arXiv:2505.10393cond-mat.str-elcs.AI2025-05

用合成数据训练神经网络,高效识别磁性相变边界。

Uncovering Magnetic Phases with Synthetic Data and Physics-Informed Training

  • 用合成数据+物理引导,让神经网络学习磁相变特征。
  • 在无标签情况下仍能准确预测临界温度与渗透阈值。
  • 适合研究复杂磁性系统,替代传统计算成本高的方法。

我们研究了利用人工神经网络在合成数据上高效学习磁性相的方法,结合计算简便性与物理引导策略。以缺乏精确解析解的稀释伊辛模型为例,探索两种互补方法:使用简单全连接网络的监督分类,以及仅基于理想自旋构型训练的卷积自编码器进行无监督相变检测。为提升模型性能,引入两类物理引导机制:一是通过网络结构偏置增强对对称性破缺特征的敏感度;二是加入显式打破ℤ₂对称性的训练样本,强化对有序相的识别能力。这些机制协同作用,即使在无明确标签条件下也能提高网络对相结构的敏感性。通过与直接数值估计的临界温度和渗透阈值对比验证了机器学习预测的有效性。结果表明,结构化、计算高效的合成数据训练方案可在复杂系统中揭示具有物理意义的相边界。该框架为凝聚态与统计物理领域提供了低成本、鲁棒性强的替代方法。

原文摘要 · Abstract (English)

We investigate the efficient learning of magnetic phases using artificial neural networks trained on synthetic data, combining computational simplicity with physics-informed strategies. Focusing on the diluted Ising model, which lacks an exact analytical solution, we explore two complementary approaches: a supervised classification using simple dense neural networks, and an unsupervised detection of phase transitions using convolutional autoencoders trained solely on idealized spin configurations. To enhance model performance, we incorporate two key forms of physics-informed guidance. First, we exploit architectural biases which preferentially amplify features related to symmetry breaking. Second, we include training configurations that explicitly break $\mathbb{Z}_2$ symmetry, reinforcing the network's ability to detect ordered phases. These mechanisms, acting in tandem, increase the network's sensitivity to phase structure even in the absence of explicit labels. We validate the machine learning predictions through comparison with direct numerical estimates of critical temperatures and percolation thresholds. Our results show that synthetic, structured, and computationally efficient training schemes can reveal physically meaningful phase boundaries, even in complex systems. This framework offers a low-cost and robust alternative to conventional methods, with potential applications in broader condensed matter and statistical physics contexts.

磁性相变神经网络合成数据

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