Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods
Complexity, (2018)DOI: 10.1155/2018/6920783
Abstract
This article presents a review on two methods based on dynamic mode decomposition and its multiple applications, focusing on higher order dynamic mode decomposition (which provides a purely temporal Fourier-like decomposition) and spatiotemporal Koopman decomposition (which gives a spatiotemporal Fourier-like decomposition). These methods are purely data-driven, using either numerical or experimental data, and permit reconstructing the given data and identifying the temporal growth rates and frequencies involved in the dynamics and the spatial growth rates and wavenumbers in the case of the spatiotemporal Koopman decomposition. Thus, they may be used to either identify and extrapolate the dynamics from transient behavior to permanent dynamics or construct efficient, purely data-driven reduced order models."/><meta name="citation_fulltext_html_url" content="https://www.hindawi.com/journals/complexity/2018/6920783/"/><meta name="citation_pdf_url" content="https://downloads.hindawi.com/journals/complexity/2018/6920783.pdf"/><meta name="citation_xml_url" content="https://downloads.hindawi.com/journals/complexity/2018/6920783.xml"/><meta name="dc.creator" content="Le Clainche, Soledad"/><meta name="dc.creator" content="Vega, José M."/><meta name="dc.title" content=Änalyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods"/><meta name="dc.description" content="This article presents a review on two methods based on dynamic mode decomposition and its multiple applications, focusing on higher order dynamic mode decomposition (which provides a purely temporal Fourier-like decomposition) and spatiotemporal Koopman decomposition (which gives a spatiotemporal Fourier-like decomposition). These methods are purely data-driven, using either numerical or experimental data, and permit reconstructing the given data and identifying the temporal growth rates and frequencies involved in the dynamics and the spatial growth rates and wavenumbers in the case of the spatiotemporal Koopman decomposition. Thus, they may be used to either identify and extrapolate the dynamics from transient behavior to permanent dynamics or construct efficient, purely data-driven reduced order models."/><meta name="dc.publisher" content="Hindawi"/><meta name="dc.format" content="text/html"/><meta name="dc.language" content="en"/><meta name="dc.identifier" content="https://doi.org/10.1155/2018/6920783"/><meta name="dc.type" content="Review Article"/><meta name="dc.date" content="2018/12/12"/><meta name="dcterms.issued" content="2018/12/12"/><meta name="prism.publicationDate" content="2018/12/12"/><meta name="prism.volume" content="2018"/><meta name="prism.section" content="Review Article"/><meta name="prism.doi" content="https://doi.org/10.1155/2018/6920783"/><meta name="prism.issn" content="1076-2787"/><meta name="dc.source" content="Complexity"/><meta name="prism.publicationName" content="Complexity"/><meta name=äuthors" content="Soledad Le Clainche | José M. Vega"/><meta name=Äuthor" content="Hindawi"/><meta name="robots" content="index"/><meta name="google-site-verification" content=ÄxEuDsL7vXGOxRe53-uFhOk2ODN0bbXMeuBy6Pfq4ww"/><script src="https://cdn.cookielaw.org/scripttemplates/otSDKStub.js" type="text/javascript" charset=ÜTF-8" data-domain-script="fbafd62a-0a4e-4f7b-a04d-56f57fa3d716"></script><link href="https://static-01.hindawi.com/articles/complexity/volume-2018/6920783/6920783-style.css" rel="stylesheet" class="next-head"/><link href="https://static-01.hindawi.com/next_assets/YPNMlXIdiNPfic8y2E3Ba/static/lib/basictable.css" rel="stylesheet" media="none" class="next-head"/><link rel="stylesheet" href="https://static-01.hindawi.com/next_assets/YPNMlXIdiNPfic8y2E3Ba/static/lib/owl.carousel.min.css" media="none" class="next-head"/><link rel="stylesheet" href="https://static-01.hindawi.com/next_assets/YPNMlXIdiNPfic8y2E3Ba/static/lib/owl.theme.default.min.css" media="none" class="next-head"/><script src="https://static-01.hindawi.com/next_assets/YPNMlXIdiNPfic8y2E3Ba/static/lib/jquery.js" class="next-head"></script><link rel="stylesheet" type="text/css" href="https://cdn.bibblio.org/rcm/4.18/bib-related-content.min.css" media="none" class="next-head"/><script src="https://cdn.bibblio.org/rcm/4.18/bib-related-content.min.js" class="next-head"></script><link rel="stylesheet" type="text/css" href="https://cdn.bibblio.org/rcm/4.18/bib-related-content.min.css" media="none" class="next-head