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How entropic regression beats the outliers problem in nonlinear system identification.

Abd AlRahman R AlMomani1, Jie Sun2, Erik Bollt1

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Chaos (Woodbury, N.Y.)
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We introduce Entropic Regression, a novel nonlinear System Identification (SID) method. This data-driven approach uses information theory to discover system dynamics, outperforming current methods and handling complex systems effectively.

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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.