Beijing National Lab for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
Phys Rev E. 2017 Nov;96(5-1):051301. doi: 10.1103/PhysRevE.96.051301. Epub 2017 Nov 16.
Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms. The latent representation of the Boltzmann machines can be designed to mediate complex interactions and identify clusters of the physical system. We demonstrate these findings with concrete examples of the classical Ising model with and without four-spin plaquette interactions. In the future, automatic searches in the algorithm space parametrized by Boltzmann machines may discover more innovative Monte Carlo updates.
玻尔兹曼机是一种物理启发的生成模型，在机器学习中有广泛的应用。它们使用潜在变量来对输入数据集的概率分布进行建模，并据此生成新的样本。将玻尔兹曼机应用于物理学中，由于其灵活性和有效性，它们是理想的推荐系统，可以加速物理系统的蒙特卡罗模拟。更有趣的是，我们表明，玻尔兹曼机的生成采样甚至可以给出不同的聚类蒙特卡罗算法。玻尔兹曼机的潜在表示可以设计为调节复杂的相互作用并识别物理系统的簇。我们通过带有和不带有四自旋 plaquette 相互作用的经典伊辛模型的具体示例证明了这些发现。未来，由玻尔兹曼机参数化的算法空间的自动搜索可能会发现更多创新的蒙特卡罗更新。
