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

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.