Many complex processes can be viewed as dynamical systems on networks. However, in real cases, only the performances of the system are known, the network structure and the dynamical rules are not observed. Therefore, recovering latent network structure and dynamics from observed time series data are important tasks because it may help us to open the black box, and even to build up the model of a complex system automatically. Although this problem hosts a wealth of potential applications in biology, earth science, and epidemics etc., conventional methods have limitations. In this work, we introduce a new framework, Gumbel Graph Network (GGN), which is a model-free, data-driven deep learning framework to accomplish the reconstruction of both network connections and the dynamics on it. Our model consists of two jointly trained parts: a network generator that generating a discrete network with the Gumbel Softmax technique; and a dynamics learner that utilizing the generated network and one-step trajectory value to predict the states in future steps. We exhibit the universality of our framework on different kinds of time-series data: with the same structure, our model can be trained to accurately recover the network structure and predict future states on continuous, discrete, and binary dynamics, and outperforms competing network reconstruction methods.

中文翻译：

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用于网络重建和动力学学习的通用深度学习框架

可以将许多复杂的过程视为网络上的动态系统。但是，在实际情况下，只有系统的性能是已知的，而没有观察到网络结构和动态规则。因此，从观察到的时间序列数据中恢复潜在的网络结构和动力学是重要的任务，因为它可以帮助我们打开黑匣子，甚至可以自动建立复杂系统的模型。尽管此问题在生物学，地球科学和流行病等方面具有大量潜在应用，但常规方法仍存在局限性。在这项工作中，我们介绍了一个新框架Gumbel Graph Network（GGN），它是一个无模型的，数据驱动的深度学习框架，可以完成网络连接及其动态性的重建。我们的模型包括两个共同训练的部分：网络生成器，该网络生成器使用Gumbel Softmax技术生成离散网络；以及动力学学习者，它利用生成的网络和一步式轨迹值来预测未来步骤中的状态。我们在不同类型的时间序列数据上展示了我们框架的通用性：使用相同的结构，可以训练我们的模型以在连续，离散和二进制动力学上准确地恢复网络结构并预测未来状态，并且胜过竞争性网络重构方法。