Neural network emulator of the Advanced LIGO and Advanced Virgo selection function

Characterization of search selection effects comprises a core element of gravitational-wave data analysis. Knowledge of selection effects is needed to predict observational prospects for future surveys and is essential in the statistical inference of astrophysical source populations from observed catalogs of compact binary mergers. Although gravitational-wave selection functions can be directly measured via injection campaigns---the insertion and attempted recovery of simulated signals added to real instrumental data---such efforts are computationally expensive. Moreover, the inability to interpolate between discrete injections limits the ability to which we can study narrow or discontinuous features in the astrophysical distribution of compact binary properties. For this reason, there is a growing need for alternative representations of gravitational-wave selection functions that are computationally cheap to evaluate and can be computed across a continuous range of compact binary parameters. In this paper, we describe one such representation. Using pipeline injections performed during Advanced LIGO and Advanced Virgo's third observing run (O3), we train a neural network emulator for $P(\mathrm{det}|\ensuremath{\theta})$, the probability that a given compact binary with parameters is successfully detected, averaged over the course of O3. The emulator captures the dependence of $P(\mathrm{det}|\ensuremath{\theta})$ on binary masses, spins, distance, sky position, and orbital orientation, and it is valid for compact binaries with component masses between 1 and $100{M}_{\ensuremath{\bigodot}}$. We test the emulator's ability to produce accurate distributions of detectable events, and demonstrate its use in hierarchical inference of the binary black hole population.