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.

Multifield Cosmology with Artificial Intelligence

Astrophysical processes such as feedback from supernovae and active galactic nuclei modify the properties and spatial distribution of dark matter, gas, and galaxies in a poorly understood way. This uncertainty is one of the main theoretical obstacles to extract information from cosmological surveys. We use 2,000 state-of-the-art hydrodynamic simulations from the CAMELS project spanning a wide variety of cosmological and astrophysical models and generate hundreds of thousands of 2-dimensional maps for 13 different fields: from dark matter to gas and stellar properties. We use these maps to train convolutional neural networks to extract the maximum amount of cosmological information while marginalizing over astrophysical effects at the field level. Although our maps only cover a small area of $(25~h^{-1}{\rm Mpc})^2$, and the different fields are contaminated by astrophysical effects in very different ways, our networks can infer the values of $\Omega_{\rm m}$ and $\sigma_8$ with a few percent level precision for most of the fields. We find that the marginalization performed by the network retains a wealth of cosmological information compared to a model trained on maps from gravity-only N-body simulations that are not contaminated by astrophysical effects. Finally, we train our networks on multifields -- 2D maps that contain several fields as different colors or channels -- and find that not only they can infer the value of all parameters with higher accuracy than networks trained on individual fields, but they can constrain the value of $\Omega_{\rm m}$ with higher accuracy than the maps from the N-body simulations.