  Reconstruction of field quantities from sparse measurements is a problem
arising in a broad spectrum of applications. This task is particularly
challenging when the mapping between sparse measurements and field quantities
is 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 super-resolution generative adversarial network (GAN) framework to
estimate field quantities from random sparse sensors without needing any
full-field high-resolution 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 excellent performance even in cases with high sparsity or with
levels of noise. To our knowledge, this is the first GAN algorithm for
full-field high-resolution estimation from randomly-seeded fields with no need
of full-field high-resolution representations.

Fluid Dynamics;Machine Learning;Computational Physics