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

TL;DR

The paper addresses reconstructing the local dark-matter density field from line-of-sight peculiar velocities, a nonlinear problem where traditional linear methods falter. It introduces a hybrid architecture that fuses a convolutional U-Net operating on velocity divergence with a local DeepSets-based point-cloud module to capture small-scale structure, guided by a confidence network that selects voxels for detailed processing. On Quijote simulations at $z=0$, the approach outperforms linear Wiener filtering and a standalone U-Net, delivering higher cross-correlation and a better transfer function, especially at scales around $k\sim 0.1-0.2\,h\mathrm{Mpc}^{-1}$. The results suggest that incorporating targeted small-scale information via the point-cloud component yields meaningful gains for local density reconstruction at moderate tracer densities, with potential implications for future peculiar-velocity datasets and cosmological inference.

Abstract

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.

Figures (3)

• Figure 1: Schematic representation of our architecture. The backbone is a U-Net evaluated on the velocity divergence. Additional small-scale information is provided by a DeepSets point-cloud architecture which is evaluated locally. Due to the high cost of the DeepSets evaluation, a pretrained and then frozen confidence U-Net is used to select a small percentage of voxels for which the DeepSets evaluation is deemed worth the expense.
• Figure 2: Performance evaluation in two-point statistics. The left panel shows the cross-correlation coefficient, while the right panel shows the transfer function. Blue is the 3D Wiener filter (which is an upper bound on linear reconstruction), magenta shows the reconstruction with a convolutional U-Net only, and red shows our complete architecture which includes small-scale information from the DeepSets component. The shaded areas correspond to the standard deviation of the metric across the whole testing dataset.
• Figure 3: Visual illustration of the effect of the small-scale DeepSets information. Compared to Fig. \ref{['fig:pic1']}, the color scale concentrates on the high-density regime. The contours represent approximately the regions which the confidence network picked for DeepSets evaluation.