Knowledge-Based Lift and Drag Coefficient Prediction of Airfoil: A Meta-Learning Structure

Knowledge-Based Lift and Drag Coefficient Prediction of Airfoil: A Meta-Learning Structure | 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 Knowledge-Based Lift and Drag Coefficient Prediction of Airfoil: A Meta-Learning Structure Hao-zhe Zhang, Yi-ming Du This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8086442/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 16 You are reading this latest preprint version Abstract Accurate and efficient prediction of lift and drag characteristics across a wide range of operating conditions is essential for airfoil aerodynamic performance evaluation and design. To address the limited accuracy of low-fidelity computational fluid dynamics (CFD) methods such as Reynolds-Averaged Navier-Stokes (RANS) in predicting nonlinear lift at high angles of attack and critical drag in transonic regimes, this study proposes a meta-learning framework incorporating physical prior knowledge for rapid prediction of lift–angle-of-attack and drag–Mach-number curves of arbitrary airfoils. The framework employs two inner-loop neural networks to model the lift and drag curve behaviors, while an outer-loop hypernetwork generates all parameters of the inner networks based on the airfoil geometry. By embedding thin-airfoil theory and the physical law of drag divergence, the model achieves enhanced physical consistency and robust predictive performance under various flow conditions. Validation results show that the proposed model attains over 97% prediction accuracy for lift and drag curves across multiple airfoils and operating conditions. Notably, in high-angle-of-attack and transonic regimes, the predictions remain stable and physically consistent, demonstrating its potential as an efficient, physics-constrained surrogate model for CFD. Combined with limited experimental data or high-fidelity CFD results such as Large Eddy Simulation (LES), this framework provides a rapid and reliable aerodynamic prediction approach for early-stage airfoil design, effectively overcoming the challenges of costly and time-consuming high-fidelity simulations. Physical sciences/Engineering Physical sciences/Mathematics and computing Knowledge-based Meta-learning Lift coefficient Drag coefficient CFD Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 12 Jan, 2026 Reviews received at journal 21 Dec, 2025 Reviews received at journal 19 Dec, 2025 Reviews received at journal 28 Nov, 2025 Reviews received at journal 28 Nov, 2025 Reviewers agreed at journal 24 Nov, 2025 Reviewers agreed at journal 21 Nov, 2025 Reviewers agreed at journal 21 Nov, 2025 Reviews received at journal 21 Nov, 2025 Reviewers agreed at journal 20 Nov, 2025 Reviewers agreed at journal 19 Nov, 2025 Reviewers invited by journal 19 Nov, 2025 Editor invited by journal 19 Nov, 2025 Editor assigned by journal 13 Nov, 2025 Submission checks completed at journal 13 Nov, 2025 First submitted to journal 11 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. 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-8086442","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":549866025,"identity":"a7d5e0f0-1ea3-4d25-8edf-f5adf3c5cdbd","order_by":0,"name":"Hao-zhe Zhang","email":"","orcid":"","institution":"Shenyang Aerospace University","correspondingAuthor":false,"prefix":"","firstName":"Hao-zhe","middleName":"","lastName":"Zhang","suffix":""},{"id":549866026,"identity":"d1985c12-d6be-4766-8d3a-08cd7d4c6db1","order_by":1,"name":"Yi-ming 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To address the limited accuracy of low-fidelity computational fluid dynamics (CFD) methods such as Reynolds-Averaged Navier-Stokes (RANS) in predicting nonlinear lift at high angles of attack and critical drag in transonic regimes, this study proposes a meta-learning framework incorporating physical prior knowledge for rapid prediction of lift\u0026ndash;angle-of-attack and drag\u0026ndash;Mach-number curves of arbitrary airfoils. The framework employs two inner-loop neural networks to model the lift and drag curve behaviors, while an outer-loop hypernetwork generates all parameters of the inner networks based on the airfoil geometry. By embedding thin-airfoil theory and the physical law of drag divergence, the model achieves enhanced physical consistency and robust predictive performance under various flow conditions. Validation results show that the proposed model attains over 97% prediction accuracy for lift and drag curves across multiple airfoils and operating conditions. 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Combined with limited experimental data or high-fidelity CFD results such as Large Eddy Simulation (LES), this framework provides a rapid and reliable aerodynamic prediction approach for early-stage airfoil design, effectively overcoming the challenges of costly and time-consuming high-fidelity simulations.\u003c/p\u003e","manuscriptTitle":"Knowledge-Based Lift and Drag Coefficient Prediction of Airfoil: A Meta-Learning Structure","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-27 17:42:14","doi":"10.21203/rs.3.rs-8086442/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-12T05:28:13+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-22T01:14:27+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-20T00:37:43+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-28T15:02:29+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-28T07:28:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"206921668600140467735746578282172716492","date":"2025-11-24T11:15:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"249653651526864456365714190353285463619","date":"2025-11-21T18:54:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"71436475377462357688789719679474469494","date":"2025-11-21T15:38:39+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-21T08:33:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"75303870134555551164503797035754540885","date":"2025-11-20T22:39:13+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"230551444355898803436818602914573555640","date":"2025-11-19T16:32:31+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-19T15:23:36+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-11-19T14:56:03+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-14T01:46:18+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-14T01:45:54+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-11-11T11:38:57+00:00","index":"","fulltext":""}],"status":"published","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}}],"origin":"","ownerIdentity":"e848b4d7-8b6b-4c04-85ba-6bdc4c09b6ce","owner":[],"postedDate":"November 27th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":58503162,"name":"Physical sciences/Engineering"},{"id":58503163,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-05-20T08:24:06+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-27 17:42:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8086442","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8086442","identity":"rs-8086442","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}