Parameter inference of millilensed gravitational waves using neural spline flows

When gravitational waves (GWs) propagate near massive objects, they undergo gravitational lensing that imprints lens model dependent modulations on the waveform. This effect provides a powerful tool for cosmological and astrophysical studies. Due to the added parameters of lenses and the uncertainty of lens models, parameter inference for lensed GW events using traditional methods is extremely time-consuming, thus requiring more efficient parameter inference methods. In this work, we explore the use of neural spline flows (NSFs) for posterior inference of millilensed GWs, and successfully apply NSFs to the inference of 11-dimensional lens parameters. Our results demonstrate that compared with traditional methods like Bilby dynesty that rely on Bayesian inference, the NSF network we built not only achieves inference accuracy comparable to traditional methods for most parameters, but also can reduce the inference time from approximately 3 days to 0.8 s on average. Additionally, the network exhibits strong generalization for the spin parameters of GW sources. It is anticipated to become a powerful tool for future low-latency searches for lensed GW signals.