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

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

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, i...

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Main Authors: Rubén Ibáñez, Emmanuelle Abisset-Chavanne, Amine Ammar, David González, Elías Cueto, Antonio Huerta, Jean Louis Duval, Francisco Chinesta
Format: Article
Language:English
Published: Hindawi-Wiley 2018-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2018/5608286
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spelling doaj-8aec06b7c92c472aba463e22e1e0da0a2020-11-24T21:26:26ZengHindawi-WileyComplexity1076-27871099-05262018-01-01201810.1155/2018/56082865608286A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized DecompositionRubén Ibáñez0Emmanuelle Abisset-Chavanne1Amine Ammar2David González3Elías Cueto4Antonio Huerta5Jean Louis Duval6Francisco Chinesta7ESI Chair, ENSAM ParisTech. 151, bvd. de l'Hôpital, F-75013 Paris, FranceESI Chair, ENSAM ParisTech. 151, bvd. de l'Hôpital, F-75013 Paris, FranceLAMPA, ENSAM ParisTech. 2, bvd. de Ronceray. F-49035 Angers, FranceAragon Institute of Engineering Research, Universidad de Zaragoza. Maria de Luna, s.n. E-50018 Zaragoza, SpainAragon Institute of Engineering Research, Universidad de Zaragoza. Maria de Luna, s.n. E-50018 Zaragoza, SpainLaboratori de Càlcul Numèric, Universitat Politècnica de Catalunya. Jordi Girona 1-3, E-08034 Barcelona, SpainESI Group. Parc Icade, Immeuble le Seville, 3 bis, Saarinen, CP 50229, 94528, Rungis Cedex, FranceESI Chair, ENSAM ParisTech. 151, bvd. de l'Hôpital, F-75013 Paris, FranceSparse 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.http://dx.doi.org/10.1155/2018/5608286
collection DOAJ
language English
format Article
sources DOAJ
author Rubén Ibáñez
Emmanuelle Abisset-Chavanne
Amine Ammar
David González
Elías Cueto
Antonio Huerta
Jean Louis Duval
Francisco Chinesta
spellingShingle Rubén Ibáñez
Emmanuelle Abisset-Chavanne
Amine Ammar
David González
Elías Cueto
Antonio Huerta
Jean Louis Duval
Francisco Chinesta
A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition
Complexity
author_facet Rubén Ibáñez
Emmanuelle Abisset-Chavanne
Amine Ammar
David González
Elías Cueto
Antonio Huerta
Jean Louis Duval
Francisco Chinesta
author_sort Rubén Ibáñez
title A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition
title_short A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition
title_full A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition
title_fullStr A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition
title_full_unstemmed A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition
title_sort multidimensional data-driven sparse identification technique: the sparse proper generalized decomposition
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2018-01-01
description 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.
url http://dx.doi.org/10.1155/2018/5608286
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