Fast sky localization of gravitational waves using deep learning seeded importance sampling

Fast, highly accurate, and reliable inference of the sky origin of gravitational waves would enable real-time multimessenger astronomy. Current Bayesian inference methodologies, although highly accurate and reliable, are slow. Deep learning models have shown themselves to be accurate and extremely fast for inference tasks on gravitational waves, but their output is inherently questionable due to the blackbox nature of neural networks. In this work, we merge Bayesian inference and deep learning by applying importance sampling on an approximate posterior generated by a multiheaded convolutional neural network. The neural network parametrizes Von Mises-Fisher and Gaussian distributions for the sky coordinates and two masses for given simulated gravitational wave injections in the LIGO and Virgo detectors. We generate skymaps for unseen gravitational-wave events that highly resemble predictions generated using Bayesian inference in a few minutes. Furthermore, we can detect poor predictions from the neural network, and quickly flag them.