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Recurrent neural networks as optimal mesh refinement strategies

Bohn, Jan; Feischl, Michael

Abstract:
We show that an optimal finite element mesh refinement algorithm for a prototypical elliptic PDE can be learned by a recurrent neural network with a fixed number of trainable parameters independent of the desired accuracy and the input size, i.e., number of elements of the mesh. Moreover, for a general class of PDEs with solutions which are well-approximated by deep neural networks, we show that an optimal mesh refinement strategy can be learned by recurrent neural networks. This includes problems for which no optimal adaptive strategy is known yet.

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Volltext §
DOI: 10.5445/IR/1000125782
Veröffentlicht am 09.11.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 11.2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000125782
Verlag KIT, Karlsruhe
Umfang 32 S.
Serie CRC 1173 Preprint ; 2020/33
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter adaptive algorithms, machine learning, neural networks, optimality, finite element method
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