Detection of Lensed Gravitational Waves from dark matter halos with deep learning

TL;DR

This work addresses the challenge of detecting lensed gravitational waves from dark matter substructures by developing a deep learning framework that leverages multiband observations from DECIGO and the Einstein Telescope. A residual 1D CNN performs end-to-end classification of time-domain waveforms into five classes (PN, UL, SIS, CIS, NFW), using a dataset of 10^6 simulated samples spanning SNRs from 5 to 100. The joint ET+DECIGO model significantly outperforms single detectors, achieving about 97% accuracy and near-perfect discrimination at moderate-to-high SNR, thereby demonstrating the strong benefit of multiband information for accurate and robust lensed GW identification in noisy environments. This approach provides a scalable, automated pathway for probing dark matter halos with future multiband GW observatories and offers a foundation for incorporating more complex lens models and parameter estimation in subsequent work.

Abstract

Lensed gravitational waves (GWs) provide a new window into the study of dark matter substructures, yet the faint interference signatures they produce are buried in detector noise. To address this challenge, we develop a deep learning framework based on a residual one-dimensional convolutional neural network for lensed GW identification under multiband observations. The model directly processes multiband waveforms from binary neutron star systems, covering the early inspiral observed by the DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) and the late inspiral observed by the Einstein Telescope (ET), corresponding approximately to the wave-optics and geometrical-optics regimes, respectively. It enables end-to-end classification of five classes: pure noise, unlensed GWs, and three representative lensed GWs corresponding to singular isothermal sphere (SIS), cored isothermal sphere (CIS), and Navarro-Frenk-White (NFW) profiles. A dataset of 10^6 simulated samples was constructed with signal-to-noise ratios (SNR) ranging from 5 to 100. The deep learning model with multiband observations achieves an accuracy of 97.0% and a macro-averaged F1 score of 0.97, significantly exceeding the single-detector performance, where DECIGO and ET reach 72.8% and 62.3%, respectively. Even in the low-SNR regime (SNR < 20), the model maintains an accuracy above 63%, while in the high-SNR regime (SNR > 80), its accuracy approaches 99.8%. These results demonstrate that multiband GW observations effectively enhance the detection of lensed GWs within complex noise environments, providing a robust and efficient pathway for the automated identification of lensed GWs in future multiband observations.

Figures (12)

• Figure 1: Amplitude spectral densitie (ASD) of DECIGO and ET compared with that of a representative BNS gravitational wave.
• Figure 2: Frequency and time domain waveforms of BNS ($m_{1}=m_{2}=1.4\,M_\odot$, $d_{L}=100~\mathrm{Mpc}$) under SIS, CIS, and NFW lensing models, as observed by DECIGO. The lens parameters are $M_{L}=2\times10^{3}\,M_\odot$, $\psi_{0}=1.0$, $r_{c}=0.3$, $r_{s}=0.3$, and $y=0.3$.
• Figure 3: Frequency and time domain waveforms of ($m_{1}=m_{2}=1.4\,M_\odot$, $d_{L}=100~\mathrm{Mpc}$) under SIS, CIS, and NFW lensing models, as observed by ET. The lens parameters are $M_{L}=2\times10^{3}\,M_\odot$, $\psi_{0}=1.0$, $r_{c}=0.3$, $r_{s}=0.3$, and $y=0.3$.
• Figure 4: SNR distributions of simulated samples for DECIGO and ET detectors.
• Figure 5: Architecture of the residual stacked convolutional network.