Accelerated inference of microlensed gravitational waves with machine learning

Gravitational waves (GWs) within the LIGO-Virgo-KAGRA sensitivity band can be microlensed by stellar and intermediate-mass black holes, producing a frequency-dependent modulation of the signal amplitude. Microlensing analyses, however, are costly due to the increased dimensionality of the parameter space and waveform computation time. As a proof of concept, we show that the deep-learning-based framework Deep Inference for Gravitational-Wave Observations (DINGO), which employs a simulation-based inference approach to estimate posterior distributions, can perform efficient parameter inference for GW microlensing by an isolated point-mass lens. Using simulated microlensed GW signals, we train a lensed-DINGO network and compare its performance with traditional Bayesian parameter estimation carried out with Bilby. Our framework can be used to rapidly identify microlensed events in large GW catalogs. When the lensed-DINGO network is combined with importance sampling, we find that although sample efficiencies are somewhat reduced compared to the unlensed-DINGO network, owing to the richer structure of microlensed signals, it still achieves $\mathcal{O}(10\times)$ speed-up relative to Bilby. We further show that this framework is useful to efficiently estimate the background Bayes-factor distribution, which is crucial for assessing the significance of candidate lensed events. However, for foreground (lensed) events, the sampling efficiency can sometimes drop when analysed with the unlensed-DINGO network, providing a diagnostic indicator of out-of-distribution data. Our approach can be straightforwardly generalised to more complex and realistic lens models, enabling detailed studies of microlensed GWs.