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

Abstract: Physics-informed neural networks (PINNs) have recently emerged as a promising alternative for extracting unknown quantities from experimental data. Despite this potential, much of the recent literature has relied on sparse, high-fidelity data from direct numerical simulations (DNS) rather than experimental sources like particle image velocimetry (PIV), which are not suitable for validating all reconstructed quantities. In the case of PIV, for example, pressure is not directly measured and the data have imperfections such as noise contamination or a limited field of view. To overcome these limitations, we present a novel methodology where PINNs are first trained on a 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 new methodology to a two-dimensional NACA 0012 airfoil inclined at an angle of attack, $α$ = 15 degrees, 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 initialisation.