Emulating compact binary population synthesis simulations with uncertainty quantification and model comparison using Bayesian normalizing flows

Population synthesis simulations of compact binary coalescences~(CBCs) play a crucial role in extracting astrophysical insights from an ensemble of gravitational wave~(GW) observations. However, realistic simulations can be costly to implement for a dense grid of initial conditions. Normalizing flows can emulate population synthesis runs to enable simulation-based inference from observed catalogs and data augmentation for feature prediction in rarely synthesizable sub-populations. However, flow predictions can be wrought with uncertainties, especially for sparse training sets. In this work, we develop a method for quantifying and marginalizing uncertainties in the emulators by implementing the Bayesian Normalizing flow, a conditional density estimator constructed from Bayesian neural networks. Using the exact likelihood function naturally associated with density estimators, we sample the posterior distribution of flow parameters with suitably chosen priors to quantify and marginalize over flow uncertainties. We demonstrate the accuracy, calibration, inference, and data-augmentation impacts of the estimated uncertainties for simulations of binary black hole populations formed through common envelope evolution. We outline the applications of the proposed methodology in the context of simulation-based inference from growing GW catalogs and feature prediction, with state-of-the-art binary evolution simulators, now marginalized over model and data uncertainties.