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

Deep neural networks for direct, featureless learning through observation: the case of 2d spin models