Non-intrusive sensing from coarse measurements by means of generative adversarial networks (GANs)*

In this study we demonstrate the applicability of super-resolution generative adversarial networks (SRGANs) to reconstruct turbulent-flow quantities from coarse wall measurements. The method is applied both for resolution enhancement of wall data and for the estimation of wall-parallel velocity fields from coarse wall-shear stress and wall-pressure measurements. We illustrate the use of the method in a turbulent open-channel flow at a friction Reynolds number of $Re_{\tau} = 180$. We use a direct-numerical-simulation (DNS) database for training, and consider spatial downsampling factors equal to 4, 8 and 16 in each wall-parallel direction. Then we reconstruct wall-parallel fluctuation fields at inner-scaled wall-normal locations $y^+$ ranging from 15 to 100. We first show that SRGAN can be successfully used to enhance the resolution of the coarse wall measurements. Furthermore, this method can be used to perform the two steps combined ({\it i.e.}, super-resolution of wall information and flow prediction), obtaining very good reconstruction results. It is shown that even for the most challenging cases the SRGAN is capable of capturing the large-scale structures of the flow. This novel methodology is also applied to perform non-intrusive sensing in turbulent urban-flow environments.