  We demonstrate the capability of a convolutional deep neural network in
predicting the nearest-neighbor energy of the 4x4 Ising model. Using its
success at this task, we motivate the study of the larger 8x8 Ising model,
showing that the deep neural network can learn the nearest-neighbor Ising
Hamiltonian after only seeing a vanishingly small fraction of configuration
space. Additionally, we show that the neural network has learned both the
energy and magnetization operators with sufficient accuracy to replicate the
low-temperature Ising phase transition. We then demonstrate the ability of the
neural network to learn other spin models, teaching the convolutional deep
neural network to accurately predict the long-range interaction of a screened
Coulomb Hamiltonian, a sinusoidally attenuated screened Coulomb Hamiltonian,
and a modified Potts model Hamiltonian. In the case of the long-range
interaction, we demonstrate the ability of the neural network to recover the
phase transition with equivalent accuracy to the numerically exact method.
Furthermore, in the case of the long-range interaction, the benefits of the
neural network become apparent; it is able to make predictions with a high
degree of accuracy, and do so 1600 times faster than a CUDA-optimized exact
calculation. Additionally, we demonstrate how the neural network succeeds at
these tasks by looking at the weights learned in a simplified demonstration.
