Gravitational-wave population inference in seconds with variational neural posteriors

The LIGO-Virgo-KAGRA observational catalog has been analyzed with an abundance of differing population models due to theoretical uncertainty in the formation of gravitational-wave sources, requiring repeated computationally costly analyses. We remove this barrier by introducing an efficient variational Bayesian approach that serves as a drop-in replacement for traditional inference methods by employing a normalizing flow to learn the population posterior directly. Inference takes just seconds with hardware acceleration for the current set of detected black-hole mergers and readily scales to increasing catalog sizes, requiring a fixed number of likelihood evaluations due to super-convergent training. The learned posteriors provide exact density evaluations and an arbitrary number of samples - unlike stochastic sampling algorithms from which the results are otherwise statistically indistinguishable - and importance-weighted evidence estimation for Bayesian model selection. Robust astrophysical inference can be both rapid and accurate, enabling hitherto intractable applications such as interactive model development, large-scale feature significance testing, and low-latency rates and populations updating.