Cosmology from Galaxy Redshift Surveys with PointNet

Sotiris Anagnostidis, Arne Thomsen, Tomasz Kacprzak, Tilman Tröster, Luca Biggio, Alexandre Refregier, Thomas Hofmann

Submitted on 22 November 2022


In recent years, deep learning approaches have achieved state-of-the-art results in the analysis of point cloud data. In cosmology, galaxy redshift surveys resemble such a permutation invariant collection of positions in space. These surveys have so far mostly been analysed with two-point statistics, such as power spectra and correlation functions. The usage of these summary statistics is best justified on large scales, where the density field is linear and Gaussian. However, in light of the increased precision expected from upcoming surveys, the analysis of -- intrinsically non-Gaussian -- small angular separations represents an appealing avenue to better constrain cosmological parameters. In this work, we aim to improve upon two-point statistics by employing a \textit{PointNet}-like neural network to regress the values of the cosmological parameters directly from point cloud data. Our implementation of PointNets can analyse inputs of O(104)O(105) galaxies at a time, which improves upon earlier work for this application by roughly two orders of magnitude. Additionally, we demonstrate the ability to analyse galaxy redshift survey data on the lightcone, as opposed to previously static simulation boxes at a given fixed redshift.


Subjects: Astrophysics - Cosmology and Nongalactic Astrophysics; Computer Science - Machine Learning


\textbf{Schematic illustration of the proposed approach.} For galaxy redshift surveys, cosmological parameter inference is traditionally performed by manually extracting summary statistics, i.e. features, from a set of points in 3D coordinates. Our approach differs in that relevant features are automatically extracted by a hierarchical PointNet directly processing the point cloud and outputting the corresponding cosmological parameters. This way, the need for introducing hand-crafted summary statistics can be entirely avoided.