Super-resolution GANs of randomly-seeded fields

Reconstruction of field quantities from sparse measurements is a problem arising in a broad spectrum of applications. This task is particularly challenging when mapping between point sparse measurements and field quantities shall be performed in an unsupervised manner. Further complexity is added for moving sensors and/or random on-off status. Under such conditions, the most straightforward solution is to interpolate the scattered data onto a regular grid. However, the spatial resolution achieved with this approach is ultimately limited by the mean spacing between the sparse measurements. In this work, we propose a novel super-resolution generative adversarial network (GAN) framework to estimate field quantities from random sparse sensors without needing any full-resolution field for training. The algorithm exploits random sampling to provide incomplete views of the high-resolution underlying distributions. It is hereby referred to as RAndomly-SEEDed super-resolution GAN (RaSeedGAN). The proposed technique is tested on synthetic databases of fluid flow simulations, ocean surface temperature distributions measurements, and particle image velocimetry data of a zero-pressure-gradient turbulent boundary layer. The results show an excellent performance of the proposed methodology even in cases with a high level of gappyness (>50\%) or noise conditions. To our knowledge, this is the first super-resolution GANs algorithm for full-field estimation from randomly-seeded fields with no need of a full-field high-resolution representation during training nor of a library of training examples.