三维伊辛模型中的Few-Shot机器学习
Few-shot machine learning in the three-dimensional Ising model
摘要：
我们利用最先进的机器学习算法对三维立方伊辛模型中的相变进行了理论研究。有监督的机器学习模型在相位分类中显示出高精度（~99\%），并且在不同自旋配置中能量的相对误差（$< 10^{-4}$）非常小。引入无监督机器学习模型研究自旋位形的重构和约简，重构后的自旋位形相位可以通过线性逻辑算法进行精确分类。在比较各种机器学习模型的基础上，我们提出了一种Few-Shot策略来从较小晶格中的训练样本预测较大晶格中的相变。三维伊辛模型的Few-Shot机器学习策略使我们能够有效地研究三维伊辛模型，并为其他自旋模型提供了一种新的集成和高精度的方法。
英文摘要：
We investigate theoretically the phase transition in three dimensional cubic Ising model utilizing state-of-the-art machine learning algorithms. Supervised machine learning models show high accuracies (~99\%) in phase classification and very small relative errors ($< 10^{-4}$) of the energies in different spin configurations. Unsupervised machine learning models are introduced to study the spin configuration reconstructions and reductions, and the phases of reconstructed spin configurations can be accurately classified by a linear logistic algorithm. Based on the comparison between various machine learning models, we develop a few-shot strategy to predict phase transitions in larger lattices from trained sample in smaller lattices. The few-shot machine learning strategy for three dimensional(3D) Ising model enable us to study 3D ising model efficiently and provides a new integrated and highly accurate approach to other spin models.
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