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Network structures in various backgrounds play important roles in social,technological, and biological systems. However, the observable networkstructures in real cases are often incomplete or unavailable due to measurementerrors or private protection issues. Therefore, inferring the complete networkstructure is useful for understanding complex systems. The existing studieshave not fully solved the problem of inferring network structure with partialor no information about connections or nodes. In this paper, we tackle theproblem by utilizing time series data generated by network dynamics. We regardthe network inference problem based on dynamical time series data as a problemof minimizing errors for predicting future states and proposed a noveldata-driven deep learning model called Gumbel Graph Network (GGN) to solve thetwo kinds of network inference problems: Network Reconstruction and NetworkCompletion. For the network reconstruction problem, the GGN framework includestwo modules: the dynamics learner and the network generator. For the networkcompletion problem, GGN adds a new module called the States Learner to infermissing parts of the network. We carried out experiments on discrete andcontinuous time series data. The experiments show that our method canreconstruct up to 100% network structure on the network reconstruction task.While the model can also infer the unknown parts of the structure with up to90% accuracy when some nodes are missing. And the accuracy decays with theincrease of the fractions of missing nodes. Our framework may have wideapplication areas where the network structure is hard to obtained and the timeseries data is rich.

Inference for Network Structure and Dynamics from Time Series Data via Graph Neural Network