A Physics-informed Machine Learning Framework Combined with a Reduced Order Model for Efficient Prediction of Unsteady Vortex Shedding

Abstract This study introduces a novel physics-informed machine learning framework combined with a reduced order model (ROM) for efficiently modeling unsteady vortex shedding phenomena. The framework consists of offline and online stages. During the offline stage, numerical simulation data for flow past a cylinder is processed using the Proper Orthogonal Decomposition (POD) method to achieve a low-dimensional representation of the flow fields. Instead of directly solving the POD-Galerkin reduced-order dynamic system, a physics-informed neural network (PINN) is employed to map time to the temporal coefficients of the dominant POD modes. The PINN is trained by minimizing a weighted loss function that combines the error of the labeled temporal coefficients and the residual loss of the POD-Galerkin dynamic system. During the online stage, the performance of the trained PINN is evaluated for two cases of a laminar flow at a low Reynolds number and a turbulent flow at a high Reynolds number, which is solved based on Reynolds-Averaged Navier-Stokes (RANS) equations. Predictive results from the PINN based on the reduced-order dynamic system are compared to those from a PINN trained on labeled numerical simulation data, which shows the accuracy of the proposed method for unsteady flow problems. In addition, the effects of various PINN parameters on model performance are thoroughly analyzed.