  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.
