Learning Thermodynamics with Boltzmann Machines
This work provides a method for physicists to simulate thermodynamic systems using neural networks, but it is incremental as it applies an existing machine learning technique to a new domain.
The authors tackled the problem of modeling thermodynamic observables for physical systems in thermal equilibrium using a Boltzmann machine, demonstrating that it can faithfully reproduce observables compared to direct Monte Carlo sampling, with the number of neurons required increasing near criticality.
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 modelling 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.