Reconstructing the cosmological density and velocity fields from redshifted galaxy distributions using V-net

The distribution of matter that is measured through galaxy redshift and peculiar velocity surveys can be harnessed to learn about the physics of dark matter, dark energy, and the nature of gravity. To improve our understanding of the matter of the Universe, we can reconstruct the full density and velocity fields from the galaxies that act as tracer particles. In this paper, we use the simulated halos as proxies for the galaxies. We use a convolutional neural network, a V-net, trained on numerical simulations of structure formation to reconstruct the density and velocity fields. We find that, with detailed tuning of the loss function, the V-net could produce better fits to the density field in the high-density and low-density regions, and improved predictions for the probability distribution of the amplitudes of the velocities. However, the weights will reduce the precision of the estimated $\beta$ parameter. We also find that the redshift-space distortions of the halo catalogue do not significantly contaminate the reconstructed real-space density and velocity field. We estimate the velocity field $\beta$ parameter by comparing the peculiar velocities of halo catalogues to the reconstructed velocity fields, and find the estimated $\beta$ values agree with the fiducial value at the 68\% confidence level.