Learning Thermodynamics with Boltzmann Machines
Learning Thermodynamics with Boltzmann Machines
复制标题
DOI：
10.1103/physrevb.94.165134
复制
发表时间：
2016-06
期刊：
影响因子：
--
通讯作者：
G. Torlai;R. Melko
中科院分区：
文献类型：
--
作者：
G. Torlai;R. Melko
玻尔兹曼机是一种随机神经网络，已广泛用于现代机器学习应用的深层架构层。在本文中，我们开发了一个玻尔兹曼机，能够模拟热平衡的物理系统的热力学可观测量。通过无监督学习，我们使用Monte Carlo（MC）方法在不同温度下从伊辛哈密顿量的配分函数采样的自旋配置重要性构建的数据集上训练玻尔兹曼机。然后，训练的玻尔兹曼机用于生成自旋状态，我们比较热力学观测值的直接MC采样计算。我们证明了玻尔兹曼机可以忠实地再现物理系统的可观测量。此外，我们观察到，随着系统接近临界状态，获得准确结果所需的神经元数量会增加。
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.