Deep neural network assisted modeling for MHD thin film flow of Sisko hybrid nanofluids with gyrotactic microorganisms and cross-diffusion effects

Thin-film flow of liquids have various applications in numerous technologies, such as roll and film coating, solar collectors, chemical vapor deposition reactors, and biomedical microfluidic devices. The purpose of this work is to use a deep neural network to forecast the behavior of an unstable axisymmetric magnetohydrodynamic thin-film flow of a Sisko $$\\:A{l}_{2}{O}_{3}-T{iO}_{2}$$ /water hybrid nanofluid (HNF) with gyrotactic microorganisms over a radially extending surface. The model assumes an incompressible, laminar thin film with time-independent thermophysical properties. Through the proper transformations, the governing equations are reduced into a coupled system, which is then numerically solved using the fourth-order Runge–Kutta (RK–4). The numeric dataset is used to train a Bayesian-regularized deep neural network (DNN). For each of the four profiles, the DNN produced optimal MSE values of 1.8 $$\\:\\times\\:{10}^{-5}$$ , 5.2 $$\\:\\times\\:{10}^{-6}$$ , 4.8 $$\\:\\times\\:{10}^{-6}$$ , and 1.1 $$\\:\\times\\:{10}^{-6}$$ , for all datasets. Important results show that the radiation and Dufour number increase the thermal field. The Sisko fluid parameter and magnetic number, respectively, increase and decrease the velocity profile. Activation energy and Soret number increase the concentration profile. The Peclet number and bioconvection Lewis number suppress the microorganism density.