Visualizing convolutional neural network for classifying gravitational waves from core-collapse supernovae

In this study, we employ a convolutional neural network to classify gravitational waves originating from core-collapse supernovae. Training is conducted using spectrograms derived from three-dimensional numerical simulations of waveforms, which are injected onto real noise data from the third observing run of both Advanced LIGO and Advanced Virgo. To gain insights into the decision-making process of the model, we apply class activation mapping techniques to visualize the regions in the input image that are significant for the model’s prediction. The class activation maps reveal that the model’s predictions predominantly rely on specific features within the input spectrograms, namely, the $g$-mode and low-frequency modes. The visualization of convolutional neural network models provides interpretability to enhance their reliability and offers guidance for improving detection efficiency.

Figure 1

Amplitude spectral density of the plus mode of each waveform at 1 kpc. The observer is in the polar direction.

Figure 2

Sample whitened spectrograms of each class at the H1 detector in the training set. Each signal sample is observed in the polar direction and scaled to have an SNR of 40. The bounce time is fixed at 0.1 s.

Figure 3

Loss curves for the training and validation sets. During the first 40 epochs, we input samples with SNRs between [40, 50], followed by [30, 40] SNR samples in the subsequent 40 epochs, and [20, 30] SNR samples in the last 40 epochs.

Figure 4

True positive rate of each waveform in the test set against source distance.

Figure 5

Confusion matrices of the test set (left) and violin plots of the network SNR of each waveform (right) from sources with distances of 1, 5, and 10 kpc.

Figure 6

Features of the test samples at 1 kpc extracted by CNN and mapped into two-dimensional space by the t-SNE algorithm.

Figure 7

Qualitative comparison of three CAM maps for the s25 sample at 1 kpc.

Figure 8

Input spectrograms and Score-CAM maps of correctly classified samples. The SNR of each signal sample is 40.

Figure 9

s25 sample classified as s18np. (a) Input spectrogram. The red, green, and blue channels correspond to the H1, L1, and V1 data, respectively. There is a glitch in the L1 data. (b) Score-CAM map. (c) Example spectrogram of a s18np sample.

Figure 10

s13 sample classified as y20. (a) Input spectrogram. The red, green, and blue channels correspond to the H1, L1, and V1 data, respectively. (b) Score-CAM map. (c) Example spectrogram of a y20 sample.