Reconstructing the local density field with combined convolutional and point cloud architecture

We construct a neural network to perform regression on the local dark-matter density field given line-of-sight peculiar velocities of dark-matter halos, biased tracers of the dark matter field. Our architecture combines a convolutional U-Net with a point-cloud DeepSets. This combination enables efficient use of small-scale information and improves reconstruction quality relative to a U-Net-only approach. Specifically, our hybrid network recovers both clustering amplitudes and phases better than the U-Net on small scales.