用KAN网络直接从原始配置识别相变点，效果优于传统方法。
Identifying Ising and percolation phase transitions based on KAN method
- 基于柯尔莫哥洛夫-阿诺德定理构建KAN网络，输入原始系统配置
- 成功预测了自举模型和伊辛模型的相变临界点
- 适用于密度与磁通量两类不同相变机制，适合物理建模研究者
现代机器学习基于泛函逼近定理，在平衡与非平衡系统相变研究中取得显著进展。然而，仅凭原始构型识别自举模型的临界点仍是具有挑战性且引人深思的问题。本文提出使用基于柯尔莫哥洛夫-阿诺德表示定理的柯尔莫哥洛夫-阿诺德网络（KAN），将原始配置输入学习模型。结果表明，KAN确实能够预测自举模型的临界点。进一步观察发现，除与占据密度相关的模型外，KAN还能有效实现仅改变自旋方向的模型分类，此类模型的序参量表现为外部磁通量，如伊辛模型。
原文摘要 · Abstract (English)
Modern machine learning, grounded in the Universal Approximation Theorem, has achieved significant success in the study of phase transitions in both equilibrium and non-equilibrium systems. However, identifying the critical points of percolation models using raw configurations remains a challenging and intriguing problem. This paper proposes the use of the Kolmogorov-Arnold Network, which is based on the Kolmogorov-Arnold Representation Theorem, to input raw configurations into a learning model. The results demonstrate that the KAN can indeed predict the critical points of percolation models. Further observation reveals that, apart from models associated with the density of occupied points, KAN is also capable of effectively achieving phase classification for models where the sole alteration pertains to the orientation of spins, resulting in an order parameter that manifests as an external magnetic flux, such as the Ising model.
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