Physics Informed Neural Networks (PINNs) technique for hybrid nanofluid flow equipped with thermal radiation and porous media

Machine learning approaches have become more popular in recent times and with artificial intelligence, it can predict accordingly. Motivated by Neural Network technique, a mathematical model is presented for steady incompressible magnetohydrodynamic hybrid nanofluid flow with radiative porous media. The governing equations are transformed into a system of ordinary differential equations using similarity transformations. And then physics-informed neural network methodology is employed to solve the equations with L-BFGS optimizer for training loss. To validate the obtained results through neural techniques, we have used the shooting Runge-Kutta 4th order method. The mean square errors are the order of 10−6−10−9.Following this, velocity profiles, thermal profiles are visualized graphically and numerically for different control parameters and obtained velocity mean square error value 9.283×10−8,4.092×10−8, 8.213×10−7 for M=0,2,5 respectively. This investigation illustrates that the magnetic parameter and Darcy number have a negative impact on the thermal profile, but the Eckert number and radiation parameter have a positive impact. Overall, the proposed neural network approach has proven to be very reliable, effective, and easy to handle.