A Deep Learning Method for Non-Uniform Flow Field Based on KAN and MLP Neural Networks

A Deep Learning Method for Non-Uniform Flow Field Based on KAN and MLP Neural Networks | 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 Deep Learning Method for Non-Uniform Flow Field Based on KAN and MLP Neural Networks YuanGao, XinWang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5809608/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 Fluid-solid interaction(FSI) has always been a hot topic in the field of fluid mechanics. Because the flow field of FSI is highly inhomogeneous, when the initial conditions change with time, the inhomogeneity of the flow field in time and space will be further aggravated. The forward and inverse solutions of physical information neural networks (PINNs) in fluid mechanics have been widely studied and significant progress has been made. The technology of learning and reconstructing the flow field with PINNs is relatively mature. However, there are still large errors in predicting the flow field with uneven temporal and spatial distribution. Neural networks(NN) cannot capture some local details in learning. In addition, the generalization characteristics of NNs will also weaken the learning of local highlight areas. Therefore, inspired by the confidence weight, this paper proposes a local reinforcement learning (LRL) method to solve the above problems. It is found that LRL has a good effect on local learning. Based on the LRL method, the applicability of three different NN frameworks in the reconstruction of FSI flow fields is tested, namely, multilayer perceptron(MLP), KAN and KAN + MLP. For the MLP framework, the details of the inhomogeneous flow field can be learned more accurately. For the KAN framework, by setting different depths and widths for NN, it is found that the prediction accuracy of KAN does not depend on the scale of NN, but has specific settings for specific problems. However, when applying the LRL method, the prediction effect of KAN is not particularly ideal, so the KAN + MLP framework is proposed as an improved method. The prediction effect is relatively ideal, but it takes a lot of time to train. In this study, the performance of the new framework KAN in inhomogeneous flow field is tested, which provides ideas and basis for further research on its application scope and practical effect in fluid mechanics. PINNs KAN MLP deep learning fluid-structure interaction Full Text Additional Declarations The authors declare no competing interests. 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-5809608","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":400843631,"identity":"be717ed1-ac79-424e-9eb3-410bf9d0054a","order_by":0,"name":"YuanGao","email":"data:image/png;base64,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","orcid":"","institution":"TsingHua University","correspondingAuthor":true,"prefix":"","firstName":"","middleName":"","lastName":"YuanGao","suffix":""},{"id":400843632,"identity":"f7a836d0-81ce-4ac4-9be4-308738556f0e","order_by":1,"name":"XinWang","email":"","orcid":"","institution":"Peking University","correspondingAuthor":false,"prefix":"","firstName":"","middleName":"","lastName":"XinWang","suffix":""}],"badges":[],"createdAt":"2025-01-11 13:17:44","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-5809608/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5809608/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":73723121,"identity":"6fa77d26-149c-4e80-8bb2-8bd7b135f459","added_by":"auto","created_at":"2025-01-14 03:15:41","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1233887,"visible":true,"origin":"","legend":"","description":"","filename":"Submission.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5809608/v1_covered_d96b2c75-4ad1-48c5-adb2-4b2fb18baf44.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eA Deep Learning Method for Non-Uniform Flow Field Based on KAN and MLP Neural Networks\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Tsinghua University","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":"PINNs, KAN, MLP, deep learning, fluid-structure interaction","lastPublishedDoi":"10.21203/rs.3.rs-5809608/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5809608/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFluid-solid interaction(FSI) has always been a hot topic in the field of fluid mechanics. Because the flow field of FSI is highly inhomogeneous, when the initial conditions change with time, the inhomogeneity of the flow field in time and space will be further aggravated. The forward and inverse solutions of physical information neural networks (PINNs) in fluid mechanics have been widely studied and significant progress has been made. The technology of learning and reconstructing the flow field with PINNs is relatively mature. However, there are still large errors in predicting the flow field with uneven temporal and spatial distribution. Neural networks(NN) cannot capture some local details in learning. In addition, the generalization characteristics of NNs will also weaken the learning of local highlight areas. Therefore, inspired by the confidence weight, this paper proposes a local reinforcement learning (LRL) method to solve the above problems. It is found that LRL has a good effect on local learning. Based on the LRL method, the applicability of three different NN frameworks in the reconstruction of FSI flow fields is tested, namely, multilayer perceptron(MLP), KAN and KAN\u0026thinsp;+\u0026thinsp;MLP. For the MLP framework, the details of the inhomogeneous flow field can be learned more accurately. For the KAN framework, by setting different depths and widths for NN, it is found that the prediction accuracy of KAN does not depend on the scale of NN, but has specific settings for specific problems. However, when applying the LRL method, the prediction effect of KAN is not particularly ideal, so the KAN\u0026thinsp;+\u0026thinsp;MLP framework is proposed as an improved method. The prediction effect is relatively ideal, but it takes a lot of time to train. In this study, the performance of the new framework KAN in inhomogeneous flow field is tested, which provides ideas and basis for further research on its application scope and practical effect in fluid mechanics.\u003c/p\u003e","manuscriptTitle":"A Deep Learning Method for Non-Uniform Flow Field Based on KAN and MLP Neural Networks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-14 02:51:35","doi":"10.21203/rs.3.rs-5809608/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"571b5148-388b-44da-a27e-05aadc1c29e6","owner":[],"postedDate":"January 14th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-01-14T02:51:35+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-14 02:51:35","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5809608","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5809608","identity":"rs-5809608","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}