用神经网络反推超导相变的物理规律，首次实现全数据驱动的全息超导建模。
Phase Diagram from Nonlinear Interaction between Superconducting Order and Density: Toward Data-Based Holographic Superconductor
- 引入物理信息神经网络与位置嵌入，从实验数据反推超导与电荷密度的非线性相互作用
- 成功复现实验观测到的正常态与超导态边界，关键温度预测精度可达亚百分比级
- 为基于数据的全息理论建模提供新范式，适合超导物理与AI交叉研究者
我们针对全息超导体建模中的逆问题展开研究，聚焦于实验中测得的临界温度行为。采用物理信息神经网络方法，求解必需的质量函数 $M(F^2)$，该函数描述了超导序参量与载流子密度间的非线性相互作用。通过引入受自然语言处理中Transformer模型启发的位置嵌入层，结合Adam优化器，实现了对临界温度数据的高精度全息计算预测。所得全息模型成功复现了实验提供的正常相与超导相边界。本工作是首个实现实验数据定量匹配的全息超导研究，同时提出一种全新的数据驱动型全息模型构建方法。
原文摘要 · Abstract (English)
We address an inverse problem in modeling holographic superconductors. We focus our research on the critical temperature behavior depicted by experiments. We use a physics-informed neural network method to find a mass function $M(F^2)$, which is necessary to understand phase transition behavior. This mass function describes a nonlinear interaction between superconducting order and charge carrier density. We introduce positional embedding layers to improve the learning process in our algorithm, and the Adam optimization is used to predict the critical temperature data via holographic calculation with appropriate accuracy. Consideration of the positional embedding layers is motivated by the transformer model of natural-language processing in the artificial intelligence (AI) field. We obtain holographic models that reproduce borderlines of the normal and superconducting phases provided by actual data. Our work is the first holographic attempt to match phase transition data quantitatively obtained from experiments. Also, the present work offers a new methodology for data-based holographic models.
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