The novelty of the present work is to acquire continuous functions as solutions rather than the discrete ones that traditional numerical methods generally produce and to minimize simulation times and higher computation costs that are the fundamental barriers to employing any numerical method. In this study, a novel hybrid finite element-based machine learning algorithm utilizing the Levenberg-Marquardt scheme with backpropagation in a neural network (LMBNN) is presented to analyze the nanofluid flow in the presence of magnetohydrodynamics and gyrotactic microorganisms through a vertically inclined stretching surface in a porous medium. Finite Element Method is used to generate the minimum reference dataset for LMBNN by varying six flow parameters in the form of six scenarios. Surface plots are utilized to understand how these scenarios affect velocity, temperature, concentration of nanoparticles, and density of motile microorganisms. Regression analysis, error histogram analysis, and fitness curves based on mean square error all support the LMBNN's effectiveness and dependability. Results reveal that temperature increases with the rise in Brownian motion and thermophoresis parameter, whereas the reverse trend has been noticed for Prandtl number. The motile microorganism density number decreases with the rise in Prandtl numbers but improves with the porosity parameter.
Keywords: Finite Element Method; Levenberg-Marquardt technique; gyrotactic microorganisms; nanoparticles; porous medium; vertically inclined stretching surface.
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