Sample-efficient non-Gaussian noise reduction in gravitational wave data via learnable wavelets

TL;DR

This work tackles non-Gaussian noise in gravitational-wave data by introducing WaveletNet, a wavelet-based neural network that encodes an inductive bias toward glitch-like time-frequency structure. The architecture combines a learnable Morlet wavelet matched-filtering module with a small MLP head, producing an external score that can be modularly integrated into existing ranking pipelines. By training on nonlocal environmental data and summary statistics, WaveletNet achieves up to a ~15% improvement in the sensitive spacetime volume $VT$ for high-mass, asymmetric binaries, demonstrating superior data efficiency over generic CNNs. The approach is interpretable, adaptable to changing detector noise, and readily applicable to current and future GW search pipelines, including O4 and beyond.

Abstract

We introduce $\texttt{WaveletNet}$, a wavelet-based neural network architecture to identify and reduce non-Gaussian noise in gravitational wave data. Traditionally, convolutional neural networks (CNNs) have been widely used as a flexible machine learning method to mitigate non-Gaussian noise. However, training CNNs requires many data samples, especially when the input data segments are long. Glitches that mimic high-mass black hole signals are empirically known to have a wavelet-like structure. We exploit this property in $\texttt{WaveletNet}$ by using simple neural networks to learn the best family of wavelets to model glitches in the LIGO-Virgo-KAGRA O3 data. Due to its simplicity, our framework is significantly more sample-efficient than CNNs. As a use case, we build upon the $\texttt{TIER}$ method and show how $\texttt{WaveletNet}$ can improve the performance of any search pipeline. We take potential GW candidates from the pipeline, and then downweight the candidates having noisy strain regions in their vicinity. We use our framework in a modular way: we provide an output score which can be added to the pipeline's existing detection statistic score for the candidates. We test our method using candidates from the $\texttt{IAS-HM}$ search pipeline and show that it improves the search sensitive volume by up to 15% for high-mass, asymmetric binaries.

Figures (11)

• Figure 1: This figure illustrates the WaveletNet model architecture for evaluating the extended strain information in the vicinity of a GW candidate. Extended strain data in the $\pm \sim$15 s region surrounding each candidate is filtered through a bank of learnable Morlet wavelets, acting as matched filters and producing time-domain responses sensitive to transient structure in the environmental data. From each wavelet response, we extract the three largest peaks and their corresponding time indices, yielding a total of 36 wavelet-derived features across the six wavelets that we use. These features are concatenated with 20 additional summary statistical features (see Section \ref{['subsec:nonlocal']} for details), forming a combined 36+20=56 dimensional input feature vector. This vector is passed to a multi-layer perceptron with a single hidden layer of 64 units and a scalar output, which produces the final model score used for candidate ranking.
• Figure 2: Learned wavelets corresponding to a high-mass template bank (GW signals with total mass $M_\mathrm{tot} \approx 250 M_{\odot}$). Only the scale parameter of each wavelet is trained in our case. The central frequency and duration are held fixed to reduce computational cost (we find that varying them does not yield measurable performance gains in the O3 data). The resulting set of learned waveforms effectively function as a bank of glitch templates for this mass range.
• Figure 3: Examples of SNR responses of the wavelet with a glitchy data strain (left panels) and a non-glitchy data strain (right panels). The glitchy data strain containing higher non-Gaussian noise shows high SNR peaks response with wavelets compared to the non-glitchy data strain. Note that the SNR values on the y-axis are different between different panels.
• Figure 4: Comparison of a wavelet-based neural network vs. a CNN on a toy-model dataset (see section \ref{['sec:toy_model']} for details). This illustrates the effect of the inductive bias used in WaveletNet on data efficiency and training stability. Top panel: Validation accuracy as a function of training dataset size for a wavelet-based model and a CNN. The wavelet-based model achieves higher accuracy with fewer training samples. Bottom panel: Validation loss versus training epoch for the same models, showing stable convergence for the wavelet-based model and significantly larger fluctuations for the CNN. These results qualitatively demonstrate the advantage of incorporating signal-processing structure in limited-data regimes.
• Figure 5: The ranking statistic of a typical search pipeline ($\mathcal{L}_\mathrm{pipeline}$) uses local SNR from matched filtering to sort or rank a candidate event by its likelihood of being an astrophysical signal rather than noise. The TIER framework can be used to augment the ranking statistic of a pipeline by including complementary information about the extended strain data next to the candidate time (see Eq. \ref{['eq:NeymanPearson']}). We thus obtain the probability that the candidate is an astrophysical signal ($p^\mathrm{ext}$) based on the extended strain data and include it in the candidate ranking statistic.