Fast and realistic large-scale structure from machine-learning-augmented random field simulations

Producing thousands of simulations of the dark matter distribution in the Universe with increasing precision is a challenging but critical task to facilitate the exploitation of current and forthcoming cosmological surveys. Many inexpensive substitutes to full $N$-body simulations have been proposed, even though they often fail to reproduce the statistics of the smaller, non-linear scales. Among these alternatives, a common approximation is represented by the lognormal distribution, which comes with its own limitations as well, while being extremely fast to compute even for high-resolution density fields. In this work, we train a machine learning model to transform projected lognormal dark matter density fields to more realistic dark matter maps, as obtained from full $N$-body simulations. We detail the procedure that we follow to generate highly correlated pairs of lognormal and simulated maps, which we use as our training data, exploiting the information of the Fourier phases. We demonstrate the performance of our model comparing various statistical tests with different field resolutions, redshifts and cosmological parameters, proving its robustness and explaining its current limitations. The augmented lognormal random fields reproduce the power spectrum up to wavenumbers of $1 \ h \ \rm{Mpc}^{-1}$, the bispectrum and the peak counts within 10%, and always within the error bars, of the fiducial target simulations. Finally, we describe how we plan to integrate our proposed model with existing tools to yield more accurate spherical random fields for weak lensing analysis, going beyond the lognormal approximation.

Learning cosmology and clustering with cosmic graphs

We train deep learning models on thousands of galaxy catalogues from the state-of-the-art hydrodynamic simulations of the CAMELS project to perform regression and inference. We employ Graph Neural Networks (GNNs), architectures designed to work with irregular and sparse data, like the distribution of galaxies in the Universe. We first show that GNNs can learn to compute the power spectrum of galaxy catalogues with a few percent accuracy. We then train GNNs to perform likelihood-free inference at the galaxy-field level. Our models are able to infer the value of $\Omega_{\rm m}$ with a $\sim12\%-13\%$ accuracy just from the positions of $\sim1000$ galaxies in a volume of $(25~h^{-1}{\rm Mpc})^3$ at $z=0$ while accounting for astrophysical uncertainties as modelled in CAMELS. Incorporating information from galaxy properties, such as stellar mass, stellar metallicity, and stellar radius, increases the accuracy to $4\%-8\%$. Our models are built to be translational and rotational invariant, and they can extract information from any scale larger than the minimum distance between two galaxies. However, our models are not completely robust: testing on simulations run with a different subgrid physics than the ones used for training does not yield as accurate results.

Machine Learning and Cosmology

Methods based on machine learning have recently made substantial inroads in many corners of cosmology. Through this process, new computational tools, new perspectives on data collection, model development, analysis, and discovery, as well as new communities and educational pathways have emerged. Despite rapid progress, substantial potential at the intersection of cosmology and machine learning remains untapped. In this white paper, we summarize current and ongoing developments relating to the application of machine learning within cosmology and provide a set of recommendations aimed at maximizing the scientific impact of these burgeoning tools over the coming decade through both technical development as well as the fostering of emerging communities.

Augmenting astrophysical scaling relations with machine learning : application to reducing the SZ flux-mass scatter

Complex systems (stars, supernovae, galaxies, and clusters) often exhibit low scatter relations between observable properties (e.g., luminosity, velocity dispersion, oscillation period, temperature). These scaling relations can illuminate the underlying physics and can provide observational tools for estimating masses and distances. Machine learning can provide a systematic way to search for new scaling relations (or for simple extensions to existing relations) in abstract high-dimensional parameter spaces. We use a machine learning tool called symbolic regression (SR), which models the patterns in a given dataset in the form of analytic equations. We focus on the Sunyaev-Zeldovich flux$-$cluster mass relation ($Y_\mathrm{SZ}-M$), the scatter in which affects inference of cosmological parameters from cluster abundance data. Using SR on the data from the IllustrisTNG hydrodynamical simulation, we find a new proxy for cluster mass which combines $Y_\mathrm{SZ}$ and concentration of ionized gas ($c_\mathrm{gas}$): $M \propto Y_\mathrm{conc}^{3/5} \equiv Y_\mathrm{SZ}^{3/5} (1-A\, c_\mathrm{gas})$. $Y_\mathrm{conc}$ reduces the scatter in the predicted $M$ by $\sim 20-30$% for large clusters ($M\gtrsim 10^{14}\, h^{-1} \, M_\odot$) at both high and low redshifts, as compared to using just $Y_\mathrm{SZ}$. We show that the dependence on $c_\mathrm{gas}$ is linked to cores of clusters exhibiting larger scatter than their outskirts. Finally, we test $Y_\mathrm{conc}$ on clusters from simulations of the CAMELS project and show that $Y_\mathrm{conc}$ is robust against variations in cosmology, astrophysics, subgrid physics, and cosmic variance. Our results and methodology can be useful for accurate multiwavelength cluster mass estimation from current and upcoming CMB and X-ray surveys like ACT, SO, SPT, eROSITA and CMB-S4.

The CAMELS project: public data release

The Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project was developed to combine cosmology with astrophysics through thousands of cosmological hydrodynamic simulations and machine learning. CAMELS contains 4,233 cosmological simulations, 2,049 N-body and 2,184 state-of-the-art hydrodynamic simulations that sample a vast volume in parameter space. In this paper we present the CAMELS public data release, describing the characteristics of the CAMELS simulations and a variety of data products generated from them, including halo, subhalo, galaxy, and void catalogues, power spectra, bispectra, Lyman-$\alpha$ spectra, probability distribution functions, halo radial profiles, and X-rays photon lists. We also release over one thousand catalogues that contain billions of galaxies from CAMELS-SAM: a large collection of N-body simulations that have been combined with the Santa Cruz Semi-Analytic Model. We release all the data, comprising more than 350 terabytes and containing 143,922 snapshots, millions of halos, galaxies and summary statistics. We provide further technical details on how to access, download, read, and process the data at \url{https://camels.readthedocs.io}.

Weighing the Milky Way and Andromeda with Artificial Intelligence

We present new constraints on the masses of the halos hosting the Milky Way and Andromeda galaxies derived using graph neural networks. Our models, trained on thousands of state-of-the-art hydrodynamic simulations of the CAMELS project, only make use of the positions, velocities and stellar masses of the galaxies belonging to the halos, and are able to perform likelihood-free inference on halo masses while accounting for both cosmological and astrophysical uncertainties. Our constraints are in agreement with estimates from other traditional methods.

Inferring halo masses with Graph Neural Networks

Understanding the halo-galaxy connection is fundamental in order to improve our knowledge on the nature and properties of dark matter. In this work we build a model that infers the mass of a halo given the positions, velocities, stellar masses, and radii of the galaxies it hosts. In order to capture information from correlations among galaxy properties and their phase-space, we use Graph Neural Networks (GNNs), that are designed to work with irregular and sparse data. We train our models on galaxies from more than 2,000 state-of-the-art simulations from the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project. Our model, that accounts for cosmological and astrophysical uncertainties, is able to constrain the masses of the halos with a $\sim$0.2 dex accuracy. Furthermore, a GNN trained on a suite of simulations is able to preserve part of its accuracy when tested on simulations run with a different code that utilizes a distinct subgrid physics model, showing the robustness of our method. The PyTorch Geometric implementation of the GNN is publicly available on Github at https://github.com/PabloVD/HaloGraphNet

The CAMELS Multifield Dataset: Learning the Universe's Fundamental Parameters with Artificial Intelligence

We present the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) Multifield Dataset, CMD, a collection of hundreds of thousands of 2D maps and 3D grids containing many different properties of cosmic gas, dark matter, and stars from 2,000 distinct simulated universes at several cosmic times. The 2D maps and 3D grids represent cosmic regions that span $\sim$100 million light years and have been generated from thousands of state-of-the-art hydrodynamic and gravity-only N-body simulations from the CAMELS project. Designed to train machine learning models, CMD is the largest dataset of its kind containing more than 70 Terabytes of data. In this paper we describe CMD in detail and outline a few of its applications. We focus our attention on one such task, parameter inference, formulating the problems we face as a challenge to the community. We release all data and provide further technical details at https://camels-multifield-dataset.readthedocs.io.

Robust marginalization of baryonic effects for cosmological inference at the field level

We train neural networks to perform likelihood-free inference from $(25\,h^{-1}{\rm Mpc})^2$ 2D maps containing the total mass surface density from thousands of hydrodynamic simulations of the CAMELS project. We show that the networks can extract information beyond one-point functions and power spectra from all resolved scales ($\gtrsim 100\,h^{-1}{\rm kpc}$) while performing a robust marginalization over baryonic physics at the field level: the model can infer the value of $\Omega_{\rm m} (\pm 4\%)$ and $\sigma_8 (\pm 2.5\%)$ from simulations completely different to the ones used to train it.