Discovering equations from data: symbolic regression in dynamical systems

Abstract: The process of discovering equations from data lies at the heart of physics and in many other areas of research, including mathematical ecology and epidemiology. Recently, machine learning methods known as symbolic regression have automated this process. As several methods are available in the literature, it is important to compare them, particularly for dynamic systems that describe complex phenomena. In this paper, five symbolic regression methods were used for recovering equations from nine dynamical processes, including chaotic dynamics and epidemic models, with the PySR method proving to be the most suitable for inferring equations. Benchmark results demonstrate its high predictive power and accuracy, with some estimates being indistinguishable from the original analytical forms. These results highlight the potential of symbolic regression as a robust tool for inferring and modelling real-world phenomena.