{"paper_id":"3ead6538-7039-4d4e-90e1-6a175607713f","body_text":"Multi-Frequency Graph Neural Rough Differential Equations for Traffic Forecasting | 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 Multi-Frequency Graph Neural Rough Differential Equations for Traffic Forecasting Zengqiang Wang, Di Zang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3972614/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 burgeoning field of neural differential equations (NDEs) underscores a quest for models that not only boast interpretability and robustness but also function within a more generalized framework. Although the fusion of Neural Controlled Differential Equations (NCDEs) with Graph Neural Networks (GNNs) has marked significant strides in traffic forecasting, the prolonged integrative process requisite for long-term forecasts remains a detriment to model efficacy. Furthermore, while NCDEs exhibit prowess in extracting temporal trends within traffic fluctuations, the potential of spatial trend correlations has not been adequately investigated. To bridge this gap, we introduce the Multi-Frequency Graph Neural Rough Differential Equation (MFG-NRDE), an NDE-based model tailored for traffic forecasting. Our model is underpinned by the frequency principle in neural networks and leverages both wavelet and signature transforms. This dual approach not only truncates the integral length but also captures a more nuanced representation of high- and low-frequency temporal features. Complementing this temporal focus, we integrate a novel methodology for dynamically computing spatial correlations, harnessing the inherent trend characteristics of traffic variations to enhance spatial dimension analysis. Empirical validation across four real-world traffic flow datasets demonstrates the superior performance of our MFG-NRDE model, positioning it favorably against contemporary state-of-the-art baselines. This underscores the efficacy of our model in managing the intricate dynamics of traffic data forecasting, paving the way for more sophisticated and accurate predictive models in this domain. Neural rough differential equations traffic forecasting frequency principle graph neural networks Full Text Additional Declarations No competing interests reported. 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-3972614\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":274069495,\"identity\":\"39a7cb6d-4819-4125-ad3f-38392698d7b6\",\"order_by\":0,\"name\":\"Zengqiang Wang\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Tongji University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Zengqiang\",\"middleName\":\"\",\"lastName\":\"Wang\",\"suffix\":\"\"},{\"id\":274069496,\"identity\":\"21847ffc-6cd1-42d1-8e94-df055e376ecf\",\"order_by\":1,\"name\":\"Di Zang\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIiWNgGAWjYLACHgMbMG2QwMDA2ECkljQJUrUwHJaAsQlrkW8/e/jFm4LzdfzS7RcKHjDYyG44wPzsAT4tjD15aZZzDG5LSM45UwB0WJrxhgNs5gb4tDAz5JgZ8wC1GNzISQBqOZy44QAPmwQ+LWz8b0BazsG0/CeshUcix/gxj8EBoJb0A0AtBwhrkZB4Y8Y4xyBZcuaMHGAgGyQbzzzMZoZXi3x/jvGHN3/s+Pkl0p8Z/qiwk+073vwMrxaQd6AKeMwMGEBBxUxAPUjJBwjN/vgBYcWjYBSMglEwEgEACBxF9DLCohYAAAAASUVORK5CYII=\",\"orcid\":\"\",\"institution\":\"Tongji University\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Di\",\"middleName\":\"\",\"lastName\":\"Zang\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2024-02-20 11:14:14\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-3972614/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-3972614/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":52503407,\"identity\":\"5f119380-fd1d-466d-a6f4-232edc0a577c\",\"added_by\":\"auto\",\"created_at\":\"2024-03-12 10:11:44\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1585383,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"NRDE.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-3972614/v1_covered_72b93e5d-a78a-4339-9de0-8f703fec3bce.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Multi-Frequency Graph Neural Rough Differential Equations for Traffic Forecasting\",\"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\":\"info@researchsquare.com\",\"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\":\"Neural rough differential equations, traffic forecasting, frequency principle, graph neural networks\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-3972614/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-3972614/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"The burgeoning field of neural differential equations (NDEs) underscores a quest for models that not only boast interpretability and robustness but also function within a more generalized framework. 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