A Computational Analysis Employing Levenberg-Marquardt Back propagation for Nonlinear Thin Film Flow Model

A Computational Analysis Employing Levenberg-Marquardt Back propagation for Nonlinear Thin Film Flow Model | 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 A Computational Analysis Employing Levenberg-Marquardt Back propagation for Nonlinear Thin Film Flow Model Saira Sultan, Shahzad Ahmed, Aamir Rizwan, Muhammad Farman This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7121768/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract The proposed model’s computational efficacy is validated on real-world industrial datasets, showcasing its potential for real-time simulations in coating technologies, microfluidic devices, and precision lubrication systems. Key innovations include dynamic learning rate adaptation, automated hyper parameter tuning, and noise-robust training, making LMBNNs a breakthrough tool for nonlinear fluid modeling.LMBNNs establish a new benchmark for data-driven fluid dynamics solvers, integrating deep learning adaptability with mathematical optimization rigor. Future applications may extend to multi-phase flows, biomedical fluidics, and AI-enhanced computational fluid dynamics. This work covers the way for next-generation neural computing in engineering sciences. LMBNNs create a new standard for data-driven fluid dynamics techniques, integrating deep learning flexibility with mathematical optimization precision. The framework has strong generalization across hydrodynamic regimes creating a new paradigm in the solution of nonlinear PDEs with extension to multiphase and microfluidics, which is confirmed by extensive analysis of stability and bifurcation analysis. The performance of the proposed computing method LMBNNs is evaluated using absolute deviation, mean square error, learning curves, and histogram analysis and regression metrics to introduce an approach for validation, testing and training of the scheme. Levenberg-Marquardt back propagation nonlinear thin film flow supervised learning. nftools convergence numerical computation machine learning supervised neural networks High-Performance Computing Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 18 Jul, 2025 Reviewers invited by journal 16 Jul, 2025 Editor assigned by journal 15 Jul, 2025 Submission checks completed at journal 15 Jul, 2025 First submitted to journal 14 Jul, 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. 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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-7121768","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":487621421,"identity":"f6b0ad32-e173-4b8f-b897-19a5d8f67ed9","order_by":0,"name":"Saira Sultan","email":"data:image/png;base64,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","orcid":"","institution":"University of Management and Technology Lahore. 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