Cosmic Velocity Field Reconstruction Using AI
  We develop a deep learning technique to infer the non-linear velocity field
from the dark matter density field. The deep learning architecture we use is an
"U-net" style convolutional neural network, which consists of 15 convolution
layers and 2 deconvolution layers. This setup maps the 3-dimensional density
field of $32^3$-voxels to the 3-dimensional velocity or momentum fields of
$20^3$-voxels. Through the analysis of the dark matter simulation with a
resolution of $2 {h^{-1}}{\rm Mpc}$, we find that the network can predict the
the non-linearity, complexity and vorticity of the velocity and momentum
fields, as well as the power spectra of their value, divergence and vorticity
and its prediction accuracy reaches the range of $k\simeq1.4$ $h{\rm Mpc}^{-1}$
with a relative error ranging from 1% to $\lesssim$10%. A simple comparison
shows that neural networks may have an overwhelming advantage over perturbation
theory in the reconstruction of velocity or momentum fields.
