In this study, fluid flow inside of an obstructed channel under the influence of magnetic field has been analyzed using physics informed neural networks(PINNs). Governing equations have been utilized in low-order form and the solution has been obtained in dimensionless form. Geometric and physics-related dimensionless parameters have been used as input variables of the neural network in the learning process. The radius and longitudinal position of the obstruction have also been involved in the learning process and the problem has been solved parametrically. In the successive sections of the study, inverse problem has been a matter of interest, particularly in form of obtaining the Hartmann number using the proposed method. The results have indicated that the employed method determined the Hartmann number with great accuracy and entailed proper results. In this study a thorough exploration of effects of physical and geometric parameters on the magnetically influenced flow through a duct has been carried out. The accuracy of the results obtained from the solving method proposed have been compared to results generated by common methods used in computational fluid mechanics. The parametric solution of the problem can serve as a powerful tool in optimization problems. The method was also applicable to cases where the parameters were outside of defined range, indicating it's generalization capabilities.
