Learning Thermodynamics with Boltzmann Machines

TL;DR

This paper introduces a Boltzmann machine capable of modeling thermodynamic properties of physical systems in equilibrium, trained on Monte Carlo data, and able to generate accurate spin configurations.

Contribution

It develops a Boltzmann machine that learns thermodynamic observables from physical data, bridging neural networks and statistical physics.

Findings

The trained Boltzmann machine accurately reproduces thermodynamic observables.

The number of neurons needed increases near critical points.

The model effectively generates spin states consistent with Monte Carlo results.

Abstract

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.