# Learning cosmology and clustering with cosmic graphs

**Authors:** Pablo Villanueva-Domingo, Francisco Villaescusa-Navarro  
**arXiv:** [2204.13713](https://arxiv.org/abs/2204.13713)  
**Date:** 2022-04-28  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2204.13713v1/

## Key points

- Deep learning models and Graph Neural Networks (GNNs) used to analyze galaxy catalogues from CAMELS project's hydrodynamic simulations
- GNNs effectively compute power spectrum of galaxy catalogues with high accuracy
- GNNs trained to perform likelihood-free inference on cosmological parameter $\Omega_{\rm m}$ using positions of approximately 1000 galaxies
- Models achieve around 12-13% accuracy in inferring $\Omega_{\rm m}$, improved to 4-8% when incorporating additional information from galaxy properties
- Models designed to be translational and rotational invariant, capturing relevant features across different spatial scales
- Not completely robust when tested on simulations with different subgrid physics, suggesting limitations in generalizing across different physical scenarios
- Study demonstrates effectiveness of GNNs in analyzing galaxy catalogues and performing cosmological inference tasks

## Summary

In this study, the authors utilize deep learning models and Graph Neural Networks (GNNs) to analyze thousands of galaxy catalogues from the CAMELS project's state-of-the-art hydrodynamic simulations. The goal is to perform regression and inference tasks related to cosmology and clustering. The authors first demonstrate that GNNs can effectively compute the power spectrum of galaxy catalogues with a high level of accuracy, achieving results within a few percent error. This showcases the ability of GNNs to work with irregular and sparse data, such as the distribution of galaxies in the Universe. Building upon this success, the authors train GNNs to perform likelihood-free inference at the galaxy-field level. Specifically, they focus on inferring the value of $\Omega_{\rm m}$, a cosmological parameter related to matter density, using only the positions of approximately 1000 galaxies in a volume of $(25~h^{-1}{\rm Mpc})^3$ at $z=0$. Remarkably, their models achieve an accuracy of around 12-13% in inferring $\Omega_{\rm m}$ while accounting for astrophysical uncertainties modeled in CAMELS. To further improve their models' accuracy, the authors incorporate additional information from galaxy properties such as stellar mass, stellar metallicity, and stellar radius. By considering these properties alongside galaxy positions, they are able to increase the accuracy range to 4-8%. Importantly, these models are designed to be translational and rotational invariant; they can extract information from any scale larger than the minimum distance between two galaxies. This flexibility allows them to capture relevant features across different spatial scales. However, it should be noted that while these models show impressive performance on simulations with similar subgrid physics used for training; they are not completely robust when tested on simulations run with different subgrid physics. This suggests that there may be limitations in generalizing their models across different physical scenarios. In summary, this study demonstrates the effectiveness of GNNs in analyzing galaxy catalogues and performing cosmological inference tasks. The models developed here showcase potential for accurately estimating cosmological parameters using only a small number of galaxies' positions and properties; however further research is needed to enhance their robustness across different simulation setups.