SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study

In this work, we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability as a modeling tool for real dynamical systems. While SINDy is often portrayed as an appealing strategy for pursuing physics-based learning, our analysis highlights two weaknesses, i.e., the difficulties in applying this technique when dealing with unobserved states and non-smooth dynamics. Due to the ubiquity of these features in real systems in general, and control applications in particular, we complement our analysis with hands-on approaches to tackle these issues.