Journal
PHYSICAL REVIEW B
Volume 94, Issue 16, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.94.165134
Keywords
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Funding
- Natural Sciences and Engineering Research Council of Canada
- Canada Research Chair program
- Ontario Trillium Foundation
- Perimeter Institute for Theoretical Physics
- Industry Canada
- Province of Ontario through the Ministry of Research and Innovation
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A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modeling thermodynamic observables for physical systems in thermal equilibrium. Through unsupervised learning, we train the Boltzmann machine on data sets constructed with spin configurations importance sampled from the partition function of an Ising Hamiltonian at different temperatures using Monte Carlo (MC) methods. The trained Boltzmann machine is then used to generate spin states, for which we compare thermodynamic observables to those computed by direct MC sampling. We demonstrate that the Boltzmann machine can faithfully reproduce the observables of the physical system. Further, we observe that the number of neurons required to obtain accurate results increases as the system is brought close to criticality.
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