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Incremental dynamic mode decomposition: A reduced-model learner operating at the low-data limit

Type
Articles dans des revues avec comité de lecture
Author
REILLE, Agathe
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
HASCOËT, Nicolas
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
GHNATIOS, Chady
533922 Notre Dame University-Louaize [Lebanon] [NDU]
AMMAR, Amine
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
CUETO, Elías G.
95355 University of Zaragoza - Universidad de Zaragoza [Zaragoza]
DUVAL, Jean Louis
564849 ESI Group [ESI Group]
CHINESTA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
KEUNINGS, Roland
92863 Université Catholique de Louvain [UCL]

URI
http://hdl.handle.net/10985/18539
DOI
10.1016/j.crme.2019.11.003
Date
2019
Journal
Comptes Rendus Mécanique

Abstract

The present work aims at proposing a new methodology for learning reduced models from a small amount of data. It is based on the fact that discrete models, or their transfer function counterparts, have a low rank and then they can be expressed very efficiently using few terms of a tensor decomposition. An efficient procedure is proposed as well as a way for extending it to nonlinear settings while keeping limited the impact of data noise. The proposed methodology is then validated by considering a nonlinear elastic problem and constructing the model relating tractions and displacements at the observation points.

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