  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.
