ThoR: A Motion-Dependent Physics-Informed Deep Learning Framework with Constraint-Centric Theory of Functional Connections for Rainfall Nowcasting

ThoR: A Motion-Dependent Physics-Informed Deep Learning Framework with Constraint-Centric Theory of Functional Connections for Rainfall Nowcasting | 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 Article ThoR: A Motion-Dependent Physics-Informed Deep Learning Framework with Constraint-Centric Theory of Functional Connections for Rainfall Nowcasting Khang Ta Gia, Hoai Tran Van, An Phan Thanh, Nhat Phan Minh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6895030/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 26 Nov, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract Accurate precipitation nowcasting is crucial for mitigating the impacts of extreme weather, especially as climate change increases their frequency and severity. Traditional methods, such as numerical weather prediction and radar extrapolation, face limitations in short-term and high-resolution forecasting. Recently, while deep learning approaches have advanced nowcasting by learning spatiotemporal patterns from radar data, they often suffer from blurry results due to uncertainty predictions and limited physical consistency. To deal with these challenges, we propose ThoR, a Motion-Dependent Physics-Informed Deep Learning Framework with Constraint-Centric Theory of Functional Connections for Rainfall Nowcasting. ThoR integrates attention-centric spatio-temporal modeling with explicit physical constraints derived from partial differential equations (PDEs) for forward simulation, which employs a cascaded-branch architecture that integrates an attention-driven generator with an unsupervised, lead-time-conditioned module for motion field extraction. Physical consistency is enforced by weighted embedding the advection–diffusion equation directly into the optimization objective, establishing a Theory of Functional Connections (TFC) framework tailored for precipitation nowcasting. Extensive experiments on real-world radar datasets demonstrate that ThoR achieves promised performance compared to existing methods across both deterministic and probabilistic metrics, particularly at longer lead times and during extreme events, highlighting the potential of physics-informed deep learning for operational nowcasting. Physical sciences/Mathematics and computing/Applied mathematics Physical sciences/Mathematics and computing/Computational science Physical sciences/Mathematics and computing/Computer science Earth and environmental sciences/Climate sciences/Climate change/Projection and prediction Physical sciences/Physics/Applied physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 26 Nov, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 24 Jul, 2025 Reviews received at journal 20 Jul, 2025 Reviewers agreed at journal 14 Jul, 2025 Reviews received at journal 12 Jul, 2025 Reviewers agreed at journal 23 Jun, 2025 Reviewers invited by journal 23 Jun, 2025 Editor invited by journal 18 Jun, 2025 Editor assigned by journal 18 Jun, 2025 Submission checks completed at journal 17 Jun, 2025 First submitted to journal 14 Jun, 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-6895030","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":475326052,"identity":"89e48981-7bce-4f90-9034-146eb624349e","order_by":0,"name":"Khang Ta Gia","email":"","orcid":"","institution":"Ho Chi Minh City University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Khang","middleName":"Ta","lastName":"Gia","suffix":""},{"id":475326053,"identity":"4ec92b2f-d093-4c43-a361-5fb745820bf6","order_by":1,"name":"Hoai Tran Van","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYBACAyA+8LEByuMhVsvBmSAtbKRoYeYlSYs5e/PDw7Y77KIN7jcwPnjbxpC4nZAWy55jBodzzyTnbjjGwGw4F6hlZwMhh91IAGppOwDSwibN28ZgbHCAoJb0D4ctIVrYfxOpJcfgMCPUFmagFjnCWs6cKTjY25acO/NYYrPknHMSRGg53r75w882u9y+w4cPfnhTZsNDUAsSYGwAEhLEqx8Fo2AUjIJRgBsAANlQRYK7CSPiAAAAAElFTkSuQmCC","orcid":"","institution":"Ho Chi Minh City University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Hoai","middleName":"Tran","lastName":"Van","suffix":""},{"id":475326054,"identity":"635d98d1-27c5-4fa2-9c4a-2a25467cd199","order_by":2,"name":"An Phan Thanh","email":"","orcid":"","institution":"Ho Chi Minh City University of Technology","correspondingAuthor":false,"prefix":"","firstName":"An","middleName":"Phan","lastName":"Thanh","suffix":""},{"id":475326055,"identity":"80d63de3-b891-4ff5-a388-43e51224910d","order_by":3,"name":"Nhat Phan Minh","email":"","orcid":"","institution":"The University of Danang - University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Nhat","middleName":"Phan","lastName":"Minh","suffix":""}],"badges":[],"createdAt":"2025-06-14 16:38:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6895030/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6895030/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-26126-6","type":"published","date":"2025-11-26T15:58:42+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":97179631,"identity":"ef2aead1-ab60-43b1-bc48-07113222305c","added_by":"auto","created_at":"2025-12-01 16:16:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6551651,"visible":true,"origin":"","legend":"","description":"","filename":"THOR.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6895030/v1_covered_90ba11d0-72cb-45b8-bb97-a31dc2f94dd3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"ThoR: A Motion-Dependent Physics-Informed Deep Learning Framework with Constraint-Centric Theory of Functional Connections for Rainfall Nowcasting","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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6895030/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6895030/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Accurate precipitation nowcasting is crucial for mitigating the impacts of extreme weather, especially as climate change increases their frequency and severity. 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