Physics-Informed Neural Network(PINN) for Unsteady Cylinder Wakes from Complex Boundary

This paper addresses the challenges of applying Physics-Informed Neural Networks (PINN) to complex boundary problems in fluid dynamics, specifically focusing on unsteady cylinder wakes. Traditional numerical methods for solving NavierStokes equations near complex boundaries often require mesh refinement or wall functions to capture the steep velocity gradients in boundary layers. We extend PINN by proposing a novel hard constraint method and an empirical training point distribution strategy. The hard constraint method can enforce no-slip boundary conditions through a specially designed mask function based on boundary layer theory. This approach avoids the conflicting gradients between PDE and boundary losses during optimization, improving convergence and accuracy. The empirical training point distribution method provides a new idea to incorporate prior knowledge into neural network training. It strategically increases sampling density in wake regions to better capture complex flow structures. Our framework is validated on a 2D incompressible flow past multiple cylinders. The results demonstrate superior performance in high-resolution flow field reconstruction from limited labeled data. The method effectively utilizes sparse labeled data to accurately predict the entire flow system, particularly in regions with complex boundary interactions and wake structures.