An active-subspace-enhanced support vector regression model for high-dimensional uncertainty quantification

An active-subspace-enhanced support vector regression model for high-dimensional uncertainty quantification | 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 Research Article An active-subspace-enhanced support vector regression model for high-dimensional uncertainty quantification Yicheng Zhou, Xiangrui Gong, Xiaobo Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4211895/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 The computational costs of surrogate model-assisted uncertainty quantification methods become intractable for high dimensional problems. However, many high-dimensional problems are intrinsically low dimensional, if the output response exhibits some special structure that can be exploited within a low-dimensional subspace, known as the active subspace in the literature. Active subspace extracts linear combinations of all the original inputs, which may obscure the fact that only several inputs are active in the low-dimensional space. Motivated by this fact, this paper proposes a new surrogate modeling method which imposes sparsity in the active subspace to achieve a better performance for dimension reduction. Information given by sparse active subspace is integrated in the kernel structure of the support vector regression model to ensure superior performance for high dimensional problems. We demonstrate the proposed method on several benchmark applications, comprising an analytical function and two engineering applications of increasing dimensionality and complexity. active subspace support vector regression uncertainty quantification Full Text Additional Declarations No competing interests reported. Supplementary Files Highlight.docx 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-4211895","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":288270115,"identity":"06f72f5b-0569-43fb-be30-7f5c73cd3117","order_by":0,"name":"Yicheng Zhou","email":"data:image/png;base64,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","orcid":"","institution":"National Key Laboratory of Land \u0026 Air Based Information Perception and Control","correspondingAuthor":true,"prefix":"","firstName":"Yicheng","middleName":"","lastName":"Zhou","suffix":""},{"id":288270116,"identity":"e5e2fbb5-789a-486a-94b5-907f7c7da875","order_by":1,"name":"Xiangrui Gong","email":"","orcid":"","institution":"Xi’an Modern Control Technology Research Institute","correspondingAuthor":false,"prefix":"","firstName":"Xiangrui","middleName":"","lastName":"Gong","suffix":""},{"id":288270117,"identity":"b4fd9bd2-8d7b-4f4c-9c98-02b77a886c3b","order_by":2,"name":"Xiaobo Zhang","email":"","orcid":"","institution":"Hefei University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Xiaobo","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2024-04-03 10:13:40","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4211895/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4211895/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":56450225,"identity":"54ca2efb-b65a-4a6e-81e1-9ad1a0305dd7","added_by":"auto","created_at":"2024-05-14 10:25:58","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1407769,"visible":true,"origin":"","legend":"","description":"","filename":"Anactivesubspaceenhancedsupportvectorregressionmodelforhighdimensionaluncertaintyquantification.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4211895/v1_covered_17ee9615-62d9-4969-813c-6465b9865908.pdf"},{"id":54286022,"identity":"a5829a27-9885-4c3f-b134-6f2f66efb268","added_by":"auto","created_at":"2024-04-08 10:18:59","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":11997,"visible":true,"origin":"","legend":"","description":"","filename":"Highlight.docx","url":"https://assets-eu.researchsquare.com/files/rs-4211895/v1/5bfaca79f507fe0306ef18f9.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"An active-subspace-enhanced support vector regression model for high-dimensional uncertainty quantification","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"active subspace, support vector regression, uncertainty quantification","lastPublishedDoi":"10.21203/rs.3.rs-4211895/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4211895/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe computational costs of surrogate model-assisted uncertainty quantification methods become intractable for high dimensional problems. 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