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

Kyle Mills and Isaac Tamblyn
Phys. Rev. E 97, 032119 – Published 16 March 2018

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 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.

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  • Received 23 June 2017
  • Revised 31 January 2018

DOI:https://doi.org/10.1103/PhysRevE.97.032119

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Kyle Mills*

  • Department of Physics, University of Ontario Institute of Technology, Oshawa, Ontario, Canada

Isaac Tamblyn

  • Department of Physics, University of Ontario Institute of Technology, Oshawa, Ontario, Canada and Department of Physics, University of Ottawa & National Research Council of Canada, Ottawa, Ontario, Canada

  • *kyle.mills@uoit.net
  • isaac.tamblyn@nrc.ca

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Vol. 97, Iss. 3 — March 2018

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