Modeling microchannel flow of Phan–Thien–Tanner fluids using hybrid skip-physics informed neural network

This study investigates the combined electroosmotic and pressure-driven flow of viscoelastic fluids in a parallel-plate microchannel, emphasizing the interplay of flow and thermal transport under realistic electrokinetic conditions. The simplified Phan–Thien–Tanner model is used to characterize nonlinear rheology, while the electric double-layer potential is evaluated using the full Poisson–Boltzmann formulation, beyond the Debye–Hückel approximation. Closed-form solutions are obtained for the velocity field, flow rate, and stress distribution under hydrodynamically fully developed conditions. The thermally developing regime is analyzed through the energy equation, considering Joule heating and viscous dissipation. To improve predictive accuracy, a physics-informed neural network (PINN) framework is integrated with the governing equations to reconstruct velocity and temperature profiles from sparse data without mesh generation. Multiple PINN architectures were investigated, with skip connections shown to significantly enhance convergence in deeper networks. A hybrid training strategy, combining physics-constrained learning with data-driven fine-tuning, outperforms conventional neural networks. A Hybrid Skip-PINN (five hidden layers) achieves the best performance with mean squared error of 1.3783 × 10−6 and demonstrates robustness against noisy data. Parametric studies highlight the effects of viscoelastic, Brinkman, Peclet, and surface potential parameters. The proposed hybrid framework offers a robust methodology for design and optimization of microfluidic systems.