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A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition

Article dans une revue avec comité de lecture
Author
IBAÑEZ, Ruben
ccABISSET-CHAVANNE, Emmanuelle
58355 École Nationale Supérieure des Arts et Métiers [ENSAM]
ccAMMAR, Amine
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
GONZALEZ, David
161327 Aragón Institute of Engineering Research [Zaragoza] [I3A]
ccCUETO, Elias
161327 Aragón Institute of Engineering Research [Zaragoza] [I3A]
495918 European Organization for Nuclear Research [CERN]
HUERTA, Antonio
81618 Laboratori de Càlcul Numèric (LACAN) [LaCàN]
DUVAL, Jean-Louis
564849 ESI Group [ESI Group]
ccCHINESTA SORIA, Francisco
301320 École Nationale Supérieure d'Arts et Métiers [ENSAM]

URI
http://hdl.handle.net/10985/16676
DOI
10.1155/2018/5608286
Date
2018
Journal
Complexity

Abstract

Sparse model identification by means of data is especially cumbersome if the sought dynamics live in a high dimensional space. This usually involves the need for large amount of data, unfeasible in such a high dimensional settings. This well-known phenomenon, coined as the curse of dimensionality, is here overcome by means of the use of separate representations. We present a technique based on the same principles of the Proper Generalized Decomposition that enables the identification of complex laws in the low-data limit. We provide examples on the performance of the technique in up to ten dimensions.

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