A multi-dimensional data-driven sparse identification technique: the sparse Proper Generalized Decomposition

Author (s): Ibáñez, R., Abisset-Chavanne, E., Ammar, A., González, D., Cueto, E., Huerta, A., Duval, J.-L., and Chinesta, F.
Journal: Complexity

Volume: 2018, 11 pages
Date: 2018

Abstract:
Sparse model identification by means of data is specially 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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Bibtex:

@article{Complexity-IAAGCHDC:18,
        Author = {Rub\'{e}n Ib\'{a}\~nez and Emmanuelle Abisset-Chavanne and 
                  Amine Ammar and David Gonz\'alez and El\'ias Cueto and 
                  Antonio Huerta and Jean Louis Duval and Francisco Chinesta},
        Title = {A multi-dimensional data-driven sparse identification 
                 technique: the sparse Proper Generalized Decomposition},
        Fjournal = {Complexity},
        Journal = {Complexity},
        Volume = {(5608286)},
        Pages = {1--11},
        Year = {2018},
        Doi = {10.1155/2018/5608286},
        }