  Extracting non-Gaussian information from the next generation weak lensing
surveys will require fast and accurate full-sky simulations. This is difficult
to achieve in practice with existing simulation methods: ray-traced $N$-body
simulations are computationally expensive, and approximate simulation methods
(such as lognormal mocks) are not accurate enough. Here, we present GANSky, an
interpretable machine learning method that uses Generative Adversarial Networks
(GANs) to produce fast and accurate full-sky tomographic weak lensing maps. The
input to our GAN are lognormal maps that approximately describe the late-time
convergence field of the Universe. Starting from these lognormal maps, we use
GANs to learn how to locally redistribute mass to achieve simulation-quality
maps. This can be achieved using remarkably small networks ($\approx 10^3$
parameters). We validate the GAN maps by computing a number of summary
statistics in both simulated and GANSky maps. We show that GANSky maps
correctly reproduce both the mean and $\chi^2$ distribution for several
statistics, specifically: the 2-pt function, 1-pt PDF, peak and void counts,
and the equilateral, folded and squeezed bispectra. These successes makes
GANSky an attractive tool to compute the covariances of these statistics. In
addition to being useful for rapidly generating large ensembles of artificial
data sets, our method can be used to extract non-Gaussian information from weak
lensing data with field-level or simulation-based inference.
