Deep neural networks for direct, featureless learning through observation: The case of two-dimensional spin models

Physical Review. E
Kyle Mills, Isaac Tamblyn

Abstract

We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4×4 Ising model. Using its success at this task, we motivate the study of the larger 8×8 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 fas...Continue Reading

References

Apr 12, 2006·Physical Review Letters·Alexei Kitaev, John Preskill
Apr 12, 2006·Physical Review Letters·Michael Levin, Xiao-Gang Wen
Feb 27, 2015·Nature·Volodymyr MnihDemis Hassabis
Mar 31, 2015·Physical Review Letters·Luca M GhiringhelliMatthias Scheffler
Jan 23, 2016·Scientific Reports·Prasanna V BalachandranTurab Lookman
Jan 29, 2016·Nature·David SilverDemis Hassabis
Feb 12, 2017·Science·Giuseppe Carleo, Matthias Troyer

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Citations

Sep 27, 2018·Physical Review. E·Dongkyu Kim, Dong-Hee Kim
Sep 27, 2018·Physical Review. E·Kengo Nakai, Yoshitaka Saiki

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