  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.
