  Dark matter in the universe evolves through gravity to form a complex network
of halos, filaments, sheets and voids, that is known as the cosmic web.
Computational models of the underlying physical processes, such as classical
N-body simulations, are extremely resource intensive, as they track the action
of gravity in an expanding universe using billions of particles as tracers of
the cosmic matter distribution. Therefore, upcoming cosmology experiments will
face a computational bottleneck that may limit the exploitation of their full
scientific potential. To address this challenge, we demonstrate the application
of a machine learning technique called Generative Adversarial Networks (GAN) to
learn models that can efficiently generate new, physically realistic
realizations of the cosmic web. Our training set is a small, representative
sample of 2D image snapshots from N-body simulations of size 500 and 100 Mpc.
We show that the GAN-generated samples are qualitatively and quantitatively
very similar to the originals. For the larger boxes of size 500 Mpc, it is very
difficult to distinguish them visually. The agreement of the power spectrum
$P_k$ is 1-2\% for most of the range, between $k=0.06$ and $k=0.4$. An
important advantage of generating cosmic web realizations with a GAN is the
considerable gains in terms of computation time. Each new sample generated by a
GAN takes a fraction of a second, compared to the many hours needed by
traditional N-body techniques. We anticipate that the use of generative models
such as GANs will therefore play an important role in providing extremely fast
and precise simulations of cosmic web in the era of large cosmological surveys,
such as Euclid and Large Synoptic Survey Telescope (LSST).
