Velocity recostruction with graph neural networks

In this work, we seek to improve the velocity reconstruction of clusters by using Graph Neural Networks -- a type of deep neural network designed to analyze sparse, unstructured data. In comparison to the Convolutional Neural Network (CNN) which is built for structured data such as regular grids, GNN is particularly suitable for analyzing galaxy catalogs. In our GNNs, galaxies as represented as nodes that are connected with edges. The galaxy positions and properties -- stellar mass, star formation rate, and total number of galaxies within 100~\mpc -- are combined to predict the line-of-sight velocity of the clusters. To train our networks, we use mock SDSS galaxies and clusters constructed from the Magneticum hydrodynamic simulations. Our GNNs reach a precision in reconstructed line-of-sight velocity of $\Delta v$=163 km/s, outperforming by $\approx$10\% the perturbation theory~($\Delta v$=181 km/s) or the CNN~($\Delta v$=179 km/s). The stellar mass provides additional information, improving the precision by $\approx$6\% beyond the position-only GNN, while other properties add little information. Our GNNs remain capable of reconstructing the velocity field when redshift-space distortion is included, with $\Delta v$=210 km/s which is again 10\% better than CNN with RSD. Finally, we find that even with an impressive, nearly 70\% increase in galaxy number density from SDSS to DESI, our GNNs only show an underwhelming 2\% improvement, in line with previous works using other methods. Our work demonstrates that, while the efficiency in velocity reconstruction may have plateaued already at SDSS number density, further improvements are still hopeful with new reconstruction models such as the GNNs studied here.