Application of Physics Informed Neural Networks (PINNs) on combined electroosmotic-pressure driven flow

Multi-physics involved in micro-electro-mechanical systems (MEMS) is of great importance to analyze the fluid motion in biomedical and biotechnological applications, chemical synthesis, mixing and various other applications. We have implemented different architectures of physics-informed neural networks (PINNs) 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 have predicted the non-uniformly distributed zeta-potential on the fluid dynamic, and heat transfer characteristics. It is found that there is a good agreement between the Finite Volume Method (FVM) and segregated PINN approach. From the grid point distribution effect on PINNs, we also demonstrate that using boundary layer collocation points can drastically improve the training efficiency and reduce the total loss for EOF/PD flow. Furthermore, comparing the PINN results with the numerical simulation for mixing index and Nusselt number variation, we present that 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.