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 when tackling real dynamical systems. While SINDy can be an appealing strategy for pursuing physics-based learning, our analysis highlights difficulties in 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 in order to exploit SINDy also in these challenging contexts.

These approaches fall into four categories: physicconstrained, Over recent decades, advances in mechanics and electronics serial, parallel, and ensemble strategies. In have led to the development of increasingly sophisticated the physic-constrained category, techniques either integrate systems with complex and multi-physics dynamics, exposing physically meaningful features from first principles into limitations in first principle-based representations [17]. ML models or explicitly include physical constraints, such Modeling these advanced systems purely based on domain as boundary conditions, into the loss function (see, e.g., knowledge may inadequately capture the overall system behavior, the working principle of physics-informed neural networks often necessitating the formulation of complex partial (PINN)) [7,?].