Combining machine learning and domain decomposition methods for the solution of partial differential equations—A review

DOI10.1002/gamm.202100001zbMath1528.65124OpenAlexW3138259231WikidataQ115406124 ScholiaQ115406124MaRDI QIDQ6068269

Martin Lanser, Janine Weber, Axel Klawonn, Alexander Heinlein

Publication date: 15 December 2023

Published in: GAMM-Mitteilungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/gamm.202100001

zbMATH Keywords

neural networksdomain decomposition methodshybrid modelingPDEsdeep learningphysics-informed neural networksscientific machine learningdeep Ritzadaptive coarse spaces

Mathematics Subject Classification ID

Computational learning theory (68Q32) Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Artificial neural networks and deep learning (68T07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Iterative numerical methods for linear systems (65F10) Numerical methods for partial differential equations, boundary value problems (65N99) Preconditioners for iterative methods (65F08)

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