In the present work, a simple intelligence-based computation of artificial neural networks with the Levenberg-Marquardt backpropagation algorithm is developed to analyze the new ferromagnetic hybrid nanofluid flow model in the presence of a magnetic dipole within the context of flow over a stretching sheet. A combination of cobalt and iron (III) oxide (Co-Fe2O3) is strategically selected as ferromagnetic hybrid nanoparticles within the base fluid, water. The initial representation of the developed ferromagnetic hybrid nanofluid flow model, which is a system of highly nonlinear partial differential equations, is transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations. The reference data set of the possible outcomes is obtained from bvp4c for varying the parameters of the ferromagnetic hybrid nanofluid flow model. The estimated solutions of the proposed model are described during the testing, training, and validation phases of the backpropagated neural network. The performance evaluation and comparative study of the algorithm are carried out by regression analysis, error histograms, function fitting graphs, and mean squared error results. The findings of our study analyze the increasing effect of the ferrohydrodynamic interaction parameter β to enhance the temperature and velocity profiles, while increasing the thermal relaxation parameter α decreases the temperature profile. The performance on MSE was shown for the temperature and velocity profiles of the developed model about 9.1703e-10, 7.1313ee-10, 3.1462e-10, and 4.8747e-10. The accuracy of the artificial neural networks with the Levenberg-Marquardt algorithm method is confirmed through various analyses and comparative results with the reference data. The purpose of this study is to enhance understanding of ferromagnetic hybrid nanofluid flow models using artificial neural networks with the Levenberg-Marquardt algorithm, offering precise analysis of key parameter effects on temperature and velocity profiles. Future studies will provide novel soft computing methods that leverage artificial neural networks to effectively solve problems in fluid mechanics and expand to engineering applications, improving their usefulness in tackling real-world problems.

Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon

Department of Mathematics College of Science King Khalid University Abha Saudi Arabia

Department of Mathematics University of Management and Technology Lahore 54770 Lahore Pakistan

IT4Innovations VSB Technical University of Ostrava Ostrava Czech Republic

School of Mathematics Minhaj University Lahore Lahore Pakistan

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