Identifying lensed gravitational waves with physics-informed posterior learning

Gravitational lensing of gravitational waves can probe compact lenses, dark matter substructure, and cosmological distances, but identifying lensed events is difficult when unrelated binary mergers overlap in the same analysis window. We develop physics-informed posterior learning for ranking lensed multi-image signals against unrelated multiple-merger events. The method exploits the geometric-optics consistency that lensing can change amplitudes, arrival times, and Morse phase offsets while preserving the intrinsic phase evolution of the source. We infer a simulation-trained approximate posterior for the common detector-frame chirp mass and symmetric mass ratio, and fuse posterior samples with direct waveform features. Training uses generic multi-image simulations, while point-mass, singular-isothermal-sphere, singular-isothermal-ellipsoid, and shear-perturbed lenses are reserved for held-out lens-family evaluation. For the observationally motivated binary-black-hole population, the fusion ranking raises the detection efficiency from 20.8% to 35.2% at a 1% reference false-positive-rate threshold calibrated on the corresponding unrelated multiple-merger sample. It lowers the network signal-to-noise ratio needed for 50% detection efficiency from 45.3 to 33.5, which corresponds to a 1.35 times larger signal-to-noise-ratio-equivalent distance scale. The gain is limited by loud unrelated multiple-merger events that are partly source consistent, and by the need to calibrate the unrelated multiple-merger population. These results suggest that physical consistency can become a guiding principle for machine learning searches in dense gravitational-wave catalogs.