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.
Accepted:
Published online:
Agathe Reille 1; Nicolas Hascoet 1; Chady Ghnatios 2; Amine Ammar 3; Elias Cueto 4; Jean Louis Duval 5; Francisco Chinesta 1; Roland Keunings 6
@article{CRMECA_2019__347_11_780_0,
author = {Agathe Reille and Nicolas Hascoet and Chady Ghnatios and Amine Ammar and Elias Cueto and Jean Louis Duval and Francisco Chinesta and Roland Keunings},
title = {Incremental dynamic mode decomposition: {A} reduced-model learner operating at the low-data limit},
journal = {Comptes Rendus. M\'ecanique},
pages = {780--792},
publisher = {Elsevier},
volume = {347},
number = {11},
year = {2019},
doi = {10.1016/j.crme.2019.11.003},
language = {en},
}
TY - JOUR AU - Agathe Reille AU - Nicolas Hascoet AU - Chady Ghnatios AU - Amine Ammar AU - Elias Cueto AU - Jean Louis Duval AU - Francisco Chinesta AU - Roland Keunings TI - Incremental dynamic mode decomposition: A reduced-model learner operating at the low-data limit JO - Comptes Rendus. Mécanique PY - 2019 SP - 780 EP - 792 VL - 347 IS - 11 PB - Elsevier DO - 10.1016/j.crme.2019.11.003 LA - en ID - CRMECA_2019__347_11_780_0 ER -
%0 Journal Article %A Agathe Reille %A Nicolas Hascoet %A Chady Ghnatios %A Amine Ammar %A Elias Cueto %A Jean Louis Duval %A Francisco Chinesta %A Roland Keunings %T Incremental dynamic mode decomposition: A reduced-model learner operating at the low-data limit %J Comptes Rendus. Mécanique %D 2019 %P 780-792 %V 347 %N 11 %I Elsevier %R 10.1016/j.crme.2019.11.003 %G en %F CRMECA_2019__347_11_780_0
Agathe Reille; Nicolas Hascoet; Chady Ghnatios; Amine Ammar; Elias Cueto; Jean Louis Duval; Francisco Chinesta; Roland Keunings. Incremental dynamic mode decomposition: A reduced-model learner operating at the low-data limit. Comptes Rendus. Mécanique, Data-Based Engineering Science and Technology, Volume 347 (2019) no. 11, pp. 780-792. doi : 10.1016/j.crme.2019.11.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.11.003/
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