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

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.