  In this work, we developed a nonlinear System Identification (SID) method
that we called Entropic Regression. Our method adopts an information-theoretic
measure for the data-driven discovery of the underlying dynamics. Our method
shows robustness toward noise and outliers and it outperforms many of the
current state-of-the-art methods. Moreover, the method of Entropic Regression
overcomes many of the major limitations of the current methods such as sloppy
parameters, diverse scale, and SID in high dimensional systems such as complex
networks. The use of information-theoretic measures in entropic regression
poses unique advantages, due to the Asymptotic Equipartition Property (AEP) of
probability distributions, that outliers and other low-occurrence events are
conveniently and intrinsically de-emphasized as not-typical, by definition. We
provide a numerical comparison with the current state-of-the-art methods in
sparse regression, and we apply the methods to different chaotic systems such
as the Lorenz System, the Kuramoto-Sivashinsky equations, and the Double Well
Potential.
