Machine Learning-Based Parameter Estimation and Topology Identification of Uncertain Fractional-Order Complex Networks

Machine Learning-Based Parameter Estimation and Topology Identification of Uncertain Fractional-Order Complex 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 Machine Learning-Based Parameter Estimation and Topology Identification of Uncertain Fractional-Order Complex Networks Ce Liang, Weiyuan Ma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8047665/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Fractional complex networks have significant advantages in real-world modeling, such as in biological neural networks and communication systems, due to their ability to describe the long-term memory effect and high degree of freedom of the system. However, under conditions of uncertain parameters and unknown topological structure, traditional methods struggle to accurately identify the parameters and topology jointly, which limits the practical application of such networks. To address this issue, this paper proposes a framework based on machine learning, which for the first time introduces three types of neural network models (Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Reservoir Computing (RC) into the parameter estimation and topological structure identification of fractional complex networks. By generating observed data based on the Caputo fractional derivative and the Adams-Bashforth-Moulton discretization method, and through the design of a reasonable loss function combined with the Adam optimizer, the network parameters and topological structure are iteratively solved. Numerical experiments show that LSTM, GRU, and RC all have high reliability, with RC having the best overall performance. This research provides a new method for solving inverse problems in fractional complex networks, and it remains valid for integer-order complex networks. Fractional complex network Machine learning Parameter identification Topology identification Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 10 Nov, 2025 Editor assigned by journal 08 Nov, 2025 Submission checks completed at journal 07 Nov, 2025 First submitted to journal 06 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. 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-8047665","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":542650571,"identity":"9ae2a499-1ce1-46ce-96be-9467650506c1","order_by":0,"name":"Ce Liang","email":"","orcid":"","institution":"Northwest Minzu University","correspondingAuthor":false,"prefix":"","firstName":"Ce","middleName":"","lastName":"Liang","suffix":""},{"id":542650572,"identity":"7f1a4bab-2602-4766-9d52-676d7a3d0975","order_by":1,"name":"Weiyuan Ma","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAv0lEQVRIiWNgGAWjYHACxgcJBmxybOzNB4jWwmzwoYLPmI/nWALRWtgkZ5yRS5wnkaNAnHrdGTkG0rxtZultDDkMDD8qthHWYnYjx8CYty0tt43h7AHGnjO3idByO8cgmbftWG4bY18CM2MbkVoO87b9T2dj5jEgWoth44wzbAlsbERruf+smOFDBZthGw9bwkHi/HLm8PYfwKiUl5//+OCDHxVEaGFg4DCAMw8Qox4I2B8QqXAUjIJRMApGLAAAxNo8i1yx6vgAAAAASUVORK5CYII=","orcid":"","institution":"Northwest Minzu University","correspondingAuthor":true,"prefix":"","firstName":"Weiyuan","middleName":"","lastName":"Ma","suffix":""}],"badges":[],"createdAt":"2025-11-06 11:53:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8047665/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8047665/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":97137139,"identity":"cb6b862c-f8cb-49db-8268-2452a7ebd51a","added_by":"auto","created_at":"2025-12-01 09:57:24","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1002002,"visible":true,"origin":"","legend":"","description":"","filename":"MachineLearningBasedParameterEstimationandTopologyIdentificationofUncertainFractionalOrderComplexNetworks.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8047665/v1_covered_e681bcd1-dac0-4198-a948-35d36a238da1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Machine Learning-Based Parameter Estimation and Topology Identification of Uncertain Fractional-Order Complex Networks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-applied-and-computational-mathematics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [International Journal of Applied and Computational Mathematics](https://link.springer.com/journal/40819)","snPcode":"40819","submissionUrl":"https://submission.nature.com/new-submission/40819/3","title":"International Journal of Applied and Computational Mathematics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Fractional complex network, Machine learning, Parameter identification, Topology identification","lastPublishedDoi":"10.21203/rs.3.rs-8047665/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8047665/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFractional complex networks have significant advantages in real-world modeling, such as in biological neural networks and communication systems, due to their ability to describe the long-term memory effect and high degree of freedom of the system. 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