphere
J.R. Driscoll and D.M. Healy · 1994
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A Practical Guide to Pseudospectral Methods
Bengt Fornberg · 1996
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Transformation Geometry: An Introduction to Symmetry
G.E. Martin · 1996
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Fast shallow-water equation solvers in latitude-longitude coordinates
William F. Spotz, Mark A. Taylor, and Paul N. Swarztrauber · 1998
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Double Fourier Series on a Sphere: Applications to Elliptic and Vorticity Equations
Hyeong-Bin Cheong · 1999
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Applied Analysis
J.K. Hunter and B. Nachtergaele · 2001
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Atmospheric modeling, data assimilation and predictability
Eugenia Kalnay · 2003
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A Pseudospectral Approach for Polar and Spherical Geometries
Bengt Fornberg · 2006
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Mathematics of the Discrete Fourier Transform (DFT)
Julius O. Smith · 2007
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ImageNet: A large-scale hierarchical image database
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei · 2009
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Spherical harmonics and approximations on the unit sphere: an introduction , volume 2044
Kendall Atkinson and Weimin Han · 2012
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Chebyshev and Fourier Spectral Methods: Second Revised Edition
J.P. Boyd · 2013
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A Double Fourier Series (DFS) Dynamical Core in a Global Atmospheric Model with Full Physics
Hoon Park, Song-You Hong, Hyeong-Bin Cheong, and Myung-Seo Koo · 2013
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Deep inside convolutional networks: Visualising image classification models and saliency maps, 2014
Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman · 2014
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Spectral Representations for Convolutional Neural Networks, 2015
Oren Rippel, Jasper Snoek, and Ryan P. Adams · 2015
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U-Net: Convolutional Networks for Biomedical Image Segmentation
Olaf Ronneberger, Philipp Fischer, and Thomas Brox · 2015
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Computing with functions in spherical and polar geometries I. The sphere, 2015
Alex Townsend, Heather Wilber, and Grady B. Wright · 2015
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Xception: Deep Learning with Depthwise Separable Convolutions
François Chollet · 2017
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Language modeling with gated convolutional networks
Yann N. Dauphin, Angela Fan, Michael Auli, and David Grangier · 2017
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Sigmoid-weighted linear units for neural network function approximation in reinforcement learning, 2017
Stefan Elfwing, Eiji Uchibe, and Kenji Doya · 2017
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Learning SO(3) Equivariant Representations With Spherical Cnns
Carlos Esteves, Christine Allen-Blanchette, Ameesh Makadia, and Kostas Daniilidis · 2017
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MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications, 2017
Andrew G. Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam · 2017
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Alias-Free Generative Adversarial Networks
Tero Karras, Miika Aittala, Samuli Laine, Erik Härkönen, Janne Hellsten, Jaakko Lehtinen, and Timo Aila · 2021
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Machine learning–accelerated computational fluid dynamics
Dmitrii Kochkov, Jamie A. Smith, Ayya Alieva, Qing Wang, Michael P. Brenner, and Stephan Hoyer · 2021
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On universal approximation and error bounds for Fourier Neural Operators
Nikola Kovachki, Samuel Lanthaler, and Siddhartha Mishra · 2021
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis · 2021
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How Convolutional Neural Networks Deal with Aliasing
Antônio H. Ribeiro and Thomas B. Schön · 2021
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A case for new neural network smoothness constraints, 2021
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Adam: A method for stochastic optimization, 2017
Diederik P. Kingma and Jimmy Ba · 2017
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Spherical CNNs
Taco S. Cohen, Mario Geiger, Jonas Köhler, and Max Welling · 2018
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Bert: Pre-training of deep bidirectional transformers for language understanding
Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova · 2018
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Spectral Normalization for Generative Adversarial Networks
Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida · 2018
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PyTorch: An Imperative Style, High-Performance Deep Learning Library
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Mobilenetv2: Inverted residuals and linear bottlenecks, 2019
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Making Convolutional Networks Shift-Invariant Again
Richard Zhang · 2019
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Mihaela Rosca, Theophane Weber, Arthur Gretton, and Shakir Mohamed · 2021
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Impact of aliasing on generalization in deep convolutional networks
Cristina Vasconcelos, Hugo Larochelle, Vincent Dumoulin, Rob Romijnders, Nicolas Le Roux, and Ross Goroshin · 2021
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Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast, 2022
Kaifeng Bi, Lingxi Xie, Hengheng Zhang, Xin Chen, Xiaotao Gu, and Qi Tian · 2022
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Generic bounds on the approximation error for physics-informed (and) operator learning
Tim De Ryck and Siddhartha Mishra · 2022
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Spectral neural operators, 2022
V. Fanaskov and I. Oseledets · 2022
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Learning continuous models for continuous physics, 2022
Aditi S. Krishnapriyan, Alejandro F. Queiruga, N. Benjamin Erichson, and Michael W. Mahoney · 2022
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GraphCast: Learning skillful medium-range global weather forecasting, 2022
Remi Lam, Alvaro Sanchez-Gonzalez, Matthew Willson, Peter Wirnsberger, Meire Fortunato, Alexander Pritzel, Suman Ravuri, Timo Ewalds, Ferran Alet, Zach Eaton-Rosen, Weihua Hu, Alexander Merose, Stephan Hoyer, George Holland, Jacklynn Stott, Oriol Vinyals, Shakir Mohamed, and Peter Battaglia · 2022
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Fourier neural operator approach to large eddy simulation of three-dimensional turbulence
Zhijie Li, Wenhui Peng, Zelong Yuan, and Jianchun Wang · 2022
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Approximation Properties of the Double Fourier Sphere Method
Sophie Mildenberger and Michael Quellmalz · 2022
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Möbius Convolutions for Spherical CNNs
Thomas W. Mitchel, Noam Aigerman, Vladimir G. Kim, and Michael Kazhdan · 2022
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Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopadhyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, Pedram Hassanzadeh, Karthik Kashinath, and Animashree Anandkumar · 2022
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Learned simulators for turbulence
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U-FNO—An enhanced Fourier neural operator-based deep-learning model for multiphase flow
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Industry-scale CO2 Flow Simulations with Model-Parallel Fourier Neural Operators
Philipp A Witte, Russell Hewett, and Ranveer Chandra · 2022
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Ziyi Yin, Ali Siahkoohi, Mathias Louboutin, and Felix J Herrmann · 2022
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Learning-rate-free learning by D-adaptation
Aaron Defazio and Konstantin Mishchenko · 2023
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Factorized fourier neural operators
Alasdair Tran, Alexander Mathews, Lexing Xie, and Cheng Soon Ong · 2023
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Xingyu Xie, Pan Zhou, Huan Li, Zhouchen Lin, and Shuicheng Yan · 2023
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