A Parameterized Simulation and Inverse Analysis for the Determination of Physical Properties in MHD Channel Flow using the PINN Method

• Utilization of the PINN approach for parametric simulation and solving the inverse problem in MHD channel flow. • Investigation of the effects of the Hartmann number and Joule heating parameter on fluid flow and heat transfer. • Assessment of the generalization capability of the parametric solution using the PINN method. • Solving the inverse problem based on a specified channel outlet boundary condition. • Analysis of noise impact on the solutions obtained via the PINN method. This study presents a parametric simulation and inverse analysis of fluid flow and heat transfer in a two-dimensional channel under a magnetic field. A Physics-Informed Neural Network (PINN) framework is employed to solve the governing equations and investigate the coupled effects of various dimensionless parameters. The simulation incorporates the low-order derivative form of the non-dimensionalized equations, with the primary objective of inversely estimating unknown physical properties. The central aim is to evaluate the capability of the PINN method for solving both parametric and inverse problems in MagnetoHydroDynamic (MHD) channel flow. The influence of key parameters, including the Hartmann number, Reynolds number, Prandtl number, and Joule heating parameter, on the fluid's velocity and temperature fields is systematically examined. The results demonstrate that the PINN approach successfully predicts the dominant physical mechanisms, with the Hartmann number and Joule heating parameter being accurately identified with a relative error of less than 2% compared to numerical benchmarks. This research concludes that the PINN method constitutes a powerful tool for thermal-flow simulations. Specifically, the proposed framework achieves high predictive accuracy (mean relative error < 1%) while offering a computational speed-up of approximately 1.4 times compared to traditional CFD methods for parametric studies. Furthermore, the model demonstrates robust generalization capabilities, maintaining reasonable accuracy (error < 4%) even when extrapolating to parameter values outside the training range.