{"title":"Model reduction of dynamical systems with a novel data-driven approach: The RC-HAVOK algorithm.","authors":"G Yılmaz Bingöl, O A Soysal, E Günay","doi":"10.1063/5.0207907","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0207907","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
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 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.
期刊介绍:
Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.