  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.
