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Forecasting multiscale chaotic dynamical systems, such as turbulent flows, with deep learning remains a formidable challenge due to the spectral bias of neural networks, which hinders the accurate representation of fine-scale structures in long-term predictions.
The local structure of turbulence in incompressible viscous fluid for very large reynolds
Andrey Nikolaevich Kolmogorov · 1941
Earlier work this paper cites.
A logical calculus of the ideas immanent in nervous activity
Warren S McCulloch and Walter Pitts · 1943
Earlier work this paper cites.
Kolmogorov flow and laboratory simulation of it
AM Obukhov · 1983
Earlier work this paper cites.
Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
Earlier work this paper cites.
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
Tianping Chen and Hong Chen · 1995
Earlier work this paper cites.
Scale interactions during the formation of typhoon irving
Elizabeth A Ritchie and Greg J Holland · 1997
Earlier work this paper cites.
Lagrangian tetrad dynamics and the phenomenology of turbulence
Michael Chertkov, Alain Pumir, and Boris I Shraiman · 1999
Earlier work this paper cites.
The design and analysis of computer experiments, 2003
TJ Santner · 2003
Earlier work this paper cites.
U-net: Convolutional networks for biomedical image segmentation
Olaf Ronneberger, Philipp Fischer, and Thomas Brox · 2015
Earlier work this paper cites.
Sobolev training for neural networks
Wojciech M Czarnecki, Simon Osindero, Max Jaderberg, Grzegorz Swirszcz, and Razvan Pascanu · 2017
Earlier work this paper cites.
JAX: composable transformations of Python+NumPy programs, 2018
James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake VanderPlas, Skye Wanderman-Milne, and Qiao Zhang · 2018
Earlier work this paper cites.
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Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud · 2018
Earlier work this paper cites.
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Don Daniel, Daniel Livescu, and Jaiyoung Ryu · 2018
Earlier work this paper cites.
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Arthur Jacot, Franck Gabriel, and Clément Hongler · 2018
Earlier work this paper cites.
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Romit Maulik, Omer San, Adil Rasheed, and Prakash Vedula · 2019
Earlier work this paper cites.
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Earlier work this paper cites.
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Huaizhi Wang, Zhenxing Lei, Xian Zhang, Bin Zhou, and Jianchun Peng · 2019
Earlier work this paper cites.
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Earlier work this paper cites.
Fast neural poincaré maps for toroidal magnetic fields
Joshua William Burby, Qi Tang, and R Maulik · 2020
Earlier work this paper cites.
Ziqi Liu, Wei Cai, and Zhi-Qin John Xu · 2020
Earlier work this paper cites.
Spatio-temporal deep learning models of 3d turbulence with physics informed diagnostics
Arvind T Mohan, Dima Tretiak, Misha Chertkov, and Daniel Livescu · 2020
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Matthew Tancik, Pratul Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan Barron, and Ren Ng · 2020
Earlier work this paper cites.
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Bo Wang, Wenzhong Zhang, and Wei Cai · 2020
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Spectral bias and task-model alignment explain generalization in kernel regression and infinitely wide neural networks
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Aaron Towne, Scott TM Dawson, Guillaume A Brès, Adrián Lozano-Durán, Theresa Saxton-Fox, Aadhy Parthasarathy, Anya R Jones, Hulya Biler, Chi-An Yeh, Het D Patel, et al · 2023
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