Mixed data-source transfer learning for a turbulence model augmented physics-informed neural network

Abstract Physics-informed neural networks (PINNs) are a promising alternative for extracting additional time-averaged (mean) flow quantities from experimental data. In the case of particle image velocimetry (PIV), for example, the measured mean flow field is contaminated by noise, has a limited field of view, is restricted to a uniform grid, and does not provide the pressure field. To overcome these limitations, we present a methodology in which PINNs are first trained on a Reynolds-averaged Navier–Stokes (RANS) simulation such that it learns all states at every location in the domain. We then apply transfer learning, which updates the PINN using sub-sampled PIV data. The resulting predictions are in significantly better agreement with the full PIV dataset than PINNs, which are trained on experimental data only. This work builds on the recent literature by integrating a Spalart-Allmaras turbulence model and applying hard constraints to the no-slip wall boundary condition. We apply this methodology to a two-dimensional NACA 0012 airfoil inclined at an angle of attack, α $ \alpha $ alpha = 15°, for two Reynolds numbers of Re = 10,000 and 75,000. The proposed methodology is initially validated using large eddy simulation (LES) data and then demonstrated on experimental PIV data. Our transfer learning approach results in improved predictions and a reduction in training time when compared to using a random network initialization.