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

From National Research Council Canada

Download
  1. (PDF, 1 MB)
DOIResolve DOI: https://doi.org/10.1103/PhysRevE.97.032119
AuthorSearch for: ; Search for: 1
Name affiliation
  1. National Research Council of Canada. Security and Disruptive Technologies
FormatText, Article
Journal titlePhysical Review E
ISSN2470-0045
2470-0053
Volume97
Issue3
Article number032119
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.
Publication date
PublisherAmerican Physical Society
LanguageEnglish
Peer reviewedYes
NPARC number23003148
Export citationExport as RIS
Report a correctionReport a correction
Record identifier242549d0-5bb6-4b87-8b29-54a66f767d5f
Record created2018-05-01
Record modified2020-05-30
Report a problem on this page
Date modified: