We train neural networks to perform likelihood-free inference from (25 h −1 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 ( 100 h −1 kpc) while performing a robust marginalization over baryonic physics at the field level: the model can infer the value of Ωm(±4%) and σ8(±2.5%) from simulations completely different to the ones used to train it.

We train graph neural networks on halo catalogs from Gadget N-body simulations to perform field-level likelihood-free inference of cosmological parameters. The catalogs contain ≲5000 halos with masses ≳1010 h −1 M ⊙ in a periodic volume of ( 25 h − 1 Mpc ) 3 ; every halo in the catalog is characterized by several properties such as position, mass, velocity, concentration, and maximum circular velocity. Our models, built to be permutationally, translationally, and rotationally invariant, do not impose a minimum scale on which to extract information and are able to infer the values of Ωm and σ 8 with a mean relative error of ∼6%, when using positions plus velocities and positions plus masses, respectively. More importantly, we find that our models are very robust: they can infer the value of Ωm and σ 8 when tested using halo catalogs from thousands of N-body simulations run with five different N-body codes: Abacus, CUBEP3M, Enzo, PKDGrav3, and Ramses. Surprisingly, the model trained to infer Ωm also works when tested on thousands of state-of-the-art CAMELS hydrodynamic simulations run with four different codes and subgrid physics implementations. Using halo properties such as concentration and maximum circular velocity allow our models to extract more information, at the expense of breaking the robustness of the models. This may happen because the different N-body codes are not converged on the relevant scales corresponding to these parameters.

We present the Cosmology and Astrophysics with Machine Learning Simulations (CAMELS) Multifield Data set (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 more than 2000 distinct simulated universes at several cosmic times. The 2D maps and 3D grids represent cosmic regions that span ∼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 data set of its kind containing more than 70 TB 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.

We use a generic formalism designed to search for relations in high-dimensional spaces to determine if the total mass of a subhalo can be predicted from other internal properties such as velocity dispersion, radius, or star formation rate. We train neural networks using data from the Cosmology and Astrophysics with MachinE Learning Simulations project and show that the model can predict the total mass of a subhalo with high accuracy: more than 99% of the subhalos have a predicted mass within 0.2 dex of their true value. The networks exhibit surprising extrapolation properties, being able to accurately predict the total mass of any type of subhalo containing any kind of galaxy at any redshift from simulations with different cosmologies, astrophysics models, subgrid physics, volumes, and resolutions, indicating that the network may have found a universal relation. We then use different methods to find equations that approximate the relation found by the networks and derive new analytic expressions that predict the total mass of a subhalo from its radius, velocity dispersion, and maximum circular velocity. We show that in some regimes, the analytic expressions are more accurate than the neural networks. The relation found by the neural network and approximated by the analytic equation bear similarities to the virial theorem.