Physics Informed Neural Network application on mixing and heat transfer in combined electroosmotic-pressure driven flow

In the current research, different architectures of physics-informed neural networks (PINNs) are implemented to investigate the mixed electroosmotic pressure driven (EOF/PD) flow in microchannels with non-uniform zeta-potential distribution on the walls. Through performing a detailed numerical simulation and PINN solutions based on Poisson-Boltzmann, Laplace, Navier-Stokes, concentration, and energy equations, we predict the non-uniformly distributed zeta-potential on the fluid dynamic, and heat transfer characteristics. It is observed that there is a good agreement between the Finite Volume Method (FVM) and segregated PINN approach. Comparing the PINN results with the numerical simulation, we show that amalgamating losses in all governing equations and applying a single PINN leads to higher training loss when compared to the multi-structured PINN, where a PINN is separately trained for each governing equation. Specifically, the normalized mean absolute percentage errors in the velocity prediction of the single and segregated PINNs are 20.17% and 9.2% respectively. In addition to the structure of the PINN, we also examine the effect of grid point distribution on PINNs. We demonstrate that using boundary layer collocation points can drastically improve the training efficiency and reduce the total loss for EOF/PD flow.