AI 中文总结
研究三维勒布霍尔-拉舍模型各向同性-向列相转变，发现主成分分析和卷积自编码器处理原始构型难识别转变，转换表示后可行，有监督卷积神经网络给定标签可准确预测序参，区分了无监督相发现与有监督序参回归。
AI 中文摘要
机器学习对相变的检测不仅取决于学习算法，还取决于输入表示是否保留系统对称性。我们针对三维勒布霍尔-拉舍模型的弱一级各向同性-向列相转变进行研究，其非极性且连续简并的向列相使原始分子构型成为无监督学习的挑战性输入。主成分分析（PCA）和卷积自编码器（CAE）无法从原始构型识别转变，而转换为旋转不变局部相关表示后能恢复敏感特征。有监督的三维卷积神经网络（CNN）在给定序参标签时可从原始构型准确预测标量序参。该模型区分了无监督相发现和有监督序参回归，表明取向有序系统的无监督机器学习需要尊重对称性的输入表示。
英文摘要
Machine-learning detection of phase transitions depends not only on the learning algorithm, but also on whether the input representation preserves the symmetries of the system. We examine this for the weak first-order isotropic--nematic transition of the three-dimensional Lebwohl--Lasher model, whose apolar and continuously degenerate nematic phase makes raw molecular configurations a challenging input for unsupervised learning. Principal component analysis (PCA) and a convolutional autoencoder (CAE) fail to identify the transition from raw configurations because rotationally equivalent nematic states can appear far apart in the input space. When the same configurations are transformed into a rotationally invariant local-correlation representation, both methods recover transition-sensitive signatures and bimodal coexistence distributions. A supervised three-dimensional convolutional neural network (CNN), by contrast, accurately predicts the scalar order parameter from raw configurations when given order-parameter labels. The Lebwohl-Lasher model therefore separates unsupervised phase discovery from supervised order-parameter regression and shows that symmetry-respecting input representations are needed for unsupervised machine learning in orientationally ordered systems.
