Multivariate Identification via Linear Projection of Eigenvectors

Multivariate Identification via Linear Projection of Eigenvectors | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Multivariate Identification via Linear Projection of Eigenvectors Dong-Hwan Kim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8290526/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract A data-driven system identification algorithm which utilizes eigenvector is presented. The eigenvectors are extracted from an unified solution space comprising both input and output subspaces. To expand the input subspace, a higher-order subspace out of input subspaces are augmented with the measured input subspace; this higher-order subspace exhibits additional cross-correlations with both the input and output subspaces, thus producing more informative eigenvectors and linearizing the system. The extracted eigenvectors are then deployed to sequentially project new input snapshots first onto the input subspace and subsequently onto the output subspace to predict the output. The algorithm effectively reconstructs the original governing equations of a dynamic system, providing an inference that the original system is a series of data projection via eigenvectors, and also implying the possibility of reconstructing the low-rank governing equation with limited number of eigenvectors thus yielding a linearized representation of the system from the data. Notably, identifying the system from the well expanded, high-dimensional nonlinear solution space requires only a limited duration of data snapshots, indicating that the essential spatial features manifested by the governing equation are determined rapidly. Physical sciences/Mathematics and computing/Applied mathematics Physical sciences/Mathematics and computing/Computational science system identification eigenvector linear representation Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8290526","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":556191431,"identity":"53d1f70f-8c03-43f9-be5a-7fe8c9b204e8","order_by":0,"name":"Dong-Hwan Kim","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvElEQVRIiWNgGAWjYDCCMzwMzH8qbIAsxsYDRGth4DmTBtLSQIIW3pbDYDZxWvjOnD32QbLhvN3a9sNAW2psoglqkTzblzzDcMft5G1nEoFajqXlNhDSYnCex5gh8cztZLMDQC2MDYeJ1HKw7Vyy2fmHxGo522PM2Nh2wM7sBrG2SJ45l8zMcCY5wewG0JYEYvzCdyb3MDNDhZ292fn0hw8+1NgQ1gIDiWCVCcQqBwF7UhSPglEwCkbBCAMA2WFK5C73cXcAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-6904-7585","institution":"Chungnam National University","correspondingAuthor":true,"prefix":"","firstName":"Dong-Hwan","middleName":"","lastName":"Kim","suffix":""}],"badges":[],"createdAt":"2025-12-05 19:55:47","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8290526/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8290526/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99316637,"identity":"0f874901-070a-4b6a-bf09-74e9e922bc55","added_by":"auto","created_at":"2025-12-31 16:28:47","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":773241,"visible":true,"origin":"","legend":"","description":"","filename":"milpe18NATUREMI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8290526/v1_covered_afd54708-c4e5-440a-8ef1-a83914c69d3e.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Multivariate Identification via Linear Projection of Eigenvectors","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"system identification, eigenvector, linear representation","lastPublishedDoi":"10.21203/rs.3.rs-8290526/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8290526/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"A data-driven system identification algorithm which utilizes eigenvector is presented. 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