A door to model reduction in high-dimensional parameter space

Charles Paillet; David Néron; Pierre Ladevèze

doi:10.1016/j.crme.2018.04.009

Model reduction, data-based and advanced discretization in computational mechanics

A door to model reduction in high-dimensional parameter space

Charles Paillet ¹ ; David Néron ¹; Pierre Ladevèze ¹

¹ LMT (ENS Paris-Saclay, CNRS, Université Paris-Saclay), 61, avenue du Président-Wilson, 94235 Cachan cedex, France

Comptes Rendus. Mécanique, Model reduction, data-based and advanced discretization in computational mechanics / Réduction de modèles, données et techniques de discrétisation avancées en mécanique numérique, Volume 346 (2018) no. 7, pp. 524-531.

Abstract
Résumé

Model reduction techniques such as Proper Generalized Decomposition (PGD) are decision-making tools that are about to revolutionize many domains. Unfortunately, their computation is still problematic for problems involving many parameters, for which one has to face the “curse of dimensionality”. An answer to this challenge is given in solid mechanics by the so-called “parameter-multiscale PGD”, which is based on Saint-Venant's principle. In this article, a model problem composed of up to a thousand parameters is presented, showing that the method is able to overcome the “curse of dimensionality”.

Les modèles réduits, en particulier ceux basés sur la Proper Generalized Decomposition (PGD) sont des outils de conception qui s'apprêtent à révolutionner la simulation numérique. Malheureusement, pour les problèmes à grand nombre de paramètres, la « malédiction de la dimensionnalité » semble être une limitation majeure. Nous proposons, avec la parameter-multiscale PGD, une solution à ce problème basée sur le principe de Saint-Venant. Un cas test comprenant jusqu'à mille paramètres est présenté dans cet article et prouve que la méthode permet bien de s'affranchir de la « malédiction de la dimensionnalité ».

Received: 2017-12-12
Accepted: 2018-04-02
Published online: 2018-05-02

DOI: 10.1016/j.crme.2018.04.009

Keywords: Reduced Order Model (ROM), PGD, Multiparametric
Mots-clés : Réduction de modèles, PGD, Multiparamétrique

Author's affiliations:

Charles Paillet ¹; David Néron ¹; Pierre Ladevèze ¹

¹ LMT (ENS Paris-Saclay, CNRS, Université Paris-Saclay), 61, avenue du Président-Wilson, 94235 Cachan cedex, France

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     author = {Charles Paillet and David N\'eron and Pierre Ladev\`eze},
     title = {A door to model reduction in high-dimensional parameter space},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {524--531},
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     volume = {346},
     number = {7},
     year = {2018},
     doi = {10.1016/j.crme.2018.04.009},
     language = {en},
}

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Charles Paillet; David Néron; Pierre Ladevèze. A door to model reduction in high-dimensional parameter space. Comptes Rendus. Mécanique, Model reduction, data-based and advanced discretization in computational mechanics / Réduction de modèles, données et techniques de discrétisation avancées en mécanique numérique, Volume 346 (2018) no. 7, pp. 524-531. doi : 10.1016/j.crme.2018.04.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.04.009/

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