Machine Learning-Based Computational Analysis of Carreau Nanofluid Flow in a Stretched Cylinder Using Bayesian Regularization Scheme

The proper forecasting of nonlinear nanofluid transport behavior is necessary for the development and enhancement of advanced thermal engineering apparatus. This research offers a smart computational scheme for studying magnetohydrodynamic bioconvection Carreau-type nanofluid circulation along a nonlinear stretching cylinder while considering activation energy, Brownian motion thermophoresis Cattaneo-Christov mass and heat flux, heat sink/source, and gyrotactic microorganisms. The innovation of this paper is the proposal of a Bayesian Regularization Scheme Neural Network (BRSNN) that is capable of accurately modeling the nonlinearities of the main flow variables, at the same time, through this approach, the model's generalization ability is improved, and overfitting is minimized. Appropriate similarity transformations are applied to convert the governing partial differential equations into ordinary differential equations and the resulting numerical solution by Python solve_bvp is used to create a reference dataset. A number of 8008 data points generated from eight independent computational scenarios across the computational domain (0 ≤ η ≤ 5) are used for training, validating, and testing the proposed BRSNN. The network architecture was determined experimentally by evaluating the loss function, and the configuration yielding the minimum mean squared error (MSE) was selected. Predictions made by BRSNN show very good compatibility with numerical solutions and the values of MSE lie within the limits (5.21 × 10 -13 ) and (2.14 × 10 -10 ). The magnetism parameter is found to restrict the velocity field while the curvature parameter accelerates the fluid motion. Besides, the Prandtl number, Brownian motion thermophoresis Peclet number, and bioconvection Lewis number have a significant impact on the heat, concentration, and microorganism profiles. The BRSNN proposed successfully reproduces the nonlinear transport characteristics besides agreeing well with the published benchmark result and thereby confirming its reliability. It serves as an accurate surrogate for the non-Newtonian transport model, such that the computationally heavy nonlinear system of equations does not have to be solved again and again to make a precise prediction of the coupled flow and temperature fields. This offers a practical computation alternative to complex transport problems linked to thermal and energy systems.