NS-PINN for Solving the Incompressible Navier-Stokes Equations

This paper proposes a Physics-Informed Neural Network (NS-PINN) for solving incompressible NavierStokes equations and reconstructing flow fields by embedding governing equations and boundary conditions into a unified loss function via automatic differentiation, enabling mesh-free modeling of complex fluid dynamics. To enhance accuracy and efficiency, adaptive residual-based sampling and dynamic loss weighting (SoftAdapt) are introduced. The method is validated on benchmark problems including Kovasznay flow, lid-driven cavity flow, and flow past a cylinder, where it achieves accurate predictions of velocity and pressure fields. Moreover, transfer learning across different Reynolds numbers accelerates convergence while maintaining accuracy, demonstrating that the proposed NS-PINN provides an efficient and flexible framework for flow field reconstruction.