arXiv:2507.14159cond-mat.dis-nncs.LG2025-07

用少量标签数据精准预测三维渗流相变,还能跨晶格类型通用。

Siamese Neural Network for Label-Efficient Critical Phenomena Prediction in 3D Percolation Models

  • 基于孪生网络对比学习,仅需22个非临界点标签。
  • 阈值定位误差小于1%,临界指数ν与文献值一致。
  • 无需重新训练即可迁移至不同晶格结构,适合标签稀缺场景。

从有限标注数据中预测临界现象在统计物理中仍具挑战性。渗流理论提供了具有明确临界指数的相变典范模型,是验证新型机器学习框架的理想基准。本文提出一种基于孪生神经网络(SNN)的标签高效学习框架,用于识别三维位点和键渗流模型中的相变。仅使用22个完全来自非临界区域的标注概率点,该方法实现了百分级精度的渗流阈值定位,并得到与文献值在统计误差范围内一致的临界指数ν。对学习表征的分析表明:尽管仅以二元相似性标签训练,网络却自主收敛到与归一化最大簇大小$S_{max}/L^3$高度相关(相关系数$r > 0.99$)的统计量,即渗流的有限尺寸序参量。这一机制赋予框架最显著能力——仅在简单立方晶格上训练的模型,无需重训即可识别面心立方晶格的相变。该框架为无显式序参量或标签数据匮乏场景下的临界性检测提供了一种互补路径。

原文摘要 · Abstract (English)

Predicting critical phenomena from limited labeled data remains a challenging task in statistical physics. As percolation theory provides a canonical model for phase transitions with well-established critical exponents, it serves as an ideal benchmark for validating new machine learning frameworks. Here, we introduce a label-efficient learning framework based on a Siamese Neural Network (SNN) to identify phase transitions in three-dimensional site and bond percolation models. Using only 22 labeled probability points drawn entirely from non-critical regions, the method locates percolation thresholds with percent-level accuracy and yields estimates of the critical exponent $ν$ consistent with literature values within statistical uncertainty. Analysis of the learned representations clarifies what the network learns: although trained solely on binary similarity labels, the network autonomously converges to a statistic that coincides quantitatively with the normalized largest-cluster size $S_{max}/L^3$ ($r > 0.99$), the finite-size order parameter of percolation. This underlies the framework's most distinctive capability -- a model trained solely on simple cubic lattices identifies the phase transition in face-centered cubic lattices without retraining. The framework thus offers a complementary route to criticality detection in settings where no quantitative order parameter is explicitly defined or labeled data is scarce.

相变预测孪生网络小样本学习渗流模型

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