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

Abstract EN

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.