Interpretability analysis of Symbolic Regression models for dynamical systems

Symbolic Regression (SR) is a machine learning paradigm that focuses on the automatic discovery of mathematical equations that best describe the relationship between input and output features in experimental datasets. Such an approach leads to interpretable models that make it easy to incorporate the knowledge available in the system. This article addresses the application of SR as an interpretable modelling approach for industrial applications involving nonlinear dynamical systems. Interpretability in model identification is crucial for understanding system processes. While SR models are inherently interpretable, the inclusion of explainability techniques such as SHAP is being explored to improve model validation while facilitating model interpretation by process technologists. In this paper, the Narendra-Li system, which is commonly used as a testbed for dynamical system identification, is considered. The performance of the proposed solutions is evaluated using appropriate interpretability metrics that provide insight into their efficiency in capturing the underlying dynamics of the system.