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Graph neural networks unveil universal dynamics in directed percolation |
| Ji-Hui Han(韩继辉)1, Cheng-Yi Zhang(张程义)1, Gao-Gao Dong(董高高)2,†, Yue-Feng Shi(石月凤)3, Long-Feng Zhao(赵龙峰)4, and Yi-Jiang Zou(邹以江)5 |
1 School of Computer Science and Technology, Zhengzhou University of Light Industry, Zhengzhou 450000, China;
2 School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China;
3 Information Management Center, Zhengzhou University of Light Industry, Zhengzhou 450000, China;
4 School of Management, Northwestern Polytechnical University, Xi'an 710129, China;
5 School of Economics, Anyang Normal University, Anyang 455000, China |
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Abstract Recent advances in statistical physics highlight the significant potential of machine learning for phase transition recognition. This study introduces a deep learning framework based on graph neural network to investigate non-equilibrium phase transitions, specifically focusing on the directed percolation process. By converting lattices with varying dimensions and connectivity schemes into graph structures and embedding the temporal evolution of the percolation process into node features, our approach enables unified analysis across diverse systems. The framework utilizes a multi-layer graph attention mechanism combined with global pooling to autonomously extract critical features from local dynamics to global phase transition signatures. The model successfully predicts percolation thresholds without relying on lattice geometry, demonstrating its robustness and versatility. Our approach not only offers new insights into phase transition studies but also provides a powerful tool for analyzing complex dynamical systems across various domains.
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Received: 21 March 2025
Revised: 21 April 2025
Accepted manuscript online: 07 May 2025
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PACS:
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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64.60.Ht
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(Dynamic critical phenomena)
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64.60.A-
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(Specific approaches applied to studies of phase transitions)
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05.45.-a
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(Nonlinear dynamics and chaos)
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| Fund: Project supported by the Fund from the Science and Technology Department of Henan Province, China (Grant Nos. 222102210233 and 232102210064), the National Natural Science Foundation of China (Grant Nos. 62373169 and 72474086), the Young and Mid-career Academic Leader of Jiangsu Province, China (Grant No. Qinglan Project in 2024), the National Statistical Science Research Project (Grant No. 2022LZ03), Shaanxi Provincial Soft Science Project (Grant No. 2022KRM111), Shaanxi Provincial Social Science Foundation (Grant No. 2022R016), the Special Project for Philosophical and Social Sciences Research in Shaanxi Province, China (Grant No. 2024QN018), and the Fund from the Henan Office of Philosophy and Social Science (Grant No. 2023CJJ112). |
Corresponding Authors:
Gao-Gao Dong
E-mail: gago999@126.com
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Cite this article:
Ji-Hui Han(韩继辉), Cheng-Yi Zhang(张程义), Gao-Gao Dong(董高高), Yue-Feng Shi(石月凤), Long-Feng Zhao(赵龙峰), and Yi-Jiang Zou(邹以江) Graph neural networks unveil universal dynamics in directed percolation 2025 Chin. Phys. B 34 080702
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