Abstract
In the present study, numerical work is carried out to investigate the third-grade fluid flow model using the algorithm of Levenberg Marquardt with backpropagated neural networks. We inspect a two-dimensional, incompressible, and steady laminar flow over a stretched sheet with gyrotactic microorganisms, where the flow is electro-conductive and magnetized, and the flow is generated by the stretching. In the mathematical modeling, we used the Buongiorno nanofluid model. The governing partial differential equations are transformed into a system of ordinary differential equations. These ordinary differential equations are solved by the Homotopy Analysis Method in the Mathematica software to generate the reference dataset with the various physical parameters. The approximated solution of the considered model is computed in MATLAB software using the reference dataset. By testing, training, and validation processes, we examined the correctness and the validation of the proposed model. These stochastic techniques have many applications in medicines, nanophysics, telecommunication industries, etc. The impacts of the variation of physical parameters on the velocity, temperature, concentration, and motile density profiles are examined, where the results for Nusselt number, Entropy generation, Sherwood number and Motile density number are also discussed in the present article. The best performance values 1.34E−09, 1.03E−09, 9.22E−10, 1.34E−09, 1.18E−09, and 1.32E−08 are attained at 311, 595, 347, 297, 581 and 521 epochs, respectively, for different scenarios. The values of Gradient are 9.96E−08, 9.97E−08, 9.94E−08, 9.98E−08, 9.90E−08, and 9.93E−08, whereas the values of Mu are 1E−08, 1E−08, 1E−08, 1E−08, 1E−08 and 1E−08 at 281, 505, 459, 388, 181, and 410, respectively for various instances. The regression value is R = 1 for training, testing, and validation data. The absolute error values are 10-6 to 10-4, 10-7 to 10-4, 10-9 to 10-4, 10-7 to 10-4, 10-7 to 10-4, 10-7 to 10-3, 10-7 to 10-4, 10-7 to 10-4, 10-7 to 10-4, 10-7 to 10-2, 10-7 to 10-4, 10-7 to 10-3 and 10-7 to 10-2 for (I-XIII) scenarios.