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: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/5608286 |
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| author | Rubén Ibáñez Emmanuelle Abisset-Chavanne Amine Ammar David González Elías Cueto Antonio Huerta Jean Louis Duval Francisco Chinesta |
| author_facet | Rubén Ibáñez Emmanuelle Abisset-Chavanne Amine Ammar David González Elías Cueto Antonio Huerta Jean Louis Duval Francisco Chinesta |
| author_sort | Rubén Ibáñez |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-8aec06b7c92c472aba463e22e1e0da0a |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-8aec06b7c92c472aba463e22e1e0da0a2025-08-20T03:37:34ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/56082865608286A 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2018/5608286 |
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