A fast deep-learning approach to probing primordial black hole populations in gravitational wave events

Primordial black holes (PBHs), envisioned as a compelling dark matter candidate and a window onto early-Universe physics, may contribute to the part of the gravitational-wave (GW) signals detected by the LIGO-Virgo-KAGRA network. Traditional hierarchical Bayesian analysis, which relies on precise GW-event posterior estimates, for extracting the information of potential PBH population from GW events become computationally prohibitive for catalogs of hundreds of events. Here, we present a fast deep-learning framework, leveraging Transformer and normalizing flows, that maps GW-event posterior samples to joint posterior distributions over the hyperparameters of the PBH population. Our approach yields accurate credible intervals while reducing end-to-end inference time to $\mathcal{O}(1)$ s on a single GPU. These results underscore the potential of deep learning for fast, high-accurately PBH population studies in the era of next-generation GW detectors.