A meshless data-tailored approach to compute statistics from scattered data with adaptive radial basis functions

A meshless data-tailored approach to compute statistics from scattered data with adaptive radial basis functions | 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 A meshless data-tailored approach to compute statistics from scattered data with adaptive radial basis functions Damien Rigutto, Manuel Ratz, Miguel Alfonso Mendez This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8205230/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing formulations based on isotropic kernels often suffer from spurious oscillations in regions with sharp gradients or strong flow anisotropy. This work introduces an anisotropic, gradient-informed, and adaptively sampled extension of the constrained RBF framework for regression of scattered data. Gradient information is estimated via local polynomial regression at collocation points, smoothed, and used to (1) re-sample data, maximizing sampling density near steep gradients while downsampling in smooth regions, and (2) construct a local anisotropic metric that shapes each basis function according to the flow directionality. In addition, a gradient-informed regularization is introduced by embedding observed gradients into the least-squares system as weighted soft constraints. The resulting formulation is fully meshless, linear, and computationally efficient, while significantly improving reconstruction quality in challenging regions. The method is evaluated on both synthetic and experimental datasets, including direct numerical simulation (DNS) data of a turbulent channel and time-resolved particle tracking velocimetry of a turbulent jet. Results show that the proposed approach outperforms isotropic and gradient-free RBF formulations in accuracy, smoothness, and physical consistency---particularly near shear layers and boundaries---while reducing the number of bases by an order of magnitude. To support the application, we have created a repository ( https://github.com/mendezVKI/SPICY_VKI ) that provides access to the investigated datasets. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 08 Feb, 2026 Reviews received at journal 08 Feb, 2026 Reviews received at journal 25 Jan, 2026 Reviewers agreed at journal 02 Jan, 2026 Reviews received at journal 31 Dec, 2025 Reviewers agreed at journal 30 Dec, 2025 Reviewers agreed at journal 09 Dec, 2025 Reviewers agreed at journal 07 Dec, 2025 Reviewers invited by journal 07 Dec, 2025 Editor assigned by journal 07 Dec, 2025 Submission checks completed at journal 02 Dec, 2025 First submitted to journal 25 Nov, 2025 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-8205230","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":556670427,"identity":"c667d81b-93c9-4901-9cc1-15fe5c7d259c","order_by":0,"name":"Damien 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functions\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"experiments-in-fluids","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"exif","sideBox":"Learn more about [Experiments in Fluids](http://link.springer.com/journal/348)","snPcode":"348","submissionUrl":"https://submission.nature.com/new-submission/348/3","title":"Experiments in Fluids","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8205230/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8205230/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing formulations based on isotropic kernels often suffer from spurious oscillations in regions with sharp gradients or strong flow anisotropy. This work introduces an anisotropic, gradient-informed, and adaptively sampled extension of the constrained RBF framework for regression of scattered data. Gradient information is estimated via local polynomial regression at collocation points, smoothed, and used to (1) re-sample data, maximizing sampling density near steep gradients while downsampling in smooth regions, and (2) construct a local anisotropic metric that shapes each basis function according to the flow directionality. In addition, a gradient-informed regularization is introduced by embedding observed gradients into the least-squares system as weighted soft constraints. The resulting formulation is fully meshless, linear, and computationally efficient, while significantly improving reconstruction quality in challenging regions. The method is evaluated on both synthetic and experimental datasets, including direct numerical simulation (DNS) data of a turbulent channel and time-resolved particle tracking velocimetry of a turbulent jet. Results show that the proposed approach outperforms isotropic and gradient-free RBF formulations in accuracy, smoothness, and physical consistency---particularly near shear layers and boundaries---while reducing the number of bases by an order of magnitude. To support the application, we have created a repository (https://github.com/mendezVKI/SPICY_VKI) that provides access to the investigated datasets.","manuscriptTitle":"A meshless data-tailored approach to compute statistics from scattered data with adaptive radial basis functions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-10 05:21:29","doi":"10.21203/rs.3.rs-8205230/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-02-08T15:20:40+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-08T09:33:48+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-25T13:32:19+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"162208398511001701998867652243396517468","date":"2026-01-02T14:34:24+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-31T07:25:34+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"167142655263649280405944781692204357655","date":"2025-12-30T18:00:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"164678525486626503352500351041337319419","date":"2025-12-10T03:04:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"107728297966274966140489448192670977365","date":"2025-12-08T03:15:51+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-08T02:56:50+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-07T17:49:55+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-03T03:51:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"Experiments in Fluids","date":"2025-11-25T16:19:22+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"experiments-in-fluids","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"exif","sideBox":"Learn more about [Experiments in Fluids](http://link.springer.com/journal/348)","snPcode":"348","submissionUrl":"https://submission.nature.com/new-submission/348/3","title":"Experiments in Fluids","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"f6a4c8ba-802c-4c89-9c0e-9355a2f07ad9","owner":[],"postedDate":"December 10th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-15T14:53:19+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-10 05:21:29","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8205230","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8205230","identity":"rs-8205230","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}