Scientific Fuzzy Machine Learning

Scientific Fuzzy Machine Learning | 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Article Scientific Fuzzy Machine Learning Elyas Abbasi Jannatabadi, Masoud Goharimanesh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6723937/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 11 You are reading this latest preprint version Abstract The prosperity of physics-informed neural networks (PINNS) in solving partial differential equations (PDEs) is steadily improving due to their effective interactions with the physics behind different PDEs. While previous investigations in PINNS have mainly tackled improving loss functions during the training process, the use of different optimization schemes for solving PDEs has been overlooked. This study introduces a novel physics-informed optimization method using an adaptive neural-fuzzy inference system (ANFIS) that integrates reasoning and learning. The pattern Search algorithm is exploited to propagate solutions properly from initial- boundary points to the interior collocation points and balance the interplay between losses derived from these points. In particular, PDE parameters are first mapped into fuzzy membership functions (MFs). Then Pattern Search method steers the ANFIS model to converge properly by tuning the MFs. The proposed method improved convergence speed and prevented the algorithm from getting stuck in poor local minima. Comprehensive experimental results for different partial differential equations confirm the effectiveness of the proposed method. To our knowledge, this is the first time that a PDE has been tackled by employing the scientific fuzzy machine learning. Partial differential equations Fuzzy inference system Physics-informed machine learning ANFIS Optimization Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 01 Jul, 2025 Reviews received at journal 30 Jun, 2025 Reviews received at journal 29 Jun, 2025 Reviews received at journal 12 Jun, 2025 Reviewers agreed at journal 03 Jun, 2025 Reviewers agreed at journal 29 May, 2025 Reviewers agreed at journal 29 May, 2025 Reviewers invited by journal 29 May, 2025 Editor assigned by journal 22 May, 2025 Submission checks completed at journal 22 May, 2025 First submitted to journal 22 May, 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. We do this by developing innovative software and high quality services for the global research community. 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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-6723937","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":463864121,"identity":"8d6e957d-cce4-476b-a7ee-f3b5dee52365","order_by":0,"name":"Elyas Abbasi Jannatabadi","email":"","orcid":"","institution":"University of Torbat Heydarieh","correspondingAuthor":false,"prefix":"","firstName":"Elyas","middleName":"Abbasi","lastName":"Jannatabadi","suffix":""},{"id":463864124,"identity":"3eabf2d8-a00a-475a-a620-b3e64bb5aa94","order_by":1,"name":"Masoud Goharimanesh","email":"data:image/png;base64,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","orcid":"","institution":"University of Torbat Heydarieh","correspondingAuthor":true,"prefix":"","firstName":"Masoud","middleName":"","lastName":"Goharimanesh","suffix":""}],"badges":[],"createdAt":"2025-05-22 10:23:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6723937/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6723937/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83743121,"identity":"1979ab72-a184-4db6-8e56-36d1ec610dc2","added_by":"auto","created_at":"2025-06-02 02:11:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1226650,"visible":true,"origin":"","legend":"","description":"","filename":"Scientificfuzzymachinelearning.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6723937/v1_covered_6460b85d-6b2c-4c93-aaf6-0ae187ad293d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Scientific Fuzzy Machine Learning","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":"engineering-with-computers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ewco","sideBox":"Learn more about [Engineering with Computers](http://link.springer.com/journal/366)","snPcode":"366","submissionUrl":"https://submission.nature.com/new-submission/366/3","title":"Engineering with Computers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Partial differential equations, Fuzzy inference system, Physics-informed machine learning, ANFIS, Optimization","lastPublishedDoi":"10.21203/rs.3.rs-6723937/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6723937/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe prosperity of physics-informed neural networks (PINNS) in solving partial differential equations (PDEs) is steadily improving due to their effective interactions with the physics behind different PDEs. 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