Recovering the Governing Equations of Chua’s Circuit by Sparse Identification from Experimental Data

This work shows the applicability of the Sparse Identification of Nonlinear Dynamical Systems (SINDy) method to experimental data, in particular data obtained from a nonlinear electronic circuit, i.e. Chua's circuit. 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 paper, we propose a novel iterative method to enforce sparsity, namely the variance-based sequential least-squares method, and identify several appropriate 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. Since the circuit equations can also be derived from first principles (Kirchhoff's laws), Chua's circuit provides an ideal benchmark for validating the approach. Through the analysis of this case study, we show that the 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.