A Hybrid Deep Learning Approach to Cosmological Constraints From Galaxy
  Redshift Surveys
  We present a deep machine learning (ML)-based technique for accurately
determining $\sigma_8$ and $\Omega_m$ from mock 3D galaxy surveys. The mock
surveys are built from the AbacusCosmos suite of $N$-body simulations, which
comprises 40 cosmological volume simulations spanning a range of cosmological
models, and we account for uncertainties in galaxy formation scenarios through
the use of generalized halo occupation distributions (HODs). We explore a trio
of ML models: a 3D convolutional neural network (CNN), a power-spectrum-based
fully connected network, and a hybrid approach that merges the two to combine
physically motivated summary statistics with flexible CNNs. We describe best
practices for training a deep model on a suite of matched-phase simulations and
we test our model on a completely independent sample that uses previously
unseen initial conditions, cosmological parameters, and HOD parameters. Despite
the fact that the mock observations are quite small
($\sim0.07h^{-3}\,\mathrm{Gpc}^3$) and the training data span a large parameter
space (6 cosmological and 6 HOD parameters), the CNN and hybrid CNN can
constrain $\sigma_8$ and $\Omega_m$ to $\sim3\%$ and $\sim4\%$, respectively.
