On the physical consistency of evolution laws obtained with sparse regression
Résumé
This work employs the technique known as sparse identifica-tion of nonlinear dynamics (SINDy) to infer, from a set of informationprovided by a given time-series, the evolution law of a dynamical systemof interest, accessing the physical consistency of the obtained dynamicmodel. The Duffing oscillator is used as a benchmark due to the vari-ety and richness of its dynamical behavior. The numerical experimentsattempt to identify whether the method is capable of recognizing thecorrect evolution law and respecting basic principles of physics such asthe balance of momentum and energy. The numerical results illustratethe method’s ability to obtain approximations to the system evolutionlaw that provides physically consistent behavior for short time intervals.
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