We present a random sampling method for learning high-dimensional sparse dynamical systems from limited and possibly noisy snapshots over time. The learning problem takes the form of a sparse least-squares fitting over a large set of candidate functions. Combining tools from compressive sensing with a Bernstein-like inequality for partly dependent random variables, we provide theoretical guarantees on the recovery rate of the sparse coefficients and the identification of the candidate functions for the corresponding problem. This formulation has several advantages including ease of use, theoretical guarantees of success, and computational efficiency with respect to ambient dimension and number of candidate functions.
Joint work with Hayden Schaeffer (Carnegie Mellon University) and Giang Tran (University of Waterloo).
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