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, cilt.34, sa.8, ss.831431-8314318, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 8
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1063/5.0207907
  • Dergi Adı: CHAOS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Computer & Applied Sciences, EMBASE, INSPEC, MEDLINE, zbMATH, DIALNET
  • Sayfa Sayıları: ss.831431-8314318
  • Erciyes Üniversitesi Adresli: Evet

Özet

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.