Often, closed -- form analytic formulations are not available and forecasting or decision making tasks have to rely on noisy, irregularly sampled observations. This class of systems offers a crystal clear example of inductive relational biases. Introducing inductive biases in statistics or machine learning is a well known approach to improving sample efficiency and generalization performance. From the choice of objective function, to the design of ad -- hoc deep learning architectures suited to the specific problem at hand, biases are common and effective. Relational inductive biases [1] represent a special class of biases, concerned with relationship between entities.

We extend the framework of graph neural networks (GNN) to continuous time. Graph neural ordinary differential equations (GDEs) are introduced as the counterpart to GNNs where the input--output relationship is determined by a continuum of GNN layers. The GDE framework is shown to be compatible with the majority of commonly used GNN models with minimal modification to the original formulations. We evaluate the effectiveness of GDEs on both static as well as dynamic datasets: results prove their general effectiveness even in cases where the data is not generated by continuous time processes.