A wavelet filter for gravitational waves: hearing the cosmos without templates ✎

Original: "The Wavelet Detection Filter: a real time unmodeled pipeline for gravitational wave transients, ranking coincidences with a graph neural network"
· Elena Cuoco
arXiv:2609.12797v1 · 2026-09-11 · arXiv non-exclusive · independent analysis · 3 min
A new pipeline catches gravitational bursts without any precomputed signal models and ranks coincidences with a graph neural network.

Context

Gravitational-wave astronomy is booming: the LIGO, Virgo and KAGRA detectors regularly register mergers of compact objects. Most confident detections come from matched filtering, which demands accurate signal models. Yet not every source can be described by such models: supernova bursts, neutron-star oscillations, post-merger emission and unexpected short transients have an uncertain or entirely unknown shape. That is why we need searches that do not presuppose a fixed family of templates. They typically hunt for excess energy or coherent structure in a time-frequency representation. This work sits alongside efforts to build template-free searches such as coherent WaveBurst and BayesWave, but it stands out by taking the wavelet approach all the way to a full low-latency pipeline with coincidence ranking by a graph neural network.

Methods

The pipeline processes detector data as a continuous stream. First the data are whitened with a zero-phase autoregressive filter, which preserves the shape of a transient and operates with a fixed delay. Then each analysis block of 250 ms is decomposed over ten orthonormal wavelet bases. Coefficients above a threshold set by the noise level are kept, and their norm serves as the detection statistic. Triggers from consecutive windows are grouped into single-detector events by geometric rules of proximity in time, frequency and energy. Events from different detectors become nodes of a graph, and edges connect pairs compatible in arrival time and frequency support. This graph is ranked by a graph neural network trained either with supervision on injected signals or without supervision on random coincidences.

Results

On simulated data with noise coloured according to the Advanced LIGO sensitivity curve, the search recovers 0.99 of binary black holes, 0.87–0.86 of black hole–neutron star systems, 0.47–0.50 of binary neutron stars and 0.60–0.63 of supernova bursts in a single detector. On real O4 data the efficiency is higher: 0.995–0.999 for binary black holes, 0.943–0.966 for black hole–neutron star systems, 0.799–0.859 for binary neutron stars and 0.524–0.572 for supernovae. Network ranking with the graph neural network beats the deterministic statistic: at one false alarm per day on real data the GNN recovers 0.28 of the coincident population against 0.08 for Rmor, and at ten per day, 0.85 against 0.56. For the event GW250114 the template-free pipeline identifies it as the loudest candidate with zero delay in the analysed segment.

Implications

The work shows that a wavelet representation can support detection, ranking and reconstruction of transients within a single pipeline. Unlike neighbouring studies, which often focus on one stage, here the entire path from whitened data to a calibrated candidate and sky region runs without a signal model. Using a graph neural network to rank coincidences directly on the trigger graph is the first of its kind for template-free searches. This paves the way to a more sensitive real-time hunt for unexpected sources.

Future development

The topic could grow toward parameter estimation with normalizing flows on the same coefficients that gave the pipeline its name. Another direction is a full low-latency test of the chain with the frontend ported to hardware platforms such as FPGAs. Both directions are already built into the architectural choices of the work.

Impact

The method will influence gravitational-wave astronomy, especially the search for supernova bursts and other non-modelled sources. It may also prove useful for automatic classification of instrumental noise.

Next steps

Analysing longer stretches of real data to measure efficiency at rates typical of an observing run. Training the model on real noise with labelled events.

Key open problems

The key unsolved problem of gravitational-wave astronomy is detecting transients without precise models, especially from supernova bursts. The work addresses this problem head-on, offering a pipeline that assumes no signal shape yet still delivers calibrated significance and reconstruction.

The event GW250114 was found by the pipeline without templates, even though its network signal-to-noise is around 80 and the false alarm rate is extremely small. The wavelet filter uses ten different bases so that every signal is represented in its most compact form.

The idea of hearing the cosmos without ready-made templates echoes Carl Sagan's novel Contact, where a signal of extraterrestrial origin was detected precisely because it did not resemble the expected noise.

\rho^{(b)}_{WDF} = \frac{\|c^{(b)}\|_2}{\sigma}
Amplitude signal-to-noise ratio of the reconstruction
s_{ij} = \frac{\langle \log(1+W_i), \log(1+W_j) \rangle}{\|\log(1+W_i)\|_2 \|\log(1+W_j)\|_2}
Cosine similarity of shapes, independent of amplitudes
R^{mor}_{ij} = \left| \sum_{(k,l)} \frac{c^{(i)}_k}{\sigma_i} \frac{c^{(j)}_l}{\sigma_j} \right|
Coherent energy of the pair in units of the squared noise

Key numbers

  • processing speed: about 10 ms per second of data for two detectors on a single core
  • pipeline latency: about 3 seconds, fixed by the filters
  • accuracy of arrival-time difference: 0.44 ms on real O4 data at SNR ≥ 40
  • efficiency for binary black holes in a single detector: 0.995–0.999 on real O4 data
  • network efficiency at one false alarm per day: 0.28 against 0.08 for the deterministic statistic
Scientists
Bernhard RiemannJoseph WeberKarl SchwarzschildKip ThorneRainer WeissAlbert Einstein
Concepts
wavelet transform matched filter gravitational wave noise filtering template Filtering gravitational wave detection optical filter wavelet analysis white dwarf pulsar timing array Doppler effect waveform gwtc waveguide silicon wafer Wright–Fisher model radiation detector interferometer Wheeler-DeWitt equation outlier rejection