Numerical paradigm to explore the chemically reacting Williamson nanofluid flow with the influence of bioconvection effects using neural networks

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This research focuses on using a type of advanced computer program called artificial neural networks (ANNs) using the Levenberg–Marquardt backpropagation technique (LMBPT-NNs) to stimulate the behavior of bioconvective effects on heat and mass transport in non-Newtonian chemically Williamson nanofluid through stretched surface (BEHMT-NNCRWNF-SS). Williamson nanofluid flow refers to specially engineered fluids with nanoparticles dispersed within them and moving when subjected to external forces. Understanding their flow behavior is crucial to effectively use them in various applications, especially in the field of heat and mass transfer and fluid dynamics. Before being solved numerically, a couple of governing partial differential equations are transformed into ordinary differential equations through suitable similarity functions. The finite difference method (FDM) (Lobatto IIIA) is applied for the solution of a nonlinear nanofluidic system by selecting different collocation points. These collocation points play a crucial role in approximating the solution and ensuring accurate results. To address various fluidic problems, it's important to use the appropriate results of FDM to create a reference dataset for the LMBPT-NNs. Statistical analysis should then be performed on the training, testing, and validation of the reference datasets to obtain the optimal scheme for different fluidic flow issues.. The precision of the LMBPT-NNs is checked through ANN tools like mean square error (MSE), regression analysis, curve fitness, and histogram error.