Recovering the governing equations of the Chua's circuit by sparse identification from experimental data

This work investigates the applicability of the Sparse Identification of Nonlinear Dynamical Systems (SINDy) method to experimental data, in particular data obtained from a nonlinear electronic circuit. Specifically, we focus on the Chua’s circuit, measuring its state variables and applying the SINDy framework to reconstruct the governing equations of the circuit. Since the circuit equations can also be derived from first principles (Kirchhoff’s laws), this system provides an ideal benchmark for validating the approach. The method relies on defining a suitable set of linear and nonlinear terms that may appear in the reconstructed equations, forming the “vocabulary” through which the model is expressed, and on applying sparse identification techniques to determine the terms required to reconstruct the dynamical equations that best fit the input data. In this work, we propose a new iterative least-squares–based method to enforce sparsity and define several error metrics tailored to the analysis of chaotic systems. We apply the method first to numerical data obtained from a circuit model and then to experimental data obtained from real measurements. In doing so, we consider four libraries of different sizes in order to elucidate their role in system reconstruction. Through the analysis of this case study, we show that the SINDy method is robust with respect to the choice of the function library, supporting its application to nonlinear circuits with unknown topologies or components exhibiting unmodeled behavior.