Graph neural networks unveil universal dynamics in directed percolation

doi:10.1088/1674-1056/add505

中国物理B ›› 2025, Vol. 34 ›› Issue (8): 80702-080702.doi: 10.1088/1674-1056/add505

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

收稿日期:2025-03-21 修回日期:2025-04-21 接受日期:2025-05-07 出版日期:2025-07-17 发布日期:2025-08-12
通讯作者: Gao-Gao Dong E-mail:gago999@126.com
基金资助:
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).

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

Received:2025-03-21 Revised:2025-04-21 Accepted:2025-05-07 Online:2025-07-17 Published:2025-08-12
Contact: Gao-Gao Dong E-mail:gago999@126.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: graph neural networks, non-equilibrium phase transition, directed percolation model, nonlinear dynamics

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.

Key words: graph neural networks, non-equilibrium phase transition, directed percolation model, nonlinear dynamics

中图分类号: (Neural networks, fuzzy logic, artificial intelligence)

07.05.Mh

64.60.Ht (Dynamic critical phenomena) 64.60.A- (Specific approaches applied to studies of phase transitions) 05.45.-a (Nonlinear dynamics and chaos)

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[J]. 中国物理B, 2025, 34(8): 80702-080702.

参考文献

[1] Mahesh B 2020 IJSR 9 381
[2] Carleo G, Cirac I, Cranmer K, Daudet L, Schuld M, Tishby N, Vogt- Maranto L and Zdeborová L 2019 Rev. Mod. Phys. 91 045002
[3] Broecker P, Assaad F F and Trebst S 2017 arXiv:1707.00663[condmat]
[4] Carrasquilla J and Melko R G 2017 Nat. Phys. 13 431
[5] Xu R, FuWand Zhao H 2019 arXiv:1901.00774[cond-mat.stat-mech]
[6] Zhang W, Liu J and Wei T C 2019 Phys. Rev. E 99 032142
[7] Carleo G and Troyer M 2017 Science 355 602
[8] VanderPlas J, Connolly A J and Gray A 2012 2012 Conference on Intelligent Data Understanding 18 47
[9] Mehta P, Bukov M, Wang C H, Day A G, Richardson C, Fisher C K and Schwab D J 2019 Phys. Rep. 810 1
[10] Carleo G, Cirac I, Cranmer K, Daudet L, Schuld M, Tishby N, Vogt- Maranto L and Zdeborová L 2019 Rev. Mod. Phys. 91 045002
[11] Landau D and Binder K 2021 A guide to Monte Carlo simulations in statistical physics (Cambridge: Cambridge University Press)
[12] Shen J, Li W, Deng S and Zhang T 2021 Phys. Rev. E 103 052140
[13] Hinrichsen H 2000 Adv. Phys. 49 815
[14] Takeuchi K A, Kuroda M, Chate H and Sano M 2007 Phys. Rev. Lett. 99 234503
[15] Carrasquilla J and Melko R G 2017 Nat. Phys. 13 431
[16] Tanaka A and Tomiya A 2017 J. Phys. Soc. Jpn. 86 063001
[17] Horani A, Ustione A, Huang T, Firth A L, Pan J, Gunsten S P, Haspel J A, Piston D W and Brody S L 2018 Proc. Natl. Acad. Sci. USA 115
[18] Wang L 2016 Phys. Rev. B 94 195105
[19] Hughes R I 1999 Phys. Ideas Context 52 97
[20] Van Nieuwenburg E P L, Liu Y H and Huber S D 2017 Nat. Phys. 13 435
[21] Marro J and Dickman R 2005 Nonequilibrium Phase Transitions in Lattice Models
[22] Anon 2008 Non-Equilibrium Phase Transitions (Dordrecht: Springer Netherlands)
[23] Obukhov S P 1980 Physica A 101 145
[24] Battiston F, Amico E, Barrat A, Bianconi G, Ferraz de Arruda G, Franceschiello B, Iacopini I, Kéfi S, Latora V and Moreno Y 2021 Nat. Phys. 17 1093
[25] Carleson L and Gamelin T Complex dynamics 1996 Complex dynamics (Springer Science, Business Media)
[26] Bec J, Gustavsson K and Mehlig B 2024 Annu. Rev. Fluid Mech. 56 189
[27] Canet L 2004 Processus de réaction-diffusion: une approche par le groupe de renormalisation non perturbatif
[28] Newman M E J 2002 Phys. Rev. E 66 016128
[29] Takeuchi K A, Kuroda M, Chate H and Sano M 2009 Phys. Rev. E 80 051116
[30] Corso G, Stark H, Jegelka S, Jaakkola T and Barzilay R 2024 Nature Reviews Methods Primers 4 17
[31] Vivas D, Madronero J, Bucheli V, Gomez L and Reina J 2022 arXiv:2204.12966[quant-ph]
[32] Steeven J, Aurelien B, Madiha N, Julie D, Nicolas T and Christian W 2023 arXiv:2302.10803[cs.LG]
[33] Munikoti S, Das L and Natarajan B 2022 Neurocomputing 468 211
[34] Velickovic P, Cucurull G, Casanova A, Romero A, Lio P and Bengio Y 2018 Graph Attention Networks 2018 arXiv:1710.10903[stat]
[35] Gholamalinezhad H and Khosravi H 2020 arXiv:2009.07485[cs]

Graph neural networks unveil universal dynamics in directed percolation

Graph neural networks unveil universal dynamics in directed percolation

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