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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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2018-01, Vol.2018 (2018), p.1-11
Main Authors: Chinesta, Francisco, Huerta, Antonio, Cueto, Elías, González, David, Ammar, Amine, Abisset-Chavanne, Emmanuelle, Ibáñez, Rubén, Duval, Jean Louis
Format: Article
Language:English
Subjects:
70 Mechanics of particles and systems
70Q05 Control of mechanical systems
74 Mechanics of deformable solids
74S Numerical methods
Anàlisi numèrica
Archives & records
Automatic control
Classificació AMS
Control automàtic
Data analysis
Decomposition
Engineering
Engineering Sciences
Identification
Matemàtica aplicada a les ciències
Matemàtiques i estadística
Materials
Mechanics
Methods
Multidimensional data
Mètodes numèrics
Numerical analysis
Principal components analysis
Science
Àrees temàtiques de la UPC
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Summary: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.
ISSN:1076-2787
1099-0526
1099-0526
DOI:10.1155/2018/5608286