LAUSR

This study examines the two-dimensional flow of a Carreau nanofluid over a thin stretching surface, incorporating melting heat effects and considering both thermal and concentration stratification under an inclined magnetic field and multiple slip conditions. Milk is used as the base fluid, with magnesium oxide nanoparticles added to enhance thermal properties and support biomedical cooling and drug delivery applications. The governing momentum, temperature, and concentration equations are transformed into a nonlinear ordinary differential equations system using local similarity variables. These equations are initially solved using the three-stage Lobatto IIIa implicit Runge–Kutta method to generate a reference dataset. Subsequently, a data-driven modeling approach is employed, utilizing an artificial neural network trained with a backpropagation algorithm and Bayesian regularization to ensure solution accuracy and stability. To evaluate the robustness of the network, Gaussian noise of varying intensity is added exclusively to the test data, while the model is trained on clean reference data. The performance is then assessed on both noise-free and noisy test inputs using relative error based on the Euclidean norm. Furthermore, six regression models, linear, ridge, and lasso (linear models), along with decision tree, support vector regression, and Gaussian process regression (nonlinear models), are employed to estimate key engineering parameters, including the Nusselt number, the Sherwood number, and the skin friction coefficient. These predictions are quantitatively verified using the correlation matrices, mean squared error, and coefficient of determination, comprehensively assessing each model's accuracy. This study integrates regression-based techniques with data-driven neural networks to derive heat and mass transfer solutions in stratified nanofluid flow. The proposed methodology offers a robust framework for analyzing nonlinear thermal systems with uncertainties, with promising applications in biomedical and industrial domains.