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 behaviors 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 we 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.

中文翻译：

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从离散或连续动态数据重建复杂网络和节点动态的通用框架

复杂系统的许多动力学过程可以理解为一组节点在给定网络结构上相互作用的动力学。然而，从节点行为的时间序列中找到这样的交互结构和节点动态是很困难的。传统方法要么专注于网络结构推理任务，要么专注于动力学重建问题，很少有人能同时兼顾两者。本文提出了一个通用框架，用于从观察到的节点时间序列数据同时重构网络结构和节点动态。我们使用可微分伯努利采样过程来生成候选网络结构，我们使用神经网络来模拟基于候选网络的节点动态。然后，我们使用随机梯度下降算法调整所有参数，以最大化数据上定义的似然函数。实验表明，我们的模型可以同时高精度地恢复各种网络结构和节点动态。它还可以很好地处理二进制、离散和连续的时间序列数据，并且重建结果对噪声和丢失信息具有鲁棒性。