Deep learning-based prediction of boger hybrid nanofluid flow over the nonlinear porostretching cylinder with sensitivity optimization

This work presents a novel artificial neural network (ANN) methodology combining nonlinear autoregressive with exogenous inputs (NARX) and the backpropagation Levenberg-marquardt technique (LMT) for predicting irregular heat source behavior in boger hybrid nanofluid flow systems. The study examines a two-dimensional axisymmetric incompressible boger hybrid (AA7072+AA7075/SA) nanofluid flow model (BHNFM) over a nonlinear stretched porous cylinder with radius R: Radius of cyclinder under Variable thermal conductivity (ε) conditions. Additionally, the effects of porous media effects, magnetic field, Nr: thermal radiation, and convective boundary are considered in this investigation. The foundational mathematical structure comprises partial differential equations (PDEs) converted to ordinary differential equations (ODEs) via similarity transformation, with synthetic data generated through the bvp4c numerical method. K-fold cross-validation is used to accurately evaluate the ANN model, which shows excellent generalization and accuracy. Model validation across eight scenarios with three cases each demonstrates NARX-LMT predictions consistently align with numerical observations such as correlation coefficient R² ≈ 1, mean absolute error (MAE) (10⁻⁵ to 10⁻⁶), and mean squared error (MSE) between 10^-8 to 10^-11. Performance evaluation includes iterative convergence curves, optimization control metrics, error autocorrelation, error histograms, regression outputs, and correlation analysis. Rapid computational performance is demonstrated through convergence in 39-261 epochs with 2-3 seconds of training time, enabling real-time industrial applications. Quantitative sensitivity analysis using response surface methodology (RSM) reveals that relaxation time parameter and thermal conductivity are most influential for drag force and heat transfer rate, respectively, providing explicit design guidelines for industrial optimization. Sensitivity analysis reveals that thermal conductivity and porosity are critical factors in determining system efficiency, specifically in terms of heat transfer rate and drag force. The methodology delivers substantial practical impact, including 30-40% reduction in design optimization costs, 15-26% improvement in enhanced oil recovery (EOR) efficiency, 20-40% drag reduction in pipeline transport, and real-time process control capability for drilling operations. This work establishes a validated computational framework immediately deployable for drilling fluid design, EOR process optimization, and thermal management in oil and gas operations, representing a significant advancement in AI-powered fluid dynamics prediction.