Flow Domain Parameterization and Training of Generalized Physics-Informed Neural Networks for Solving Navier-Stokes Equations

Physics-informed neural networks (PINNs) have shown promise in solving the Navier-Stokes equations for fluid flow problems, but most existing approaches require retraining for each new flow case, limiting their applicability to a wide range of scenarios. This study addresses the challenge of multi-dimensional parameterization of flow domain geometries, which has not been extensively explored in previous research. We propose an approach for parameterizing the flow domain for solving the stationary Navier-Stokes equations for Newtonian fluid flow using PINNs. The proposed approach allows scaling PINN for new cases not considered in training and significantly reduces computational costs in comparison with the numerical solution.