Network structures in various backgrounds play important roles in social, technological, and biological systems. However, the observable network structures in real cases are often incomplete or unavailable due to measurement errors or private protection issues. Therefore, inferring the complete network structure is useful for understanding complex systems. The existing studies have not fully solved the problem of inferring network structure with partial or no information about connections or nodes. In this paper, we tackle the problem by utilizing time series data generated by network dynamics. We regard the network inference problem based on dynamical time series data as a problem of minimizing errors for predicting future states and proposed a novel data-driven deep learning model called Gumbel Graph Network (GGN) to solve the two kinds of network inference problems: Network Reconstruction and Network Completion. For the network reconstruction problem, the GGN framework includes two modules: the dynamics learner and the network generator. For the network completion problem, GGN adds a new module called the States Learner to infer missing parts of the network. We carried out experiments on discrete and continuous time series data. The experiments show that our method can reconstruct up to 100% network structure on the network reconstruction task. While the model can also infer the unknown parts of the structure with up to 90% accuracy when some nodes are missing. And the accuracy decays with the increase of the fractions of missing nodes. Our framework may have wide application areas where the network structure is hard to obtained and the time series data is rich.

中文翻译：

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通过图神经网络从时间序列数据推断网络结构和动态

各种背景下的网络结构在社会、技术和生物系统中发挥着重要作用。然而，由于测量错误或隐私保护问题，实际情况下可观察的网络结构往往不完整或不可用。因此，推断完整的网络结构对于理解复杂系统很有用。现有的研究还没有完全解决在部分或没有连接或节点信息的情况下推断网络结构的问题。在本文中，我们通过利用网络动态生成的时间序列数据来解决这个问题。我们将基于动态时间序列数据的网络推理问题视为预测未来状态的误差最小化问题，并提出了一种新的数据驱动深度学习模型 Gumbel Graph Network (GGN) 来解决两类网络推理问题：重建和网络完成。对于网络重构问题，GGN 框架包括两个模块：动态学习器和网络生成器。对于网络完成问题，GGN 添加了一个名为 States Learner 的新模块来推断网络的缺失部分。我们对离散和连续的时间序列数据进行了实验。实验表明，我们的方法可以在网络重建任务上重建高达 100% 的网络结构。当某些节点缺失时，该模型还可以以高达 90% 的准确率推断结构的未知部分。并且精度随着缺失节点比例的增加而衰减。我们的框架可能具有广泛的应用领域，其中网络结构难以获得且时间序列数据丰富。