  Many dynamical processes of complex systems can be understood as the dynamics
of a group of nodes interacting on a given network structure. However, finding
such interaction structure and node dynamics from time series of node
behaviours is tough. Conventional methods focus on either network structure
inference task or dynamics reconstruction problem, very few of them can work
well on both. This paper proposes a universal framework for reconstructing
network structure and node dynamics at the same time from observed time-series
data of nodes. We use a differentiable Bernoulli sampling process to generate a
candidate network structure, and use neural networks to simulate the node
dynamics based on the candidate network. We then adjust all the parameters with
a stochastic gradient descent algorithm to maximize the likelihood function
defined on the data. The experiments show that our model can recover various
network structures and node dynamics at the same time with high accuracy. It
can also work well on binary, discrete and continuous time-series data, and the
reconstruction results are robust against noise and missing information.

Physics and Society;Chaotic Dynamics;Molecular Networks