Physics And Geometry-Informed Neural Networks For Flow Prediction In Bifurcated Ducts Under Periodic Boundary Conditions

Understanding and accurately quantifying fluid flow in small, multi-scale bifurcated structures subjected to peristaltic boundary conditions is critical in diverse engineering and biomedical applications, ranging from pipe flow to vascular hemodynamics to respiratory airflow. Traditional computational fluid dynamics (CFD) methods, while accurate, are often computationally expensive and limited by complex geometries and boundary conditions. In this study, we propose a novel Geometry and Physics-Informed Neural Network (G-PINN) framework that seamlessly integrates geometric constraints and the governing non-linear partial differential equations (Navier-Stokes equations) and interface conservation laws into a unified deep learning model to predict steady and transient fluid flow in Y-shaped bifurcated ducts. The G-PINN is trained solely on sparse velocity data without requiring pressure field supervision, yet it effectively reconstructs high-fidelity pressure and velocity distributions throughout the domain. Comparative analyses with reference CFD solutions from ANSYS FLUENT demonstrate that the G-PINN accurately captures flow separation, secondary recirculation, and pressure drops across bifurcations under both steady and pulsatile inflow conditions. Moreover, the model demonstrates robust generalization across different flow regimes in distal ducts as small as 0.25mm. This work underscores the synergy between physics-based machine learning and traditional fluid dynamics, paving the way for efficient, data-driven modeling of complex flow systems.