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Data-Driven Model Reduction and Transfer Operator Approximation.

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Title: Data-Driven Model Reduction and Transfer Operator Approximation.
Authors: Klus, Stefan1 stefan.klus@fu-berlin.de, Nüske, Feliks1, Koltai, Péter1, Wu, Hao1, Kevrekidis, Ioannis2,3, Schütte, Christof1,3, Noé, Frank1
Source: Journal of Nonlinear Science. Jun2018, Vol. 28 Issue 3, p985-1010. 26p.
Subjects: Dynamical systems, Transfer operators, Molecular dynamics, Independent component analysis, Eigenfunctions
Abstract: In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis, dynamic mode decomposition, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Nonlinear Science is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: <searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Transfer+operators%22">Transfer operators</searchLink><br /><searchLink fieldCode="DE" term="%22Molecular+dynamics%22">Molecular dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Independent+component+analysis%22">Independent component analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenfunctions%22">Eigenfunctions</searchLink>
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  Data: In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as <italic>time-lagged independent component analysis</italic>, <italic>dynamic mode decomposition</italic>, and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Nonlinear Science is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00332-017-9437-7
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        Text: English
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        PageCount: 26
        StartPage: 985
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        Type: general
      – SubjectFull: Transfer operators
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      – SubjectFull: Molecular dynamics
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      – SubjectFull: Independent component analysis
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      – SubjectFull: Eigenfunctions
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              Text: Jun2018
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