Analytic formulas of peak current in cyclic voltammogram: Machine learning as an alternative way?

Cyclic voltammetry is most widely used in the study of electrode kinetics. The peak current density (I_p) in a cyclic voltammogram (CV) is a function of many parameters involved in the kinetics, thereby being an indicator of the reaction mechanism. Analytic expressions of I_p for reversible and irreversible reactions, proposed by Randles–Sevcik equations via dimensional analysis and numerical solutions of dimensionless equations, play the central role in the analysis of experimental results of CV. Great difficulties are encountered, however, to derive an expression of I_p in the quasireversible region by classical methods, and hence, an analytic formula is lacking yet to cover the entire reaction spectrum. The present work demonstrates the success of machine learning (ML) as an alternative way to find simple and analytic formulas of I_p for the reversible and irreversible reactions and then for the entire reaction spectrum, purely based on data from CV simulations. Two analytic formulas of I_p, both with high accuracy, are proposed by using symbolic regression combining with sparse regression. The simpler and physically meaningful one is obtained by combining ML with expert knowledge of mathematical expressions. The paper illustrates the powerful capability of ML, or by combining with expert knowledge, as a promising universal and practical tool to analyze complex electrochemical kinetics.