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

Type
Articles dans des revues avec comité de lecture
Auteur
IBAÑEZ, Rubén
301320 École Nationale Supérieure d'Arts et Métiers [ENSAM]
ABISSET-CHAVANNE, Emmanuelle
58355 École Nationale Supérieure des Arts et Métiers [ENSAM]
AMMAR, Amine
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
GONZALEZ, David
161327 Aragón Institute of Engineering Research [Zaragoza] [I3A]
CUETO, 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]
CHINESTA, 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

Résumé

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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  • Laboratoire Angevin de Mécanique, Procédés et InnovAtion (LAMPA)

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    IBÁÑEZ, Rubén; ABISSET-CHAVANNE, Emmanuelle; GONZÁLEZ, David; DUVAL, Jean Louis; CUETO, Elias; CHINESTA, Francisco (Springer-Verlag France, 2019)
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  • Some applications of compressed sensing in computational mechanics: model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction 
    IBAÑEZ, R.; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elías G.; AMMAR, Amine; DUVAL, Jean Louis; CHINESTA, Francisco (Springer, 2019)
    Compressed sensing is a signal compression technique with very remarkable properties. Among them, maybe the most salient one is its ability of overcoming the Shannon–Nyquist sampling theorem. In other words, it is able to ...
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    IBÁÑEZ PINILLO, Rubén; AMMAR, Amine; CUETO, Elías G.; HUERTA, Antonio; DUVAL, Jean Louis; CHINESTA, Francisco (Wiley, 2019)
    Solutions of partial differential equations could exhibit a multiscale behavior. Standard discretization techniques are constraints to mesh up to the finest scale to predict accurately the response of the system. The ...
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    IBAÑEZ, Ruben; ABISSET-CHAVANNE, Emmanuelle; CHINESTA, Francisco; HUERTA, Antonio; CUETO, Elías G. (Wiley, 2019)
    It is well known that model order reduction techniques that project the solution of the problem at hand onto a low-dimensional subspace present difficulties when this solution lies on a nonlinear manifold. To overcome these ...
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    This work aims at proposing a new procedure for parametric problems whose separated representation has been considered difficult, or whose SVD compression impacted the results in terms of performance and accuracy. The ...

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