Yılmaz Bingöl G, Soysal O A, Günay E
Department of Electrical and Electronics Engineering, Erciyes University, Kayseri 38039, Türkiye.
Chaos. 2024 Aug 1;34(8). doi: 10.1063/5.0207907.
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.
本文介绍了一种用于柯普曼算子的新型数据驱动近似方法，称为RC - HAVOK算法。RC - HAVOK算法结合了储层计算（RC）和柯普曼的汉克尔替代视图（HAVOK），以降低线性柯普曼算子的规模并降低错误率。在类洛伦兹系统和具有各种非线性的动力系统上评估了RC - HAVOK算法的准确性和可行性，这些非线性包括二次和三次非线性、双曲正切函数以及分段线性函数。实现结果表明，所提出的模型优于一系列其他数据驱动的模型识别算法，特别是在应用于常用的洛伦兹时间序列数据时。
