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Data-driven machine learning approaches are being increasingly used to solve partial differential equations (PDEs).
Iterative procedures for nonlinear integral equations
Donald G Anderson · 1965
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A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows
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Chebyshev and Fourier spectral methods
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Numerical solution of nonlinear elliptic problems via preconditioning operators: Theory and applications , volume 11
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Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems
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Implementing spectral methods for partial differential equations: Algorithms for scientists and engineers
David A Kopriva · 2009
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Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2010
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Gaussian error linear units (gelus)
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The finite volume method
Fadl Moukalled, Luca Mangani, Marwan Darwish, F Moukalled, L Mangani, and M Darwish · 2016
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Reviving and improving recurrent back-propagation
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Shaojie Bai, J Zico Kolter, and Vladlen Koltun · 2019
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Yohai Bar-Sinai, Stephan Hoyer, Jason Hickey, and Michael P Brenner · 2019
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Learning neural pde solvers with convergence guarantees
Jun-Ting Hsieh, Shengjia Zhao, Stephan Eismann, Lucia Mirabella, and Stefano Ermon · 2019
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Parametric complexity bounds for approximating PDEs with neural networks
Tanya Marwah, Zachary Lipton, and Andrej Risteski · 2021
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A physics-informed operator regression framework for extracting data-driven continuum models
Ravi G Patel, Nathaniel A Trask, Mitchell A Wood, and Eric C Cyr · 2021
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Factorized Fourier neural operators
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Path independent equilibrium models can better exploit test-time computation
Cem Anil, Ashwini Pokle, Kaiqu Liang, Johannes Treutlein, Yuhuai Wu, Shaojie Bai, J Zico Kolter, and Roger B Grosse · 2022
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Message passing neural pde solvers
Johannes Brandstetter, Daniel Worrall, and Max Welling · 2022
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Neural network approximations of PDEs beyond linearity: Representational perspective
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Neural operator: Learning maps between function spaces with applications to PDEs
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