The Cosmic Graph: Optimal Information Extraction from Large-Scale Structure using Catalogues

Abstract

We present an implicit likelihood approach to quantifying cosmological information over discrete catalogue data, assembled as graphs. To do so, we explore cosmological parameter constraints using mock dark matter halo catalogues. We employ Information Maximising Neural Networks (IMNNs) to quantify Fisher information extraction as a function of graph representation. We a) demonstrate the high sensitivity of modular graph structure to the underlying cosmology in the noise-free limit, b) show that graph neural network summaries automatically combine mass and clustering information through comparisons to traditional statistics, c) demonstrate that networks can still extract information when catalogues are subject to noisy survey cuts, and d) illustrate how nonlinear IMNN summaries can be used as asymptotically optimal compressed statistics for Bayesian simulation-based inference. We reduce the area of joint Ω m , σ 8 parameter constraints with small (∼100 object) halo catalogues by a factor of 42 over the two-point correlation function, and demonstrate that the networks automatically combine mass and clustering information. This work utilizes a new IMNN implementation over graph data in Jax, which can take advantage of either numerical or auto-differentiability. We also show that graph IMNNs successfully compress simulations away from the fiducial model at which the network is fitted, indicating a promising alternative to n-point statistics in catalogue simulation-based analyses.

Robust Field-level Inference of Cosmological Parameters with Dark Matter Halos

“…Furthermore, it has been shown that neural networks can also extract information, while marginalizing over baryonic effects, on 2D maps from state-of-the-art hydrodynamic simulations (Villaescusa-Navarro et al 2021a. These methods not only work for 2D/3D grids but can also be applied to galaxy and halo catalogs (Ntampaka et al 2020;Villanueva-Domingo & Villaescusa-Navarro 2022;Makinen et al 2022).…”

“…While GNNs have been previously used on halo catalogs from the Quijote simulations (Villaescusa-Navarro et al 2020) in Makinen et al (2022), there are several differences with that work. First, we concentrate on much smaller scales than Makinen et al (2022; 25 h −1 Mpc boxes versus 1000 h −1 Mpc).…”

“…While GNNs have been previously used on halo catalogs from the Quijote simulations (Villaescusa-Navarro et al 2020) in Makinen et al (2022), there are several differences with that work. First, we concentrate on much smaller scales than Makinen et al (2022; 25 h −1 Mpc boxes versus 1000 h −1 Mpc). Second, our main goal in this work is to study robustness, and therefore we concentrate our analysis on evaluating the performance of the models on halo catalogs generated from different codes.…”

Robust Field-level Likelihood-free Inference with Galaxies

“…Using different summary statistics as input data, Perez et al (2022) are able to derive cosmological parameters without the need for additional input from theoretical models, thus providing a powerful generalization of the usual Monte Carlo-based methods. In particular, likelihood-free inference methods work by taking data directly from the simulations (without the need for summary statistics and, thus, model comparison), and many papers have shown competitive results compared with the usual statistical inference methods (Ravanbakhsh et al 2017;Hassan et al 2020;Mangena et al 2020;Ntampaka et al 2020;Villaescusa-Navarro et al 2021a;Shao et al 2022b;Cole et al 2022;Makinen et al 2022;. At a level closer to the observations and simulations, many papers exploring the halogalaxy connection are able to make predictions that are comparable to the output of numerical/analytical methods (Kamdar et al 2016;Jo & Kim 2019;Yip et al 2019;Zhang et al 2019;Kasmanoff et al 2020;Wadekar et al 2020;Moster et al 2021;Villanueva-Domingo et al 2021;Shao et al 2022a;Jespersen et al 2022;Delgado et al 2022;Lovell et al 2022;McGibbon & Khochfar 2022;von Marttens et al 2022;Rodrigues et al 2023).…”

“…For instance, in the context of cosmology, they do not impose any cut on the considered physical scales, and different physical symmetries (e.g., translational and rotational invariance) can be easily implemented in the models (see Villanueva-Domingo & Villaescusa-Navarro 2022). GNNs have been used for a variety of tasks, such as parameter inference (Shao et al 2022b;Anagnostidis et al 2022;Makinen et al 2022;, inferring halo masses (Villanueva-Domingo et al 2021), speeding up semi-analytic models (Jespersen et al 2022), and rediscovering Newton's law (Cranmer et al 2020).…”