  The peculiar velocities of dark matter halos are crucial to study many issues
in cosmology and galaxy evolution. In this study, by using the state-of-the-art
deep learning technique, a UNet-based neural network, we propose to reconstruct
the peculiar velocity field from the redshift-space distribution of dark matter
halos. Through a point-to-point comparison and examination of various
statistical properties, we demonstrate that, the reconstructed velocity field
is in good agreement with the ground truth. The power spectra of various
velocity field components, including velocity magnitude, divergence and
vorticity, can be successfully recovered when $k\lesssim 1.1$ $h/\rm Mpc$ (the
Nyquist frequency of the simulations) at about 80% accuracy. This approach is
very promising and presents an alternative method to correct the redshift-space
distortions using the measured 3D spatial information of halos. Additionally,
for the reconstruction of the momentum field of halos, UNet achieves similar
good results. Hence the applications in various aspects of cosmology are very
broad, such as correcting redshift errors and improving measurements in the
structure of the cosmic web, the kinetic Sunyaev-Zel'dovich effect, BAO
reconstruction, etc.
