论文标题
将不同的相转换映射到神经网络
Mapping distinct phase transitions to a neural network
论文作者
论文摘要
我们通过卷积神经网络证明，二维ISING模型中所学的特征足以预测所考虑系统中对称性相变的结构，无论是普遍性类别，秩序以及离散或持续自由度的存在如何。在目标系统中不需要有关相变存在的先验知识，并且可以使用多个直方图重新加权扫描其整个参数空间以发现一个。我们在Q-State Potts模型中建立了我们的方法，并使用从神经网络实现中得出的数量来对关键耦合和$ ϕ^{4} $标量场理论的关键指数进行计算。我们将机器学习算法视为映射，将各种系统的每种配置都关联到其相应的阶段，并详细介绍了发现未知相转换的影响。
We demonstrate, by means of a convolutional neural network, that the features learned in the two-dimensional Ising model are sufficiently universal to predict the structure of symmetry-breaking phase transitions in considered systems irrespective of the universality class, order, and the presence of discrete or continuous degrees of freedom. No prior knowledge about the existence of a phase transition is required in the target system and its entire parameter space can be scanned with multiple histogram reweighting to discover one. We establish our approach in q-state Potts models and perform a calculation for the critical coupling and the critical exponents of the $ϕ^{4}$ scalar field theory using quantities derived from the neural network implementation. We view the machine learning algorithm as a mapping that associates each configuration across different systems to its corresponding phase and elaborate on implications for the discovery of unknown phase transitions.
