A Swarm-Based Search for Gravitational-Wave Echoes

Searching for overlapping cosmic signals

Gravitational waves carry information about the compact objects that produce them. If a massive foreground object bends their path, multiple copies can reach an observer with different strengths and arrival times. When those copies overlap, their interference changes the measured waveform, complicating the task of identifying the source.

In a November 9, 2026 arXiv preprint, Weiqing Yu, Meng Zhang, Xiaobo Zou and Xiao Guo investigate particle swarm optimization, or PSO, as a tool for this problem. Their results come from simulated signals, not a newly observed lensed event. The supplied manuscript is a preprint; it does not establish peer-reviewed acceptance.

How the swarm works

PSO sends many candidate solutions through a mathematical search space. Each candidate—a “particle”—adjusts its movement using both its own best result and the best result discovered by the group. Here, success means finding a predicted gravitational-wave signal that closely matches the simulated detector data.

The researchers model a network with the locations and orientations of LIGO Hanford, LIGO Livingston, Virgo and KAGRA. They combine information across the network, accounting for how a signal would arrive at each detector.

Some parameters are handled analytically, and the signal’s arrival time is searched using a fast Fourier transform. That leaves six quantities for the swarm: two parameters related to the binary’s masses, two sky coordinates, and two describing lensing.

Those lensing quantities are the relative flux of the secondary image and its delay behind the primary image. They describe observable interference without requiring the search to estimate a particular lens’s mass directly. However, this is not a universal lensing model: the simulations use a specific lens prescription, and the search assumes two-image interference in the geometric-optics regime.

Each search uses 50 particles and up to 1,000 iterations. The team runs 12 independent searches per sample to reduce dependence on random starting positions.

Good matches—and misleading ones

The dataset contains 1,050 samples: 350 lensed signals, 350 unlensed signals and 350 noise-only examples. Of the signal examples, 70% use the same restricted second-order post-Newtonian waveform approximation as the search template. The remaining 30% use IMRPhenomD, a more complete waveform model that includes merger and ringdown.

When signal and template models match, the authors report generally successful recovery of chirp mass, mass ratio, sky position and lensing parameters. Chirp mass is a combination of the two component masses that strongly controls how the signal’s frequency rises.

The mismatch experiment exposes an important limitation. Searching the more complete signals with the simpler template produces substantial mass biases; many inferred mass ratios become unphysical. Sky position and lensing parameters fare better in the reported comparisons. Finding a strong mathematical match, therefore, does not guarantee accurate physical parameters when the template is inadequate.

What 86% accuracy conceals

The classification pipeline combines votes from the 12 searches with signal-strength and flux-ratio thresholds. It correctly labels 905 of 1,050 samples, giving the reported 86.19% overall accuracy.

Performance differs sharply by category. It identifies 339 of 350 noise samples and 328 of 350 unlensed signals correctly, but only 238 of 350 lensed signals—about 68%.

The weakest secondary images are especially troublesome. For signals whose true secondary-to-primary flux ratio is below 0.15, only 17.9% are correctly classified as lensed. Every error in that subset is an unlensed label rather than a noise label. The method often recognizes that a gravitational wave is present while missing its lensing signature.

These results describe an equally balanced simulated dataset, not the probability that a candidate in an observational search would genuinely be lensed.

Faster uncertainty estimates, with a caveat

PSO produces best-fit points, not full uncertainty distributions. The authors therefore use its results to construct a mixture of Gaussian distributions that becomes the prior for nested sampling, a Bayesian inference method. They call the combination PSO_GAUSS_MIX.

For matched waveforms, nested sampling alone falls from roughly 401 seconds to 141 seconds on average. Including the initial PSO search brings the combined time to about 290 seconds: an overall speedup of approximately 1.38 times, rather than the sampling-only 2.84 times.

The authors report broadly consistent main posterior regions and narrower intervals. But narrower is not automatically more accurate. Because the new prior is constructed from searches of the same data, this comparison does not by itself demonstrate unchanged uncertainty calibration. Restricting the prior also risks excluding regions the swarm missed.

Finally, the simulations use Gaussian noise and the same assumed sensitivity spectrum for all four detectors. Real non-Gaussian disturbances remain untested. The study supports further investigation of PSO as a search accelerator, not a demonstrated observational lensing detector.