Regularized least absolute deviation-based sparse identification of dynamical systems.
Feng Jiang1, Lin Du1, Fan Yang1
1MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi'an 710072, China.
Chaos (Woodbury, N.Y.)
|February 1, 2023
Summary
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.
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.
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