Classifying the equation of state from rotating core collapse gravitational waves with deep learning

In this paper, we seek to answer the question ``given a rotating core collapse gravitational wave signal, can we determine its nuclear equation of state?'' To answer this question, we employ deep convolutional neural networks to learn visual and temporal patterns embedded within rotating core collapse gravitational wave (GW) signals in order to predict the nuclear equation of state (EOS). Using the 1824 rotating core collapse GW simulations by Richers et al. [Phys. Rev. D 95, 063019 (2017).], which have 18 different nuclear EOSs, we consider this to be a classic multiclass image classification and sequence classification problem. We attain up to 72% correct classifications in the test set, and if we consider the ``top five'' most probable labels, this increases to up to 97%, demonstrating that there is a moderate and measurable dependence of the rotating core collapse GW signal on the nuclear EOS.