A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition. (1st November 2018)

• Record Type: Journal Article
• Authors: Ibáñez, Rubén; Abisset-Chavanne, Emmanuelle; Ammar, Amine; González, David; Cueto, Elías; Huerta, Antonio; Duval, Jean Louis; Chinesta, Francisco
• Other Names: Chen Diyi Academic Editor.
• Is Part Of: Complexity. Volume 2018(2018)
• Publication Date: 2018-11-01
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2018/5608286
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : 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.