Research On Reconstructing Network Structure From Time Series Data Based On Graph Network

Complex network is a new research hotspot of interdisciplinary.People’s interest in complex networks mainly stems from that almost all systems can be modeled into corresponding complex networks for research and analysis.For example,electric power networks,neural networks,transportation networks,computer networks,social networks,economic and financial networks and so on.Network topology plays an important role in complex network systems under various backgrounds.It is of great significance to recover the potential network structure from the observed time series data.In reality,it is often difficult to detect the edge of the network directly.Therefore,inferring network structure(network reconstruction)from measurable time series data is becoming an important frontier topic in the study of complex networks.Among the existing network reconstruction methods,one is the reconstruction method based on statistics.For example,correlation analysis,information entropy,Granger causality and Bayesian inference.These methods usually reconstruct functional networks,which reflect the functional coupling and some statistical characteristics between network nodes,which are not necessarily the same as the real network physical connection.The other is reconstruction methods based on dynamic equations,such as driving response and compressed sensing.Although these methods may be able to reconstruct the real network structure,some of them do not consider the influence of noise,some may not be able to deal with strong noise,and some need a specific dynamic model.Recently,deep learning technology has been booming.With the advantages of model free and strong fitting ability,they have achieved success in many fields,but there is little work to apply them to network reconstruction.At the same time,many deep learning methods are often black boxes,which can extract the feature of information from high dimensions,but it is very difficult for people to understand,which limits its application in scenes requiring interpretability.Therefore,applying deep learning technology to complex network reconstruction and node state prediction is the starting point of this paper.At the same time,we understand and design deep learning model from the perspective of network dynamics system,so that our model can be more interpretable.Based on the dynamic process of diffusion coupling and unidirectional coupling,this study designs the graph deep learning network reconstruction method GAT-GS by using Graph Attention Network(GAT),Gumbel softmax(GS)and other machine learning algorithms.The following innovative research results are obtained:GAT-GS model can realize the reconstruction of complex networks and the prediction of node states by using measurable time series data.It is mainly composed of node state learner and adjacency matrix learner,which are trained independently.The graph attention network is introduced into the node state learner.With the help of the state information of the node,the weight of the attention coefficient between the neighbor nodes can be calculated,and the attention coefficient is equivalent to the coupling strength coefficient in the dynamic equation.With the constraints of the network structure generated by the adjacency matrix learner,the global attention coefficient will be selectively retained or eliminated,so as to eliminate those node pairs that have strong correlation but are not actually connected.In the framework of GAT-GS model,we design the GAT-GS model algorithm under diffusion coupling.In this algorithm,the network structure adopts Laplace matrix,and the algorithm is applied to diffusion coupled image lattice system and Lorentz system.The results show that the algorithm has high reconstruction accuracy and good robustness in dealing with regular network,BarabasAlbert(BA)scale-free network and Watts Strogatz(WS)small world network,time series data from regular to complete chaos.At the same time,under the framework of GAT-GS model,the algorithm of GAT-GS model under unidirectional coupling is designed.In this algorithm,the network structure adopts adjacency matrix.The algorithm is applied to the unidirectional coupled Lorentz system and good reconstruction results are obtained.Taking the diffusion coupled map lattice system as an example,the GAT-GS model algorithm under diffusion coupling and GAT-GS model algorithm under unidirectional coupling are compared.