Resolution-Invariant Fluid Dynamics Modeling: Fourier Neural Operators vs. Convolutional Networks

Resolution-Invariant Fluid Dynamics Modeling: Fourier Neural Operators vs. Convolutional 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 Method Article Resolution-Invariant Fluid Dynamics Modeling: Fourier Neural Operators vs. Convolutional Networks Amitoj Singh Miglani, Mayank Goswami This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8218223/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 Modeling the dynamics of fluid flow from data has become an important problem in computational physics and data-driven PDE learning, especially as high-resolution simulations remain computationally expensive. Recent operator-learning approaches, such as Fourier Neural Operators (FNOs) \cite{li2020fno}, promise resolution-independent learning of PDE solution maps, but their practical advantages over traditional deep learning models are still not fully understood. In this work, we study the ability of FNOs to learn Navier–Stokes dynamics under changes in spatial resolution and directly compare their behavior to standard convolutional neural networks (CNNs) \cite{guo2016cnnfluid,fukami2019superres}. While CNNs learn local, grid-dependent filters, FNOs operate in Fourier space and are designed to approximate solution operators independent of discretization as Fourier transform is itself resolution invariant. We train both models on a single resolution of a high-fidelity Navier–Stokes dataset and evaluate their performance across coarser and finer grids without retraining. Our experiments show that FNOs retain stable accuracy across resolutions, whereas CNNs exhibit significant degradation once the test grid deviates from the training grid. We further evaluate both models on in-distribution and out-of-distribution initial conditions to probe whether FNOs truly capture the underlying fluid physics rather than memorizing a distribution of initial states. To our knowledge, no thorough comparative study between CNNs and FNOs has been conducted in this setting; this work provides a detailed examination of their relative strengths and limitations for data-driven fluid dynamics and climate modeling. Computational Physics Artificial Intelligence and Machine Learning Computational Fluid Dynamics AI 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-8218223","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":551520492,"identity":"824834b8-a38c-44e8-bc95-94956c687805","order_by":0,"name":"Amitoj Singh Miglani","email":"","orcid":"","institution":"Indian institute of technology Roorkee","correspondingAuthor":false,"prefix":"","firstName":"Amitoj","middleName":"Singh","lastName":"Miglani","suffix":""},{"id":551523179,"identity":"a9b16f41-3c8e-4edf-a53e-c288531e307f","order_by":1,"name":"Mayank Goswami","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0001-8829-9980","institution":"Indian institute of technology Roorkee","correspondingAuthor":true,"prefix":"","firstName":"Mayank","middleName":"","lastName":"Goswami","suffix":""}],"badges":[],"createdAt":"2025-11-27 05:51:27","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8218223/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8218223/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":97137093,"identity":"4ebc589e-d942-4883-83de-591226c736a2","added_by":"auto","created_at":"2025-12-01 09:57:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":519376,"visible":true,"origin":"","legend":"","description":"","filename":"ResolutionInvariantFluidDynamicsModelingFourierNeuralOperatorsvsConvolutionalNetworks.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8218223/v1_covered_9f92e4a5-a753-44dc-aff4-1f5a49e4b08b.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eResolution-Invariant Fluid Dynamics Modeling: Fourier Neural Operators vs. Convolutional Networks\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Indian Institute of Technology Roorkee","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":"Computational Fluid Dynamics , AI","lastPublishedDoi":"10.21203/rs.3.rs-8218223/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8218223/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eModeling the dynamics of fluid flow from data has become an important problem in computational physics and data-driven PDE learning, especially as high-resolution simulations remain computationally expensive. Recent operator-learning approaches, such as Fourier Neural Operators (FNOs) \\cite{li2020fno}, promise resolution-independent learning of PDE solution maps, but their practical advantages over traditional deep learning models are still not fully understood. In this work, we study the ability of FNOs to learn Navier–Stokes dynamics under changes in spatial resolution and directly compare their behavior to standard convolutional neural networks (CNNs) \\cite{guo2016cnnfluid,fukami2019superres}. While CNNs learn local, grid-dependent filters, FNOs operate in Fourier space and are designed to approximate solution operators independent of discretization as Fourier transform is itself resolution invariant. We train both models on a single resolution of a high-fidelity Navier–Stokes dataset and evaluate their performance across coarser and finer grids without retraining. 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