Equation of State Classification of Core-Collapse Supernovae with a Network of Gravitational-Wave Detectors

Gravitational waves from core-collapse supernovae may provide a unique probe of the equation of state (EOS) of dense nuclear matter. In previous work, we assessed the potential of machine-learning methods for EOS classification for rapidly rotating supernovae using individual gravitational-wave detectors. Here, we extend the framework to detector networks and investigate the impact of detector configuration, source distance, arrival time, and sky location on the classification. Using convolutional neural networks, we perform 10-class EOS classification directly from noisy detector data for both second- and third-generation observatories. We find that detector geometry strongly influences classification performance. For Galactic events, current detector networks can achieve promising classification performance, but the reach depends sensitively on the detector network antenna response. Adding detectors improves time-averaged performance and produces more uniform classification across the sky. Third-generation observatories extend the classification reach to 100 kpc for favorable source orientations but do not remove the dependence on detector geometry.