Convolutional neural networks for the detection of the early inspiral of a gravitational-wave signal

GW170817 has led to the first example of multimessenger astronomy with observations from gravitational wave interferometers and electromagnetic telescopes combined to characterize the source. However, detections of the early inspiral phase by the gravitational wave detectors would allow the observation of the earlier stages of the merger in the electromagnetic band, improving multimessenger astronomy and giving access to new information. In this paper, we introduce a new machine-learning-based approach to produce early-warning alerts for an inspiraling binary neutron star system, based only on the early inspiral part of the signal. We give a proof of concept to show the possibility to use a combination of small convolutional neural networks trained on the whitened detector strain in the time domain to detect and classify early inspirals. Each of those is targeting a specific range of chirp masses dividing the binary neutron star category into three subclasses: light, intermediate, and heavy. In this work, we focus on one LIGO detector at design sensitivity and generate noise from the design power spectral density. We show that within this setup it is possible to produce an early alert up to 100 seconds before the merger for the best-case scenario. We also present some future upgrades that will enhance the detection capabilities of our convolutional neural networks. Finally, we also show that the current number of detections for a realistic binary neutron star population is comparable to that of matched filtering and that there is a high probability to detect GW170817- and GW190425-like events at design sensitivity.

Figure 1

Evolution of the PI SNR as a function of the duration of the early inspiral for a BNS with component masses of $1M_{\odot }$. On the vertical axis, the PI SNR is normalized by the optimal SNR, and on the horizontal axes, duration of the early inspiral is normalized by the duration of the full template.

Figure 2

The top panel represents an intermediate BNS template where the component masses are $m_1=m_2=2M_{\odot }$. The bottom panel shows the frequency evolution of the template with time. In both plots, the inspiral part considered for our ML-based approach is colored in red.

Figure 3

Representation of the noise and the injected waveform before the whitening. The CBC signal corresponds to a BNS where both component masses are $1.8M_{\odot }$ and the binary is placed at a luminosity distance of 100 Mpc. At the time of training and testing of the CNNs, we do not pass this full frame to the network, but only the first 50 s (denoted by the two red lines), which is the chosen OTW length for this BNS category.

Figure 4

Architecture of the best performing CNN for all the categories. From one BNS type to the other, one needs to adapt the input size.

Figure 5

The top panel represents the results of the three networks, each trained on its category, as a function of the distance. In the second panel, we compute the mean $\mu$ PI SNR and its standard error $\epsilon$, as $\mu (\mathrm{PI}\mathrm{SNR})\pm \epsilon (\mathrm{PI}\mathrm{SNR})$ for each distance and a confidence of $2\sigma$, represented by the colored band. For each graph the FAP is fixed at 0.01.

Figure 6

Representation of the performance of the CNN trained on the heavy BNS systems for different OTWs. One sees that a longer window gives a higher number of detections. However, it also means the detection happens closer to the merger time. The mean times before merger are 35, 30, 25, and 20 seconds for the 20, 25, 30, and 35 seconds OTW, respectively.

Figure 7

The PI SNR for a low-pass filter at 32 Hz for each BNS with a full SNR higher than 8. The black crosses represent the events missed by the CNNs, and the red squares are the events correctly found. The orange diamonds are triggers that correspond to noise fluctuations (false positives).

Figure 8

Comparison of the TAP as a function of the distance for the GW sources with and without basic curriculum learning for the heavy BNS class. One sees that even a very rudimentary curriculum learning setup helps improve the TAP at higher distances. Note that the blue curve is the same than in Fig. 5.

Figure 9

The loss variation for the training set and the validation set of CNN 3 as a function of the epoch.

Figure 10

Data distributions as functions of the SNR and PI SNR.