On the Physical Consistency of Evolution Laws Obtained with Sparse Regression

Abstract

This work employs the technique known as sparse identification of nonlinear dynamics (SINDy) to infer, from a set of information provided by a given time-series, the evolution law of a dynamical system of interest, accessing the physical consistency of the obtained dynamic model. The Duffing oscillator is used as a benchmark due to the variety and richness of its dynamical behavior. The numerical experiments attempt to identify whether the method is capable of recognizing the correct evolution law and respecting basic principles of physics such as the balance of momentum and energy. The numerical results illustrate the method's ability to obtain approximations to the system evolution law that provides physically consistent behavior for short time intervals.