  Many different studies have shown that a wealth of cosmological information
resides on small, non-linear scales. Unfortunately, there are two challenges to
overcome to utilize that information. First, we do not know the optimal
estimator that will allow us to retrieve the maximum information. Second,
baryonic effects impact that regime significantly and in a poorly understood
manner. Ideally, we would like to use an estimator that extracts the maximum
cosmological information while marginalizing over baryonic effects. In this
work we show that neural networks can achieve that. We made use of data where
the maximum amount of cosmological information is known: power spectra and 2D
Gaussian density fields. We also contaminate the data with simplified baryonic
effects and train neural networks to predict the value of the cosmological
parameters. For this data, we show that neural networks can 1) extract the
maximum available cosmological information, 2) marginalize over baryonic
effects, and 3) extract cosmological information that is buried in the regime
dominated by baryonic physics. We also show that neural networks learn the
priors of the data they are trained on. We conclude that a promising strategy
to maximize the scientific return of cosmological experiments is to train
neural networks on state-of-the-art numerical simulations with different
strengths and implementations of baryonic effects.
