阶段过渡的深度学习,使用最小的例子
Ahmed Abuali1, David A Clarke2, Morten Hjorth-Jensen3,4
1University of Houston, Physics Department, Houston, Texas 77204, USA.
Physical review. E
|October 21, 2025
概括
深度学习模型可以识别物理系统中的相位过渡. 在有限的数据 (T=0和T=∞) 上训练一个卷积神经网络仍然允许对Ising模型进行临界温度 (T_{c}) 和临界指数 (ν) 识别.
科学领域:
- 统计物理学的统计物理.
- 机器学习 机器学习
- 计算物理学的计算物理.
背景情况:
- 深度神经网络 (DNN) 在识别物理系统中的相位过渡方面表现有前途.
- DNN预测通常模仿顺序参数,帮助定位临界温度 (T_{c}) 和估计临界指数.
- 卷积神经网络 (CNN) 越来越多地用于分析物理系统配置.
研究的目的:
- 调查CNN在确定2DIsing模型关键参数方面的有效性.
- 评估受限训练数据 (仅T=0和T=∞) 对CNN绩效的影响.
- 为了比较受过极端温度数据训练的CNN与受过温度范围数据训练的CNN.
主要方法:
- 使用卷积神经网络 (CNN) 架构.
- 训练CNN在T=0和T=∞时对2D Ising模型的配置进行训练.
- 将CNN的表现与在T_{c}以下和以上的多个温度数据上训练的网络进行比较.
- 分析CNN识别T_{c}和关键指数 (ν, γ) 的能力.
主要成果:
- 在T=0和T=∞训练的CNN成功地确定了2D Ising模型的临界温度 (T_{c}).
- 在有限的数据上训练的CNN也准确地估计了临界指数n.
- 在受限训练数据集中,提取临界指数 γ 证明更具挑战性.
- 在有限的数据上训练的网络的表现与在T_{c}和n.的广泛数据上训练的网络的表现相似.
结论:
- 即使使用高度受限制的训练数据,CNN也可以有效地识别关键温度和某些关键指数.
- 极端温度训练 (T=0,T=∞) 是一些物理系统中检测相变的可行策略.
- 需要进一步的研究来优化CNN以提取所有关键指数,特别是γ,在数据约束下.
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