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October 20, 2025Open Access

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

JJJun-Qian JiangUniversity of Trento HHH. X. HuangChina Institute of Atomic Energy JHJibin HeChina Geological Survey

Key Points

Using deep learning, the framework processes GW events in seconds, enhancing PBH population estimates.
Transformers and normalizing flows provide accurate posterior distributions while allowing for rapid computations.
Traditional Bayesian methods struggle with large GW catalogs, but this approach remains efficient for hundreds of events.
The findings indicate the substantial potential of deep learning in next-generation gravitational wave studies.

Abstract

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 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.

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