Topology Identification For Complex Dynamical Networks Based On Machine Learning

In complex dynamical networks,the mutual coupling between nodes and the interaction between different networks constitute a complex relationship.As one of the basic attributes of the network,network topology is the research basis of many problems such as network fault diagnosis.However,in the real world,the topology of most networks and the interaction between different networks cannot be accurately measured or completely unknown.Therefore,the topology identification of single-layer and multi-layer complex dynamical networks has attracted the attention of many researchers.Researchers have proposed different topology identification strategies based on constructing the drive and response network,compressive sensing,pattern matching,causality and other theories.However,due to the limitations of various physical conditions and theories,these methods have their own limitations.For example,the method of constructing the drive and response network needs to satisfy the linear independence condition and the Lipschitz continuous condition,and the compressive sensing has certain requirements on the time interval of the data and the sparsity of the network.With the advent of the era of big data,the accumulation of data and the development of machine learning methods have opened up new ideas for topology identification for complex dynamical network.Based on the time series data of node state,using machine learning algorithm to identify topology of complex dynamical network has the advantages of high accuracy,small impact on the original network and low application cost.The main contents and innovations of this thesis are as follows:(1)Aiming at the problem of topology identification for single-layer complex dynamical networks,an identification method based on traditional machine learning algorithm Extreme Gradient Boosting(XGBoost)is proposed.Firstly,by designing different types of feature extractors,the feature sequence is extracted from the original time series data of the node,and the training data set is constructed and input into XGBoost.In the training process of XGBoost,the information gain of each input feature is calculated when constructing the classification and regression tree,and the matrix representing information gain score between nodes is constructed.Then,the adjacency matrix is obtained by clustering and binarization of the matrix representing information gain score and the fusion of the matrix representing information gain score to realize topology identification.Finally,the effectiveness of the method is verified by simulation data and real data sets,and the influence of different noises and training data with different sample numbers on the identification effect of the method is studied.(2)Considering the diverse interactions between nodes in multi-layer complex dynamical networks,the topology identification method for single-layer complex dynamical networks cannot be directly applied to multi-layer complex dynamical networks.Therefore,an improved topology identification method based on multiple feature extractors and XGBoost is proposed for multi-layer complex dynamical networks with the same type and number of nodes in each layer and arbitrary connection of nodes between layers,and multi-layer complex dynamical networks with different type and number of nodes in each layer and arbitrary connection of nodes between layers.Compared with single-layer complex dynamical networks,the topology of multi-layer complex dynamical networks includes intra-layer topology and inter-layer topology.When the node types of each layer are the same,the feature extractor and XGBoost are used to calculate the total matrix representing information gain score containing the intra-layer driving relationship and the inter-layer driving relationship,and the topology is obtained by clustering,binarization and fusion of the total matrix representing information gain score.When the types of nodes in each layer are different,different network layers have different dynamic characteristics,so the feature extractors adapted to each layer are also different.The candidate set of the feature extractor combination is designed and the size of the candidate set is reduced by pre-selection.The matrix representing information gain score is calculated by using the topology identification method when the node types of each layer are the same,and the adjacency matrix of the intra-layer topology and the inter-layer topology is derived according to the driving relationship type to realize the topology identification.Finally,the effectiveness of the method is verified by numerical simulation,and the influence of different training data and different time steps on the identification results is studied.(3)Considering the dependence of traditional machine learning methods on feature engineering,the graph deep learning algorithm is used to automatically extract features.Aiming at the multi-layer complex dynamical network with the same type of nodes and one-to-one correspondence between nodes in each layer and the above two types of networks,an identification method based on Graph Neural Networks(GNN)is proposed.For the multi-layer complex dynamical networks with the same type of nodes in each layer,the model is divided into two parts.The first part is the topology generator,which is represented by a parameter matrix.In this part,the spliced and encoded node vectors are input into the Graph Neural Networks.Based on the topology generated by the topology generator,multiple sets of Multilayer Perceptron(MLP)are used to simulate the transmission and aggregation of information between nodes,and the dynamics of the nodes are fitted.The Gumbel Softmax sampling method is used to generate the topology,so that the gradient can be propagated back to the topology generator parameter matrix.Considering the sparsity of complex dynamical networks,this prior knowledge is added to the objective function.The Gumbel Softmax sampling method is used to generate the topology,so that the gradient can be propagated back to the topology generator parameter matrix.Considering the sparsity of complex dynamical networks,this prior knowledge is added to the objective function.After the model training is completed,the adjacency matrix of the network topology can be obtained by sampling the topology generator parameter matrix to realize topology identification.For multi-layer complex dynamical networks with different types and numbers of nodes in each layer,the network layer encoder is introduced on the basis of the above model.The new vector representation is mapped by MLP to distinguish the weight parameters that simulate different dynamics of each network layer in the parameter space.Through numerical simulation,the effectiveness of the method is verified by comparing with other Baseline algorithms.At the same time,the influence of different data volume training sets and different node numbers on the identification performance of the method is studied.