  Learning continuous-time dynamics on complex networks is crucial for
understanding, predicting and controlling complex systems in science and
engineering. However, this task is very challenging due to the combinatorial
complexities in the structures of high dimensional systems, their elusive
continuous-time nonlinear dynamics, and their structural-dynamic dependencies.
To address these challenges, we propose to combine Ordinary Differential
Equation Systems (ODEs) and Graph Neural Networks (GNNs) to learn
continuous-time dynamics on complex networks in a data-driven manner. We model
differential equation systems by GNNs. Instead of mapping through a discrete
number of neural layers in the forward process, we integrate GNN layers over
continuous time numerically, leading to capturing continuous-time dynamics on
graphs. Our model can be interpreted as a Continuous-time GNN model or a Graph
Neural ODEs model. Our model can be utilized for continuous-time network
dynamics prediction, structured sequence prediction (a regularly-sampled case),
and node semi-supervised classification tasks (a one-snapshot case) in a
unified framework. We validate our model by extensive experiments in the above
three scenarios. The promising experimental results demonstrate our model's
capability of jointly capturing the structure and dynamics of complex systems
in a unified framework.
