17330

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

K. Mills, I. Tamblyn
Deparment of Physics, University of Ontario Institute of Technology
arXiv:1706.09779 [cond-mat.mtrl-sci], (29 Jun 2017)

@article{mills2017deep,

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

   author={Mills, K. and Tamblyn, I.},

   year={2017},

   month={jun},

   archivePrefix={"arXiv"},

   primaryClass={cond-mat.mtrl-sci}

}

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We train a deep convolutional neural network to accurately predict the energies and magnetizations of Ising model configurations, using both the traditional nearest-neighbour Hamiltonian, as well as a long-range screened Coulomb Hamiltonian. We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbour 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-neighbour 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. Finally, we teach the convolutional deep neural network to accurately predict a long-range interaction through a screened Coulomb Hamiltonian. In this case, the benefits of the neural network become apparent; it is able to make predictions with a high degree of accuracy, 1600 times faster than a CUDA-optimized "exact" calculation.
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