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Regularized least absolute deviation-based sparse identification of dynamical systems.

Feng Jiang1, Lin Du1, Fan Yang1

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This study introduces a robust method for identifying dynamical systems, even with outlier data. The regularized least absolute deviation-based sparse identification of dynamics (RLAD-SID) method enhances accuracy by using absolute deviation loss.

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Area of Science:

  • Dynamical Systems Theory
  • Machine Learning
  • Data Science

Background:

  • Classical sparse identification methods struggle with outliers due to metric-based loss functions.
  • Existing frameworks lack robustness when dealing with noisy or erroneous data points.

Purpose of the Study:

  • To develop a robust sparse identification of dynamics (SID) method resistant to outliers.
  • To introduce a novel loss function and optimization algorithm for improved dynamical system identification.

Main Methods:

  • Developed a regularized least absolute deviation-based sparse identification of dynamics (RLAD-SID) method.
  • Utilized absolute deviation loss instead of traditional Euclidean loss.
  • Implemented an efficient optimization algorithm based on the alternating direction method of multipliers.

Main Results:

  • RLAD-SID demonstrated significant robustness against substantial outliers in numerical experiments.
  • The method was validated on nonlinear systems including the van der Pol equation, Lorenz system, and logistic map.
  • Comparative analyses showed superior performance over existing metric-based sparse regression techniques.

Conclusions:

  • RLAD-SID effectively addresses outlier problems in dynamical system identification.
  • The proposed method offers a robust and effective extension of the metric-based sparse regression framework.