AI-Powered Reconstruction of Dark Matter Velocity Fields from Redshift-Space Halo Distribution

We propose a UNet-based deep learning model to reconstruct the real-space dark matter (DM) velocity field from the redshift-space distribution of sparse DM halos. Using various statistical measures, we show that the reconstructed velocity components--including velocity magnitude, momentum, and divergence--closely match the ground truth, achieving better than 10% relative error and a correlation coefficient of 0.88. In the power spectrum comparison over $k \in [0.05, 0.3] h/{\rm Mpc}$, the UNet reconstruction outperforms linear theory and agrees with the true field within $2\sigma$. The model also effectively corrects redshift-space distortions (RSD), yielding unbiased power spectrum multipoles of DM fields within $2\sigma$. Notably, the UNet remains robust even with incomplete halo mass information. These results highlight the model's broad applicability to cosmological analyses, including RSD, cosmic web studies, the kinetic Sunyaev-Zel'dovich effect, and BAO reconstruction.