Continuous-Depth Neural Models for Dynamic Graph Prediction
This work addresses dynamic graph prediction problems for domains such as traffic forecasting and genetic regulatory networks, representing a novel method for a known bottleneck.
The authors tackled the problem of dynamic graph prediction by introducing continuous-depth graph neural networks (Neural GDEs), which blend discrete graph structures with differential equations to model input-output relationships through a continuum of layers. Results demonstrate improved performance in applications like traffic forecasting and genetic regulatory networks by exploiting underlying dynamics geometry and handling irregularly sampled data.
We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN layers, blending discrete topological structures and differential equations. The proposed framework is shown to be compatible with static GNN models and is extended to dynamic and stochastic settings through hybrid dynamical system theory. Here, Neural GDEs improve performance by exploiting the underlying dynamics geometry, further introducing the ability to accommodate irregularly sampled data. Results prove the effectiveness of the proposed models across applications, such as traffic forecasting or prediction in genetic regulatory networks.