A hybrid machine learning algorithm for studying magnetized nanofluid flow containing gyrotactic microorganisms via a vertically inclined stretching surface

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. A novel hybrid machine learning strategy has been developed that combines the Finite Element Method with the Levenberg-Marquardt scheme to study the magnetized bioconvection nanofluid flow on an inclined stretching surface. The proposed method yields continuous functional solutions rather than the discrete ones that traditional numerical methods generally produce while minimizing simulation times and computation costs, which are fundamental barriers to employing any numerical method.image