Model reduction of dynamical systems with a novel data-driven approach: The RC-HAVOK algorithm

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Yılmaz Bingöl G., Soysal O. A., Günay E.

CHAOS, vol.34, no.8, pp.831431-8314318, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 8
  • Publication Date: 2024
  • Doi Number: 10.1063/5.0207907
  • Journal Name: CHAOS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Computer & Applied Sciences, EMBASE, INSPEC, MEDLINE, zbMATH, DIALNET
  • Page Numbers: pp.831431-8314318
  • Erciyes University Affiliated: Yes

Abstract

This paper introduces a novel data-driven approximation method for the Koopman operator, called the RC-HAVOK algorithm. The RC-HAVOK algorithm combines Reservoir Computing (RC) and the Hankel Alternative View of Koopman (HAVOK) to reduce the size ofthe linear Koopman operator with a lower error rate. The accuracy and feasibility of the RC-HAVOK algorithm are assessed on Lorenz-likesystems and dynamical systems with various nonlinearities, including the quadratic and cubic nonlinearities, hyperbolic tangent function,and piece-wise linear function. Implementation results reveal that the proposed model outperforms a range of other data-driven modelidentification algorithms, particularly when applied to commonly used Lorenz time series data.

This paper introduces a novel data-driven approximation method for the Koopman operator, called the RC-HAVOK algorithm. The RC- HAVOK algorithm combines Reservoir Computing (RC) and the Hankel Alternative View of Koopman (HAVOK) to reduce the size of the linear Koopman operator with a lower error rate. The accuracy and feasibility of the RC-HAVOK algorithm are assessed on Lorenz-like systems and dynamical systems with various nonlinearities, including the quadratic and cubic nonlinearities, hyperbolic tangent function, and piece-wise linear function. Implementation results reveal that the proposed model outperforms a range of other data-driven model identification algorithms, particularly when applied to commonly used Lorenz time series data.