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A multidimensional data-driven sparse identification technique: the sparse proper generalized decomposition. (English) Zbl 1407.93063

Summary: 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.

MSC:

93A15 Large-scale systems
93E12 Identification in stochastic control theory
93B35 Sensitivity (robustness)

Software:

SINDy
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Full Text: DOI

References:

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