Neural network reconstruction of density and velocity fields from the 2MASS Redshift Survey

Aims. Our aim is to reconstruct the 3D matter density and peculiar velocity fields in the local Universe up to a distance of 200 h^a-1 Mpc from the Two-Micron All-Sky Redshift Survey (2MRS) using a neural network (NN). Methods. We employed an NN with a U-net autoencoder architecture and a weighted mean squared error loss function trained separately to output either the density or velocity field for a given input grid of galaxy number counts. The NN was trained on mocks derived from the Quijote N-body simulations, incorporating redshift-space distortions (RSDs), galaxy bias, and selection effects closely mimicking the characteristics of 2MRS. The trained NN was benchmarked against a standard Wiener filter (WF) on a validation set of mocks before applying it to 2MRS. Results. The NN reconstructions effectively approximate the mean posterior estimate of the true density and velocity fields conditioned on the observations. They consistently outperform the WF in terms of reconstruction accuracy and effectively capture the nonlinear relation between velocity and density. The NN-reconstructed bulk flow of the total survey volume exhibits a significant correlation with the true mock bulk flow, demonstrating that the NN is sensitive to information on "super-survey"scales encoded in the RSDs. When applied to 2MRS, the NN successfully recovers the main known clusters, some of which are partially in the Zone of Avoidance. The reconstructed bulk flows in spheres of different radii less than 100 h^a-1 Mpc are in good agreement with a previous 2MRS analysis that required an additional external bulk flow component inferred from directly observed peculiar velocities. The NN-reconstructed peculiar velocity of the Local Group closely matches the observed Cosmic Microwave Background dipole in amplitude and Galactic latitude, and only deviates by 18 in longitude. The NN-reconstructed fields are publicly available.