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We propose a novel multi-scale message passing neural network algorithm for learning the solutions of time-dependent PDEs.
Numerical methods for conservation laws (2. ed.)
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Neural message passing for quantum chemistry
Justin Gilmer, Samuel S Schoenholz, Patrick F Riley, Oriol Vinyals, and George E Dahl · 2017
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Efficient computation of all speed flows using an entropy stable shock-capturing space-time discontinuous galerkin method
A. Hiltebrand and S. Mishra · 2017
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Relational inductive biases, deep learning, and graph networks
P.W. Battaglia, J. B. Hamrick, V. Bapst, A. Sanchez-Gonzalez, V. Zambaldi, M. Malinowski, A. Tacchetti, D. Raposo, A. Santoro, and R. Faulkner et al · 2018
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Hidden physics models: Machine learning of nonlinear partial differential equations
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Deep learning observables in computational fluid dynamics
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Fourier neural operator for parametric partial differential equations
Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Burigede liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 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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MAgnet: Mesh agnostic neural PDE solver
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Message passing neural PDE solvers
Johannes Brandstetter, Daniel E. Worrall, and Max Welling · 2022
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Long expressive memory for sequence modeling
T Konstantin Rusch, Siddhartha Mishra, N Benjamin Erichson, and Michael W Mahoney · 2022
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Learned coarse models for efficient turbulence simulation
Kimberly Stachenfeld, Drummond B. Fielding, Dmitrii Kochkov, Miles Cranmer, Tobias Pfaff, Jonathan Godwin, Can Cui, Shirley Ho, Peter Battaglia, and Alvaro Sanchez-Gonzalez · 2022
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Gradient gating for deep multi-rate learning on graphs
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