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.