Identifying Ising and percolation phase transitions based on KAN method
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909549548535808 |
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| author | Xu, Dian Wang, Shanshan Li, Wei Deng, Weibing Gao, Feng Shen, Jianmin |
| author_facet | Xu, Dian Wang, Shanshan Li, Wei Deng, Weibing Gao, Feng Shen, Jianmin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17996 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Identifying Ising and percolation phase transitions based on KAN method Xu, Dian Wang, Shanshan Li, Wei Deng, Weibing Gao, Feng Shen, Jianmin Statistical Mechanics Machine Learning 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. |
| title | Identifying Ising and percolation phase transitions based on KAN method |
| topic | Statistical Mechanics Machine Learning |
| url | https://arxiv.org/abs/2503.17996 |