Modeling and Simulation of Complex Systems Based on Graph Neural Networks

doi:10.16182/j.issn1004731x.joss.25-0512

Abstract

Abstract:

Modeling and simulation of complex systems are critical issues for understanding their structural and functional properties. The ability of graph neural networks (GNNs) to learn and represent the internal correlations within data provides a new approach for modeling and simulating complex systems. Currently, there are various types of GNN models involving frequency-domain, spatial-domain, generative, heterogeneous, and spatio-temporal models. These models are widely applied in complex system modeling and simulation research in multiple fields such as industrial internet, social networks, and supply chains based on specific tasks and scenarios. Starting from three representative tasks: network topology representation, dynamic evolution modeling, and system behavior and structure generation, this paper systematically analyzed GNN applications in modeling and simulation of complex systems, and its advantages in capturing multi-level structures, dynamic interactions, and nonlinear relationships within complex systems were explored. It provided a new reference for the research on the integration of complex systems with GNNs.

Key words: complex system, graph neural networks(GNNs), structural representation, complex network, graph representation learning

CLC Number:

TP183

Lü Jinhu, Jiang Hongyi, Liu Deyuan, Tan Shaolin. Modeling and Simulation of Complex Systems Based on Graph Neural Networks[J]. Journal of System Simulation, 2025, 37(7): 1624-1638.

Figures/Tables 4

Table 1

Table 2

Fig. 1

Fig. 2

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维度	现有建模与仿真方法	基于图神经网络的建模与仿真方法
理论基础	微分方程、演化动力学等数学物理模型	图论、深度学习等统计机器学习模型
建模对象	线性系统、欧氏空间下的规则网格数据等	非欧、动态、异构的复杂数据
仿真计算效率	需进行大量精确运算，效率较低	训练成本较高，但在推理阶段速度较快
动态适应性	需针对具体对象调整模型及其参数	在性质相似的数据上具有较强泛化性
可解释性	物理意义明确	仍为开放的研究问题

类型	代表性方法
消息传递网络(MPNNs)	GCN^[16,42]、ChebNet^[15]、DCNN^[43]、GAT^[12]、GATv2^[13]、GIN^[18]、GraphSAGE^[44]等
Graph Transformer	GraphGPS^[31]、SAT^[32]、Exphormer^[33]、Graphormer^[34]、Polynormer^[35]、Graph Mamba^[36]、HDSE^[45]、GPSE^[46]等
基于随机游走的图模型	CRaWl^[47]、RAW-GNN^[48]、RWC^[49]、NeuralWalker^[50]等
基于热扩散的图模型	HiD-Net^[51]、GDC^[52]、ADC^[53]、GRAND^[54]、NDCN^[55]、NIGCN^[56]等