How entropic regression beats the outliers problem in nonlinear system identification

Area of Science:

• * Nonlinear dynamics
• * Information theory
• * System Identification

Background:

• * Current System Identification (SID) methods face limitations with noisy data, outliers, diverse scales, and high-dimensional systems.
• * Existing sparse regression techniques struggle with complex dynamics and parameter sloppiness.
• * A robust and scalable SID method is needed for analyzing complex systems.

Purpose of the Study:

• * To develop a novel nonlinear System Identification (SID) method named Entropic Regression.
• * To leverage information-theoretic measures for robust data-driven discovery of underlying system dynamics.
• * To address limitations of current SID methods, including noise sensitivity, parameter sloppiness, and high dimensionality.

Main Methods:

• * Developed Entropic Regression, a nonlinear System Identification (SID) method.
• * Utilized information-theoretic measures, specifically exploiting the Asymptotic Equipartition Property.
• * Applied the method to sparse regression and chaotic systems like Lorenz, Kuramoto-Sivashinsky, and Double-Well Potential.

Main Results:

• * Entropic Regression demonstrates robustness against noise and outliers.
• * The method outperforms existing state-of-the-art System Identification techniques.
• * Successfully applied to complex nonlinear and chaotic systems, overcoming limitations of prior approaches.

Conclusions:

• * Entropic Regression offers a powerful, information-theoretic approach to nonlinear System Identification.
• * The method's intrinsic de-emphasis of outliers makes it highly reliable.
• * It provides a significant advancement for analyzing complex dynamical systems.