Mapping Lyman-alpha forest three-dimensional large scale structure in
  real and redshift space
  This work presents a new physically-motivated supervised machine learning
method, Hydro-BAM, to reproduce the three-dimensional Lyman-$\alpha$ forest
field in real and in redshift space learning from a reference hydrodynamic
simulation, thereby saving about 7 orders of magnitude in computing time. We
show that our method is accurate up to $k\sim1\,h\,\rm{Mpc}^{-1}$ in the one-
(PDF), two- (power-spectra) and three-point (bi-spectra) statistics of the
reconstructed fields. When compared to the reference simulation including
redshift space distortions, our method achieves deviations of $\lesssim2\%$ up
to $k=0.6\,h\,\rm{Mpc}^{-1}$ in the monopole, $\lesssim5\%$ up to
$k=0.9\,h\,\rm{Mpc}^{-1}$ in the quadrupole. The bi-spectrum is well reproduced
for triangle configurations with sides up to $k=0.8\,h\,\rm{Mpc}^{-1}$. In
contrast, the commonly-adopted Fluctuating Gunn-Peterson approximation shows
significant deviations already neglecting peculiar motions at configurations
with sides of $k=0.2-0.4\,h\,\rm{Mpc}^{-1}$ in the bi-spectrum, being also
significantly less accurate in the power-spectrum (within 5$\%$ up to
$k=0.7\,h\,\rm{Mpc}^{-1}$). We conclude that an accurate analysis of the
Lyman-$\alpha$ forest requires considering the complex baryonic thermodynamical
large-scale structure relations. Our hierarchical domain specific machine
learning method can efficiently exploit this and is ready to generate accurate
Lyman-$\alpha$ forest mock catalogues covering large volumes required by
surveys such as DESI and WEAVE.
