Unravelling the role of cosmic velocity field in dark matter halo mass
  function using deep learning
  We discuss an implementation of a deep learning framework to gain insight
into the dark matter structure formation. We investigate the impact of velocity
and density field information on the construction of halo mass function through
cosmological $N$-body simulations. In this direction, we train a Convolutional
Neural Network (CNN) on the initial snapshot of an only dark matter simulation
to predict the halo mass that individual particles fall into at $z=0$, in the
halo mass range of $10.5< \log(M / M_{\odot})<14$. Our results show a
negligible improvement from including the velocity in addition to the density
information when considering simulations based on the standard model of
cosmology ($\Lambda$CDM) with the amplitude of initial scalar perturbations
$A_s = 2\times10^{-9}$. In order to investigate the ellipsoidal collapse models
and to study the effect of velocity in smaller mass ranges, we increase the
initial power spectrum such that we see the effect of velocities in larger
halos which are in the resolution of our simulation. The CNN model trained on
the simulation snapshots with large $A_s$ shows a considerable improvement in
the halo mass prediction when adding the velocity field information.
Eventually, for the simulation with $A_s = 8 \times 10^{-8}$, the model trained
with only density information shows at least $80\%$ increase in the mean
squared error relative to the model with both velocity and density information
at almost all mass scales, which indicates the failure of the density-only
model to predict the halo masses in this case. Our results indicate that the
effect of velocity field on the halo collapse is scale-dependent with a
negligible effect for the standard model of cosmology in mass scales $10.5 <
\log(M/ M_{\odot}) < 14$.
