Fast, high-fidelity Lyman $\alpha$ forests with convolutional neural
  networks
  Full-physics cosmological simulations are powerful tools for studying the
formation and evolution of structure in the universe but require extreme
computational resources. Here, we train a convolutional neural network to use a
cheaper N-body-only simulation to reconstruct the baryon hydrodynamic variables
(density, temperature, and velocity) on scales relevant to the Lyman-$\alpha$
(Ly$\alpha$) forest, using data from Nyx simulations. We show that our method
enables rapid estimation of these fields at a resolution of $\sim$20kpc, and
captures the statistics of the Ly$\alpha$ forest with much greater accuracy
than existing approximations. Because our model is fully-convolutional, we can
train on smaller simulation boxes and deploy on much larger ones, enabling
substantial computational savings. Furthermore, as our method produces an
approximation for the hydrodynamic fields instead of Ly$\alpha$ flux directly,
it is not limited to a particular choice of ionizing background or mean
transmitted flux.
