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

Agathe Reille (1) , Nicolas Hascoët (1) , Chady Ghnatios (2) , Amine Ammar (3) , Elías G. Cueto (4) , Jean Louis Duval (5) , Francisco Chinesta (1) , Roland Keunings (6)

1 PIMM - Laboratoire Procédés et Ingénierie en Mécanique et Matériaux
2 NDU - Notre Dame University-Louaize [Lebanon]
3 LAMPA - Laboratoire Angevin de Mécanique, Procédés et InnovAtion
4 University of Zaragoza - Universidad de Zaragoza [Zaragoza]
5 ESI Group - ESI Group
6 UCL - Université Catholique de Louvain = Catholic University of Louvain

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.

Mots clés: Nonlinear reduced modeling; Mode decomposition; Machine learning; Advanced regression; Tensor formats; PGD

Domaines: Matériaux

Agathe Reille, Nicolas Hascoët, Chady Ghnatios, Amine Ammar, Elías G. Cueto, et al.. Incremental dynamic mode decomposition: A reduced-model learner operating at the low-data limit. Comptes Rendus Mécanique, 2019, 347 (11), pp.780-792. ⟨10.1016/j.crme.2019.11.003⟩. ⟨hal-02561899⟩