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Adaptive integral alternating minimization method for robust learning of nonlinear dynamical systems from highly

Tao Zhang1,2, Guang Liu1,2, Li Wang1

  • 1School of Aeronautics and Astronautics, Shenzhen Campus of Sun Yat-sen University, No. 66 Gongchang Road, Guangming District, Shenzhen, Guangdong 518107, People's Republic of China.

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This study introduces an adaptive integral alternating minimization method (AIAMM) to learn nonlinear dynamical systems from corrupted data. AIAMM effectively identifies system dynamics even with significant noise and outliers, outperforming existing methods.

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Area of Science:

  • Dynamical Systems Theory
  • Machine Learning
  • Signal Processing

Background:

  • Learning nonlinear dynamical systems from noisy data is challenging.
  • Existing methods struggle with highly corrupted measurements and outliers.
  • Accurate system identification is crucial for understanding and controlling complex phenomena.

Purpose of the Study:

  • To develop a robust method for learning nonlinear dynamical systems from highly corrupted data.
  • To address the challenges of unknown sparse coefficients, initial values, and outliers.
  • To improve the accuracy and reliability of system identification in the presence of significant noise.

Main Methods:

  • Proposes an adaptive integral alternating minimization method (AIAMM).
  • Formulates the problem as sparse robust linear regression.
  • Introduces an adaptive threshold parameter selection for sparsity control.

Main Results:

  • AIAMM successfully learns nonlinear dynamical systems from highly corrupted data.
  • Demonstrated superior performance on various systems like the van der Pol oscillator and Lorenz system.
  • Outperformed advanced sparse recovery methods in robustness and accuracy.

Conclusions:

  • The AIAMM is a robust and accurate method for identifying nonlinear dynamical systems from noisy data.
  • The adaptive thresholding effectively handles model fitting errors and sparsity.
  • AIAMM offers a significant advancement for system identification with corrupted measurements.