Hybrid Neural Computing Frameworks for Nonlinear and Time-Dependent Diffusive Flow Solutions.

Hybrid Neural Computing Frameworks for Nonlinear and Time-Dependent Diffusive Flow Solutions. | 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 Hybrid Neural Computing Frameworks for Nonlinear and Time-Dependent Diffusive Flow Solutions. Saira Sultan, Shahzad Ahmad, Aamir Rizwan, Muhammad Farman This is a preprint; it has not been peer reviewed by a journal.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-7180665/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 present paper proposes a hybrid neural computing framework (LMBNNs) which has combined artificial neural networks with Levenberg-Marquardt back-propagation by applying supervised learning to resolve nonlinear, time-dependent diffusion flows presented by Burgers equation. The framework overcomes difficulties in simulation of complex fluid dynamics in which conventional techniques fail due to the presence of shock phenomena, bifurcation effects and inability to implement effective numerical approaches. Our physics-informed design embeds conservation laws directly into the learning process while adaptive optimization methods automatically adjust to solution characteristics, ensuring both accuracy and stability .The approach proves to be superior to traditional methods in terms of better predictability of flow transition and major improvements in computational performance in different regimes of viscosity. LMBNNs through rigorous validation demonstrate strong handling of time-dependent solutions and accurate identification of bifurcation point becoming key elements of taking into account interfacial dynamics in both the standard neural networks and numerical methods. This is possible due to the dynamic regularization that ensures the stability of the solution in addition to accommodation of industrial-scale problems that may vary in viscosity due to the scalability of the framework. Important innovations are an intelligent damping mechanism of ill-conditioned systems and a novel method of shock-front localization. Among current applications span microfluidics, multiphase flows, and other engineering systems where precise simulation of the nonlinear transport phenomenon is applicable. LMBNNs create a new paradigm for resolving complex PDEs that combines the pattern recognition strengths of machine learning with the precision of numerical analysis, offering transformative potential for both scientific computing and industrial applications. The generalization ability of the framework is validated with the help of extensive stability analysis which proves it to be a powerful instrument that can open the way to new possibilities of computational fluid dynamics and related academic disciplines. Burger equation– Levenberg-Marquardt algorithm combination Supervised Learning Neural Network Fitting tool MATLAB Differential equations Mathematica Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 26 Jul, 2025 Reviewers invited by journal 24 Jul, 2025 Editor assigned by journal 22 Jul, 2025 Submission checks completed at journal 22 Jul, 2025 First submitted to journal 21 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. 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-7180665","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":491598346,"identity":"0d9414cc-ecd1-466e-87e5-0e8e55ec5109","order_by":0,"name":"Saira Sultan","email":"","orcid":"","institution":"Department of Mathematics, University of Management and Technology Lahore. 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