Physics-Informed Neural Networks for Flood Modelling: Review and Canonical Test-Cases

Physics-Informed Neural Networks for Flood Modelling: Review and Canonical Test-Cases | 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 Systematic Review Physics-Informed Neural Networks for Flood Modelling: Review and Canonical Test-Cases Harry Pearson, Etienne Yntema, Vassilis Glenis, Manuel Herrera This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9655056/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 Flood hazard is intensifying globally due to climate change, pervasive land-use alterations, and ageing infrastructure, demanding modelling frameworks that are both physically consistent and computationally tractable. Flood modelling has traditionally relied on one of the two: Numerical solvers (model-driven) and data-driven approaches acting as surrogates for prediction and emulation. Each paradigm presents structural strengths and limitations. Numerical solvers ensure mechanistic consistency but can be computationally intensive and sensitive to parameter uncertainty, whereas purely data-driven models enable rapid prediction but often struggle with extrapolation and physical interpretability. Physics-informed neural networks (PINNs) aim to take the best of the two worlds, as they have been proposed as a hybrid approach that embeds governing equations directly within neural network training. This paper provides a structured review of the theoretical foundations, methodological developments, and emerging applications of PINNs in flood modelling, positioning them relative to established model-driven and data-driven approaches. To reinforce the synthesis, three canonical process-oriented test cases are examined under controlled conditions, illustrating PINN behaviour in rainfall-driven flow, flow–topography interaction, and boundary-driven wetting dynamics. The analysis identifies key methodological challenges including training stability for hyperbolic systems, boundary condition enforcement, scalability to high-resolution domains, and uncertainty quantification. PINNs represent a potentially valuable intermediate modelling strategy, but remain limited in large-scale forward flood simulation. PINNs have shown to be particularly useful for inverse problems and data-scarce or partially observed systems. Their large-scale operational deployment remains limited by unresolved issues in training stability, scalability, and boundary condition enforcement. Hydrology Artificial Intelligence and Machine Learning Civil Engineering Flood modelling Physics-informed AI Shallow water equations Hydroinformatics 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-9655056","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Systematic Review","associatedPublications":[],"authors":[{"id":636937447,"identity":"6d00323b-9cea-47a1-b7a8-25d97993648b","order_by":0,"name":"Harry Pearson","email":"","orcid":"","institution":"Newcastle University","correspondingAuthor":false,"prefix":"","firstName":"Harry","middleName":"","lastName":"Pearson","suffix":""},{"id":636937448,"identity":"f6536877-973f-4bb1-9c27-c4ff824a6ebc","order_by":1,"name":"Etienne Yntema","email":"","orcid":"","institution":"Newcastle University","correspondingAuthor":false,"prefix":"","firstName":"Etienne","middleName":"","lastName":"Yntema","suffix":""},{"id":636937449,"identity":"6c57b4d1-98ee-4abd-b9f0-c123f98cc0fe","order_by":2,"name":"Vassilis Glenis","email":"","orcid":"https://orcid.org/0000-0001-6037-9508","institution":"Newcastle University","correspondingAuthor":false,"prefix":"","firstName":"Vassilis","middleName":"","lastName":"Glenis","suffix":""},{"id":636937450,"identity":"0ccd7feb-188f-4632-a6af-4d94853955b3","order_by":3,"name":"Manuel Herrera","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABLElEQVRIie2RMWuDQBiGvyBclgPXE6H9BYULgrRU+ls8BLscUsiSoVCzpEtIV4f+CP9BLILTpa4Wh0YCmRySpSiUUgO2i6bt2OGe5fv44OF9jwOQSP4tN2C3m/V1Om9ndESh34rbTpv8WYl/V87uVwnZUfBUfVVsJreppxKn2NcVOYFhvFaw6Cim8FwtoDDWFtfGSCT5WAtcQ8c2MQC7VMFZV4m4qWMKLBQIaT7KWZhz0JtizAcOCt51lbQ09fdGWQo0rP2PZ7bMuVJXNrnz1bJfyZoUOKRghAbTWcRCnSPSFLOBHFJ6imWlcTGnhAUCKdp04bDgdWteYpeMZmRLnx57np/yUVZNLPYwR4O9/3bVLPHmpbKsU1V1inWZdJQW0nNDcPwjJRKJRPIzn858ZrZ9aqJrAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-9662-0017","institution":"Newcastle University","correspondingAuthor":true,"prefix":"","firstName":"Manuel","middleName":"","lastName":"Herrera","suffix":""}],"badges":[],"createdAt":"2026-05-08 13:58:01","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-9655056/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9655056/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108933441,"identity":"77ee3e4d-8fb3-4108-86a9-1d5523728787","added_by":"auto","created_at":"2026-05-11 03:07:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2566719,"visible":true,"origin":"","legend":"","description":"","filename":"LiteraturereviewPINNsFlooding.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9655056/v1_covered_bcfce372-f2cc-486e-9927-1091de74b1c4.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003ePhysics-Informed Neural Networks for Flood Modelling: Review and Canonical Test-Cases\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Newcastle 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":"Flood modelling, Physics-informed AI, Shallow water equations, Hydroinformatics","lastPublishedDoi":"10.21203/rs.3.rs-9655056/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9655056/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFlood hazard is intensifying globally due to climate change, pervasive land-use alterations, and ageing infrastructure, demanding modelling frameworks that are both physically consistent and computationally tractable. 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