Machine learning determination of dynamical parameters: The Ising model case
Machine learning determination of dynamical parameters: The Ising model case
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DOI：
10.1103/physrevb.100.064304
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发表时间：
2019-08-07
影响因子：
3.7
通讯作者：
Wilson, Michael
中科院分区：
文献类型：
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作者：
Cossu, Guido;Del Debbio, Luigi;Wilson, Michael
我们训练了一组限制玻尔兹曼机（rbm）在不同温度下的一维和二维伊辛自旋构型，使用蒙特卡罗模拟生成。我们通过监控几个估计器来验证训练过程，包括对数似然的测量，以及使用退火重要性抽样估计的相应的划分函数。详细讨论了各种超参数选择对RBM训练的影响，并给出了通用处方。最后，我们给出了一个封闭形式的表达式，用于提取二元系统（如Ising模型）中RBM可见节点之间的每个n点相互作用的耦合值。我们的目标是利用这项研究作为进一步研究不太知名的系统的基础。
We train a set of restricted Boltzmann machines (RBMs) on one- and two-dimensional Ising spin configurations at various values of temperature, generated using Monte Carlo simulations. We validate the training procedure by monitoring several estimators, including measurements of the log likelihood, with the corresponding partition functions estimated using annealed importance sampling. The effects of various choices of hyperparameters on training the RBM are discussed in detail, with a generic prescription provided. Finally, we present a closed-form expression for extracting the values of couplings, for every n-point interaction between the visible nodes of an RBM, in a binary system such as the Ising model. We aim at using this study as the foundation for further investigations of less well-known systems.