# How Entropic Regression Beats the Outliers Problem in Nonlinear System Identification

## TL;DR

Entropic Regression is a robust nonlinear system identification method that leverages information theory to effectively handle noise and outliers, outperforming existing techniques especially in high-dimensional and complex systems.

## Contribution

The paper introduces Entropic Regression, a novel information-theoretic approach for nonlinear system identification that addresses limitations of current methods regarding outliers, parameter sensitivity, and high-dimensional systems.

## Key findings

- Outperforms state-of-the-art methods in robustness and accuracy.
- Effectively handles noise and outliers in system data.
- Successfully applied to chaotic systems like Lorenz and Kuramoto-Sivashinsky.

## Abstract

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.