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

Rubén Ibáñez (1) , Emmanuelle Abisset-Chavanne (1) , Amine Ammar (2) , David Gonzalez (3) , Elias Cueto (3) , Antonio Huerta (4) , Jean Louis Duval (5) , Francisco Chinesta (1)

1 ENSAM - École Nationale Supérieure des Arts et Métiers
2 LAMPA - Laboratoire Angevin de Mécanique, Procédés et InnovAtion
3 I3A - Aragón Institute of Engineering Research [Zaragoza]
4 LaCàN - Laboratori de Càlcul Numèric (LACAN)
5 ESI Group - ESI Group

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.

Domaines: Matériaux

Rubén Ibáñez, Emmanuelle Abisset-Chavanne, Amine Ammar, David Gonzalez, Elias Cueto, et al.. A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition. Complexity, 2018, 2018, pp.1-11. ⟨10.1155/2018/5608286⟩. ⟨hal-02285019⟩