Neural Dynamics on Complex Networks

We introduce a deep learning model to learn continuous-time dynamics on complex networks and infer the semantic labels of nodes in the network at terminal time. We formulate the problem as an optimal control problem by minimizing a loss function consisting of a running loss of network dynamics, a terminal loss of nodes' labels, and a neural-differential-equation-system constraint. We solve the problem by a differential deep learning framework: as for the forward process of the system, rather than forwarding through a discrete number of hidden layers, we integrate the ordinary differential equation systems on graphs over continuous time; as for the backward learning process, we learn the optimal control parameters by back-propagation during solving initial value problem. We validate our model by learning complex dynamics on various real-world complex networks, and then apply our model to graph semi-supervised classification tasks. The promising experimental results demonstrate our model's capability of jointly capturing the structure, dynamics and semantics of complex systems.