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

Reille, Agathe;Hascoet, Nicolas;Ghnatios, Chady;Ammar, Amine;Keunings, Roland;et.al.
(2019) Comptes rendus de l’Académie des Siences. Mécanique — Vol. 347, n° 11, p. 780-792 (2019)

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Authors
  • Reille, AgatheaESI Group Chair @ PIMM, Arts et Métiers Institute of Technology, CNRS, CNAM, HESAM University,75013 Paris, France
    Author
  • Hascoet, NicolasaESI Group Chair @ PIMM, Arts et Métiers Institute of Technology, CNRS, CNAM, HESAM University,75013 Paris, FRANCE
    Author
  • Ghnatios, ChadyNotre Dame University – Louaize , Zouk Mikael, Zouk Mosbeh, Lebanon
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  • Ammar, AminecESI Group Chair @ LAMPA, Arts et Métiers ParisTech,49035 Angers, France
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  • Keunings, RolandUCLouvain
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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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Reille, A., Hascoet, N., Ghnatios, C., Ammar, A., Cueto, E., Duval, J. L., Chinesta, F., & Keunings, R. (2019). Incremental dynamic mode decomposition: A reduced-model learner operating at the low-data limit. Comptes rendus de l’Académie des Siences. Mécanique, 347(11), 780-792. https://doi.org/10.1016/j.crme.2019.11.003 (Original work published 2019)