  We use machine learning to classify rational two-dimensional conformal field
theories. We first use the energy spectra of these minimal models to train a
supervised learning algorithm. We find that the machine is able to correctly
predict the nature and the value of critical points of several strongly
correlated spin models using only their energy spectra. This is in contrast to
previous works that use machine learning to classify different phases of
matter, but do not reveal the nature of the critical point between phases.
Given that the ground-state entanglement Hamiltonian of certain topological
phases of matter is also described by conformal field theories, we use
supervised learning on R\'{e}yni entropies and find that the machine is able to
identify which conformal field theory describes the entanglement Hamiltonian
with only the lowest few R\'{e}yni entropies to a high degree of accuracy.
Finally, using autoencoders, an unsupervised learning algorithm, we find a
hidden variable that has a direct correlation with the central charge and
discuss prospects for using machine learning to investigate other conformal
field theories, including higher-dimensional ones. Our results highlight that
machine learning can be used to find and characterize critical points and also
hint at the intriguing possibility to use machine learning to learn about more
complex conformal field theories.
