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In this research paper, we observed the Prandtl–Eyring magneto hydrodynamic fluid model (PE-MHDFM) by applying the Bayesian regularization scheme as backpropagated artificial neural networks (BRS-BANNs). Effect of suction/injection at the wall is the source of convective steady flow. The nonlinear partial differential equations (PDEs) of PE-MHDFM are converted into ordinary differential equations (ODE) by applying some suitable similarity transformation. These ODEs are solved by utilizing Lobatto IIIA numerical procedure to acquire the reference dataset for different scenarios of BRS-BANN. The reference dataset is used to design the solver BRS-BANN. Further, the performance of BRS-BANN is clarified by MSE results, error analysis plots, regression and error histogram. Moreover, the solution of PE-MHDFM is observed through the validation, training and testing procedures. It is observed that the best correlation between the targeted values outcomes of the study is matched effectively, which definitely authenticates the validity and reliability of the designed solver. Furthermore, the impacts on the velocity profile and temperature profile are examined by the variation of different physical quantities along with their comparison with state-of-the-art Lobatto IIIA numerical approach. [ABSTRACT FROM AUTHOR]