Nonlinear 3D Cosmic Web Simulation with Heavy-Tailed Generative
  Adversarial Networks
  Fast and accurate simulations of the non-linear evolution of the cosmic
density field are a major component of many cosmological analyses, but the
computational time and storage required to run them can be exceedingly large.
For this reason, we use generative adversarial networks (GANs) to learn a
compressed representation of the 3D matter density field that is fast and easy
to sample, and for the first time show that GANs are capable of generating
samples at the level of accuracy of other conventional methods. Using
sub-volumes from a suite of GADGET-2 N-body simulations, we demonstrate that a
deep-convolutional GAN can generate samples that capture both large- and
small-scale features of the matter density field, as validated through a
variety of n-point statistics. The use of a data scaling that preserves
high-density features and a heavy-tailed latent space prior allow us to obtain
state of the art results for fast 3D cosmic web generation. In particular, the
mean power spectra from generated samples agree to within 5% up to k=3 and
within 10% for k<5 when compared with N-body simulations, and similar accuracy
is obtained for a variety of bispectra. By modeling the latent space with a
heavy-tailed prior rather than a standard Gaussian, we better capture sample
variance in the high-density voxel PDF and reduce errors in power spectrum and
bispectrum covariance on all scales. Furthermore, we show that a conditional
GAN can smoothly interpolate between samples conditioned on redshift. Deep
generative models, such as the ones described in this work, provide great
promise as fast, low-memory, high-fidelity forward models of large-scale
structure.
