Revealing the continuous dynamics on the networks is essential for understanding, predicting, and even controlling complex systems, but it is hard to learn and model the continuous network dynamics because of complex and unknown governing equations, high dimensions of complex systems, and unsatisfactory observations. Moreover, in real cases, observed time-series data are usually non-uniform and sparse, which also causes serious challenges. In this paper, we propose an Autoregressive GNN-ODE GRU Model (AGOG) to learn and capture the continuous network dynamics and realize predictions of node states at an arbitrary time in a data-driven manner. The GNN module is used to model complicated and nonlinear network dynamics. The hidden state of node states is specified by the ODE system, and the augmented ODE system is utilized to map the GNN into the continuous time domain. The hidden state is updated through GRUCell by observations. As prior knowledge, the true observations at the same timestamp are combined with the hidden states for the next prediction. We use the autoregressive model to make a one-step ahead prediction based on observation history. The prediction is achieved by solving an initial-value problem for ODE. To verify the performance of our model, we visualize the learned dynamics and test them in three tasks: interpolation reconstruction, extrapolation prediction, and regular sequences prediction. The results demonstrate that our model can capture the continuous dynamic process of complex systems accurately and make precise predictions of node states with minimal error. Our model can consistently outperform other baselines or achieve comparable performance.

本文介绍了一种基于自回归 GNN-ODE GRU 模型（AGOG）的方法，通过对复杂系统连续动态过程的建模和预测实现了任意时间节点状态的数据驱动预测，展示了在插值重建、外推预测和正常序列预测等三个任务中的精度表现。

自回归GNN-ODE GRU模型用于网络动态