Search for primordial black holes from gravitational wave populations using deep learning

Gravitational waves (GWs) signals detected by the LIGO/Virgo/KAGRA collaboration might be sourced (partly) by the merges of primordial black holes (PBHs). The conventional hierarchical Bayesian inference methods can allow us to study population properties of GW events to search for the hints for PBHs. However, hierarchical Bayesian analysis require an analytic population model, and becomes increasingly computationally expensive as the number of sources grows. In this paper, we present a novel population analysis method based on deep learning, which enables the direct and efficient estimation of PBH population hyperparameters, such as the PBH fraction in dark matter, $f_{\rm PBH}$. Our approach leverages neural posterior estimation combined with conditional normalizing flows and two embedding networks. Our results demonstrate that inference can be performed within seconds, highlighting the promise of deep learning as a powerful tool for population inference with an increasing number of GW signals for next-generation detectors.