  The origin of the diverse population of galaxy clusters remains an
unexplained aspect of large-scale structure formation and cluster evolution. We
present a novel method of using X-ray images to identify cool core (CC), weak
cool core (WCC), and non cool core (NCC) clusters of galaxies, that are defined
by their central cooling times. We employ a convolutional neural network,
ResNet-18, which is commonly used for image analysis, to classify clusters. We
produce mock Chandra X-ray observations for a sample of 318 massive clusters
drawn from the IllustrisTNG simulations. The network is trained and tested with
low resolution mock Chandra images covering a central 1 Mpc square for the
clusters in our sample. Without any spectral information, the deep learning
algorithm is able to identify CC, WCC, and NCC clusters, achieving balanced
accuracies (BAcc) of 92%, 81%, and 83%, respectively. The performance is
superior to classification by conventional methods using central gas densities,
with an average BAcc = 81%, or surface brightness concentrations, giving BAcc =
73%. We use Class Activation Mapping to localize discriminative regions for the
classification decision. From this analysis, we observe that the network has
utilized regions from cluster centers out to r~300 kpc and r~500 kpc to
identify CC and NCC clusters, respectively. It may have recognized features in
the intracluster medium that are associated with AGN feedback and disruptive
major mergers.
