Discovering Latent Physical Variables from Experimental Data in Supersonic Flow Using Physics-Informed Neural Networks (PINNs)

In recent years, advancements in the machine learning and applied mathematics community have led to the development of Physics-Informed Neural Networks (PINNs) which implement a set of governing partial differential equations (PDEs) into the framework of a classical Neural Network. Through these equations it is possible to discover latent physical quantities from an incomplete dataset such as pressure and density fields from velocity measurements. While the potential has been shown in several studies with synthetic data, there are very few publications with experimental data and even fewer for compressible, high-speed applications. In this contribution, a PIV dataset of a turbulent shockwave-boundary layer interaction at Ma = 2 is used as a base to test the PINNs ability to work with experimental data. Multiple cases are constructed to enable comparisons with analytical results and show the influence of different domain sizes and boundary conditions. The results are able do match the theoretical predictions and appear to be quite robust towards measurement noise. This suggests that PINNs can be a powerful tool to extract additional information from a given set of experimental data and future improvements in the computational framework will only increase their versatility.