计算机科学 ›› 2026, Vol. 53 ›› Issue (6A): 250700014-10.doi: 10.11896/jsjkx.250700014

• 大数据&数据科学 • 上一篇    下一篇

SINDy-GSN:面向社交群体行为的网络动力学稀疏识别模型

王钰涵1, 马涪元2, 马世旋3, 王英4   

  1. 1 吉林大学软件学院 长春 130012
    2 吉林大学人工智能学院 长春 130012
    3 吉林大学计算机科学与技术学院 长春 130012
    4 符号计算与知识工程教育部重点实验室(吉林大学) 长春 130012
  • 出版日期:2026-06-16 发布日期:2026-06-12
  • 通讯作者: 王英(wangying2010@jlu.edu.cn)
  • 作者简介:(yuhanw23@mails.jlu.edu.cn)
  • 基金资助:
    复杂动态系统智能理论与方法研究(2021ZD0112500);国家自然科学基金(62272191,62372211)

SINDy-GSN:Sparse Identification of Network Dynamics for Group Behavior in Social Graphs

WANG Yuhan1, MA Fuyuan2, MA Shixuan3, WANG Ying4   

  1. 1 College of Software,Jilin University,Changchun 130012,China
    2 College of Artificial Intelligence,Jilin University,Changchun 130012,China
    3 College of Computer Science and Technology,Jilin University,Changchun 130012,China
    4 Key Laboratory of Symbol Computation and Knowledge Engineering of the Ministry of Education,Changchun 130012,China
  • Published:2026-06-16 Online:2026-06-12
  • About author:WANG Yuhan,born in 2001,postgra-duate.Her main research interests include machine learning and deep lear-ning.
    WANG Ying,born in 1981,Ph.D,professor,Ph.D supervisor,is a member of CCF(No.18369S).Her main research interests include machine learning,social networks,data mining and search engines.
  • Supported by:
    Foundation of the Major Project of Scicnce and Technology Innovation 2030-New Generation of Artifiial Intelligence(2021ZD0112500) and National Natural Science Foundation of China(62272191,62372211).

摘要: 社交网络中群体行为的演化过程通常呈现出非线性、多主体耦合与结构异质性等特征,传统建模方法在揭示其潜在演化规律方面存在局限性。为深入刻画社交网络中群体行为的动态演化机制,提出一种结构耦合函数库驱动的改进型动力学识别模型——SINDy-GSN(Sparse Identification of Network Dynamics for Group Behavior in Social Graphs)。该方法以特征驱动的离散仿真为基础,融合用户节点行为状态、邻接传播结构与主题信息构建三元状态向量,生成适用于社交网络环境的高维非线性函数库。所构建函数库集成了一阶邻居影响、结构归一化扩散项及主题传播耦合机制,全面捕捉个体行为与网络拓扑之间的复杂动态耦合关系。基于真实社交平台特征数据构建仿真网络,并通过离散演化模拟群体立场传播过程,从而实现对群体行为演化方程的稀疏建模与机制识别。实验结果表明,SINDy-GSN 在保持建模可解释性与结构稀疏性的同时,能够有效识别社交网络中的群体传播机制与演化规律,为社交系统中复杂行为的建模与预测提供了通用化的理论工具与方法框架,展现出良好的适应性与拓展潜力。

关键词: 社交网络, 函数库构建, SINDy, 网络动力学, 稀疏回归

Abstract: The evolution of group behavior in social networks is often marked by nonlinearity,multi-agent coupling,and structural heterogeneity,posing challenges for traditional modeling methods in uncovering the underlying dynamics.To better capture these dynamics,this paper proposes an improved method for dynamic identification based on a structure-coupled function library—SINDy-GSN.The method leverages feature-driven discrete simulation,integrating user behavior states,adjacency structures,and topic information to construct a tripartite state vector,generating a high-dimensional nonlinear function library suited for social networks.The library incorporates first-order neighbor influence,normalized diffusion,and topic propagation coupling,effectively capturing the dynamic interplay between individual behavior and network structure.Using real-world social platform data,a simulation network is created,and discrete evolution models the propagation of group stances,enabling sparse modeling and identification of group behavior dynamics.Results show that SINDy-GSN maintains interpretability and sparsity while accurately identi-fying group propagation mechanisms,offering a versatile framework for modeling and predicting complex social behaviors,with strong adaptability and scalability.

Key words: Social networks, Function library construction, SINDy, Network dynamics, Sparse regression

中图分类号: 

  • TP393
[1] GAO J,BARZEL B,BARABÁSI A L.Universal resilience patterns in complex networks[J].Nature,2016,530(7590):307-312.
[2] HARUSH U,BARZEL B.Dynamic patterns of information flow in complex networks[J].Nature Communications,2017,8(1):2181.
[3] HENS C,HARUSH U,HABER S,et al.Spatiotemporal signalpropagation in complex networks[J].Nature Physics,2019,15(4):403-412.
[4] BARZEL B,BARABÁSI A L.Universality in network dynamics[J].Nature Physics,2013,9(10):673-681.
[5] BRUNTON S L,PROCTOR J L,KUTZ J N.Discovering governing equations from data by sparse identification of nonlinear dynamical systems[J].Proceedings of the National Academy of Sciences,2016,113(15):3932-3937.
[6] MANGAN N M,BRUNTON S L,PROCTOR J L,et al.Inferring biological networks by sparse identification of nonlinear dynamics[J].IEEE Transactions on Molecular,Biological,and Multi-Scale Communications,2017,2(1):52-63.
[7] KAISER E,KUTZ J N,BRUNTON S L.Sparse identification of nonlinear dynamics for modelpredictive control in the low-data limit[J].Proceedings of the Royal Society A,2018,474(2219):20180335.
[8] LIANG J,ZHANG X,WANG K,et al.Discovering dynamicmodels of COVID-19 transmission[J].Transboundary and Emerging Diseases,2022,69(4):e64-e70.
[9] QUADE M,ABEL M,NATHAN KUTZ J,et al.Sparse identification of nonlinear dynamics for rapid model recovery[J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2018,28(6):063116.
[10] JIANG Y,SUN J.Evo-SINDy:Universal Discovery of Partial Differential Equations Using Cooperative Evolutionary Computation[C]//Proceedings of the Genetic and Evolutionary Computation Conference.2025:791-799.
[11] HASTIE T,TIBSHIRANI R,WAINWRIGHT M.Statisticallearning with sparsity[J].Monographs on Statistics and Applied Probability,2015,143(143):8.
[12] ZHENG P,ASKHAM T,BRUNTON S L,et al.A unifiedframework for sparse relaxed regularizedregression:SR3[J].IEEE Access,2018,7:1404-1423.
[13] FASEL U,KUTZ J N,BRUNTON B W,et al.Ensemble-SINDy:Robust sparse model discovery in the low-data,high-noise limit,with active learning and control[J].Proceedings of the Royal Society A,2022,478(2260):20210904.
[14] PAN S,BRUNTON S L,KUTZ J N.Neural Implicit Flow:a mesh-agnostic dimensionality reductionparadigm of spatio-temporal data[J].Journal of Machine Learning Research,2023,24(41):1-60.
[15] SERVIA M Á C,SANDOVAL I O,HELLGARDT K,et al.The Automated Discovery of Kinetic Rate Models--Methodological Frameworks[J].arXiv:2301.11356,2023.
[16] SOROKINA M,SYGLETOS S,TURITSYN S.Sparse identification for nonlinear optical communication systems:SINO me-thod[J].Optics Express,2016,24(26):30433-30443.
[17] DAM M,BRØNS M,JUUL RASMUSSEN J,et al.Sparse identification of a predator-prey system from simulation data of a convection model[J].Physics of Plasmas,2017,24(2):022310.
[18] LI R,SUN C,DONG M,et al.The controllability analysis of brain networks during rhythmic propagation[J].IEEE Transactions on Network Science and Engineering,2024,11(4):3812-3823.
[19] NAKARMI U,RAHNAMAY-NAEINI M,KHAMFROUSHH.Critical component analysis in cascading failures for power grids using community structures in interaction graphs[J].IEEE Transactions on Network Science and Engineering,2019,7(3):1079-1093.
[20] KOLEY S.Critically reckoning spectrophotometric detection of asymptomatic cyanotoxins and faecal contamination in periurban agrarian ecosystems via convolutional neural networks[J].Trends in Sciences,2024,21(12):8528-8528.
[21] ZHANG Q,YU K,GUOZ,et al.Graph neural network-driven traffic forecasting for the connected internet of vehicles[J].IEEE Transactions on Network Science and Engineering,2021,9(5):3015-3027.
[22] DONG Y,ZHAN M,KOU G,et al.A survey on the fusionprocess in opinion dynamics[J].Information Fusion,2018,43:57-65.
[23] DELABAYS R,DE PASQUALE G,DÖRFLER F,et al.Hypergraph reconstruction from dynamics[J].Nature Communications,2025,16(1):2691.
[24] ZHANG L,SCHAEFFER H.On the convergence of the SINDy algorithm[J].Multiscale Modeling & Simulation,2019,17(3):948-972.
[25] BONGARD J,LIPSON H.Automated reverse engineering ofnonlinear dynamical systems[J].Proceedings of the National Academy of Sciences,2007,104(24):9943-9948.
[26] SCHMIDT M,LIPSON H.Distilling free-form natural lawsfrom experimental data[J].Science,2009,324(5923):81-85.
[27] KOZA J R.Genetic programming:On the programming of computers by means of natural selection[M].MIT Press,1992.
[28] GEAR C W,HYMAN J M,KEVREKIDID P G,et al.Equation-free,coarse-grained multiscale computation:Enabling mocroscopic simulators to perform system-level analysis[J].Commiunications in Mathematical Sciences,2003,1(4):715-762.
[29] RAISSI M,PERDIKARIS P,KARNIADAKIS G E.Physics-informed neural networks:A deep learning framework for solving forward and inverse problems involving nonlinear partial diffe-rential equations[J].Journal of Computational Physics,2019,378:686-707.
[30] LONG Z,LU Y,DONG B.PDE-Net 2.0:Learning PDEs from data with a numeric-symbolic hybrid deep network[J].Journal of Computational Physics,2019,399:108925.
[31] STEPHANY R,EARLS C.PDE-READ:Human-readable partial differential equation discovery using deep learning[J].Neural Networks,2022,154:360-382.
[32] LU L,JIN P,PANG G,et al.Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators[J].Nature machine intelligence,2021,3(3):218-229.
[33] CAMPS-VALLS G,GERHARDUS A,NINAD U,et al.Disco-vering causal relations and equations from data[J].Physics Reports,2023,1044:1-68.
[34] XU H,CHANG H,ZHANG D.DLGA-PDE:Discovery of PDEs with incomplete candidate library via combination of deep lear-ning and genetic algorithm[J].Journal of Computational Physics,2020,418:109584.
[35] CHEN Y,LUO Y,LIU Q,et al.Symbolic genetic algorithm for discovering open-form partial differential equations(SGA-PDE)[J].Physical Review Research,2022,4(2):023174.
[36] MASLYAEV M,HVATOV A,KALYUZHNAYA A V.Partial differential equations discovery with EPDE framework:Application for real and synthetic data[J].Journal of Computational Science,2021,53:101345.
[37] ATKINSON S,SUBBER W,WANG L,et al.Data-driven discovery of free-form governing differential equations[J].arXiv:1910.05117,2019.
[38] IVANCHIK E,HVATOV A.Knowledge-aware differentialequation discovery with automated background knowledge extraction[J].Information Sciences,2025,712:122131.
[39] MASLYAEV M,HVATOV A.Equation discovery framework EPDE:Towards a better equation discovery[J].arXiv:2501.14768,2025.
[40] WANG Y,LIU Y,LIU N,et al.AdaGCL+:An Adaptive Subgraph Contrastive Learning Towards Tackling Topological Bias[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2025,47(9):8073-8087.
[41] HE X,WANG Y,FAN W,et al.Mamba-based graph convolu-tional networks:Tackling over-smoothing with selective state space[J].arXiv:2501.15461,2025.
[42] JUAN X,PENG M,WANG X.Dynamic self-training with less uncertainty for graph imbalance learning[J].Expert Systems with Applications,2025,271:126643.
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