Graph Neural Ordinary Differential Equations

TL;DR

This paper introduces Graph Neural Ordinary Differential Equations (GDEs), a continuous-depth GNN framework that enhances static and dynamic graph learning by integrating differential equations, leading to computational efficiency and improved performance.

Contribution

The paper formalizes GDEs as a continuous-depth GNN framework, compatible with various models, and demonstrates their advantages in static and dynamic graph tasks.

Findings

GDEs provide computational benefits in static settings.

GDEs improve performance in dynamic graph scenarios.

The framework is compatible with multiple GNN architectures.

Abstract

We introduce the framework of continuous--depth graph neural networks (GNNs). Graph neural ordinary differential equations (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 various static and autoregressive GNN models. Results prove general effectiveness of GDEs: in static settings they offer computational advantages by incorporating numerical methods in their forward pass; in dynamic settings, on the other hand, they are shown to improve performance by exploiting the geometry of the underlying dynamics.