A Multidimensional Data-Driven Sparse Identification Technique: The Sparse Proper Generalized Decomposition. (1st November 2018) - Ibáñez, Rubén; Abisset-Chavanne, Emmanuelle; Ammar, Amine; González, David; Cueto, Elías; Huerta, Antonio; Duval, Jean Louis; Chinesta, Francisco
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.