A volumetric deep Convolutional Neural Network for simulation of mock dark matter halo catalogues

For modern large-scale structure survey techniques it has become standard practice to test data analysis pipelines on large suites of mock simulations, a task which is currently prohibitively expensive for full N-body simulations. Instead of calculating this costly gravitational evolution, we have trained a three-dimensional deep Convolutional Neural Network (CNN) to identify dark matter protohaloes directly from the cosmological initial conditions. Training on halo catalogues from the Peak Patch semi-analytic code, we test various CNN architectures and find they generically achieve a Dice coefficient of similar to 92 per cent in only 24 h of training. We present a simple and fast geometric halo finding algorithm to extract haloes from this powerful pixel-wise binary classifier and find that the predicted catalogues match the mass function and power spectra of the ground truth simulations to within similar to 10 per cent. We investigate the effect of long-range tidal forces on an object-by-object basis and find that the network's predictions are consistent with the non-linear ellipsoidal collapse equations used explicitly by the Peak Patch algorithm.