Discovering equations from data: symbolic regression in dynamical systems

The discovery of equations from observational data is one of the fundamental pillars of the traditional scientific method. From the work of Johannes Kepler, who inferred the laws of planetary motion from meticulous astronomical observations [1] collected by Tycho Brahe [2], to Isaac Newton's theoretical formulations that consolidated classical mechanics, the process of identifying mathematical relationships underlying natural phenomena has historically been characterized by its manual nature, based essentially on systematic trial-and-error procedures. However, in recent decades, the advent of Big Data, characterized by the production of an immense volume of complex, mostly nonlinear, data, in several fields has driven a new search for physical laws. Faced with the need to analyze these data sets to understand their intrinsic structure and derive symbolic representations that capture the integral behavior of a system, the demand for advanced analytical methods has become growing and indispensable. With the emergence of modern computational techniques, this process has undergone a radical transformation, driving the widespread development and use of various regression techniques.