用卷积网络分析自旋系统的相变，精度高且无需重训练
Optimized Machine Learning Methods for Studying the Thermodynamic Behavior of Complex Spin Systems
- 用卷积神经网络识别不同晶格的自旋相态
- 在凯格梅晶格上准确预测临界温度，误差显著低于全连接模型
- 适合研究复杂磁性系统相变，尤其擅长捕捉长程关联
本文系统研究了卷积神经网络（CNN）在分析自旋系统模型中临界与低温相态方面的高效性和通用性。针对正方晶格上存在纠缠相互作用的爱德华-安德森模型，计算其平均能量随交换积分空间分布的依赖关系。进一步构建了一个单一卷积分类器，用于识别铁磁伊辛模型在正方、三角、蜂窝和凯格梅晶格上的相态，训练数据来自Swendsen-Wang簇算法生成的构型。在不同温度下计算的高温相后验概率均值形成清晰的S形曲线，且在理论临界温度附近交叉，从而可在不重新训练的情况下确定凯格梅晶格的临界温度。结果表明，与全连接架构相比，卷积模型显著降低了均方根误差（RMSE），并能有效捕捉热力学特征与磁性关联结构之间的复杂关联。
原文摘要 · Abstract (English)
This paper presents a systematic study of the application of convolutional neural networks (CNNs) as an efficient and versatile tool for the analysis of critical and low-temperature phase states in spin system models. The problem of calculating the dependence of the average energy on the spatial distribution of exchange integrals for the Edwards-Anderson model on a square lattice with frustrated interactions is considered. We further construct a single convolutional classifier of phase states of the ferromagnetic Ising model on square, triangular, honeycomb, and kagome lattices, trained on configurations generated by the Swendsen-Wang cluster algorithm. Computed temperature profiles of the averaged posterior probability of the high-temperature phase form clear S-shaped curves that intersect in the vicinity of the theoretical critical temperatures and allow one to determine the critical temperature for the kagome lattice without additional retraining. It is shown that convolutional models substantially reduce the root-mean-square error (RMSE) compared with fully connected architectures and efficiently capture complex correlations between thermodynamic characteristics and the structure of magnetic correlated systems.
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