用深度学习从自旋构型中识别相变临界行为，预测3D伊辛模型的临界指数。
Computing critical exponents in 3D Ising model via pattern recognition/deep learning approach
- 用3D卷积神经网络从自旋构型中提取六类低维特征。
- 在L=20的体系上训练，测试准确率达68.75%。
- 为凝聚态物理中深度学习解释性提供新思路。
本研究采用马特罗波利斯算法与有限尺寸标度分析，在六种立方体尺度（L=20,30,40,60,80,90）下计算了3D伊辛模型的三个临界指数（α, β, γ）。通过监督式深度学习方法（3D卷积神经网络），对特定自旋构型进行训练，成功将热力学平均量（单位自旋磁化率 <m>(t)、比热 <c>(t)、磁化率 <χ>(t)）随无量纲温度 t 变化的信息压缩为六类潜在类别。在L=20的子集上，模型训练与测试准确率分别为0.92和0.6875。但如何从输出类别标签（分箱后的 m, c, χ）中量化推导临界指数，仍需进一步研究。该方法为凝聚态物理系统中深度学习模型的可解释性提供了新路径。
原文摘要 · Abstract (English)
In this study, we computed three critical exponents ($α, β, γ$) for the 3D Ising model with Metropolis Algorithm using Finite-Size Scaling Analysis on six cube length scales (L=20,30,40,60,80,90), and performed a supervised Deep Learning (DL) approach (3D Convolutional Neural Network or CNN) to train a neural network on specific conformations of spin states. We find one can effectively reduce the information in thermodynamic ensemble-averaged quantities vs. reduced temperature t (magnetization per spin $<m>(t)$, specific heat per spin $<c>(t)$, magnetic susceptibility per spin $<χ>(t)$) to \textit{six} latent classes. We also demonstrate our CNN on a subset of L=20 conformations and achieve a train/test accuracy of 0.92 and 0.6875, respectively. However, more work remains to be done to quantify the feasibility of computing critical exponents from the output class labels (binned $m, c, χ$) from this approach and interpreting the results from DL models trained on systems in Condensed Matter Physics in general.
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