Reconstruction of complex network from time series data based on graph attention network and Gumbel Softmax

It is a challenging practical problem to infer the network structure from measurable time series data. Recently, with the rapid development of graph deep learning, Zhang et al. [Appl. Netw. Sci. 4, 110 (2019)] applied graph neural network to the field of network reconstruction and proposed Gumbel Graph Network. In this paper, a graph deep learning network reconstruction method based on graph attention network and Gumbel Softmax (GAT-GS) is proposed, which can realize high accuracy network reconstruction and node state prediction of discrete and continuous systems. The GAT-GS model is designed based on the dynamic equation of nodes. It consists of two parts: a network structure learner to reconstruct a more real rather than functionally connected networks, based on Gumbel Softmax sampling to generate network structures; and a node state learner using graph attention networks to learn the state evolution of nodes, with the introduction of Laplacian matrix and adjacency matrix for better adaptation to diffusion coupling and unidirectional coupling systems. This model is trained to dynamically adjust the network adjacency matrix and attention coefficients to obtain the network structure and predict the node state. Experimental results show that the GAT-GS model has high reconstruction accuracy, strong robustness and high universality. It can be applied to various kinds of dynamic systems, including Coupled Map Lattice model and Lorenz system, can deal with time series data from regular to complete chaos, can reconstruct various kinds of complex networks, including regular network, Barabási–Albert network and Watts–Strogatz small world network, and it can also reconstruct networks from small scale to large scale with higher computational efficiency.