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.
@article{arxiv.2106.11581,
title = {Continuous-Depth Neural Models for Dynamic Graph Prediction},
author = {Michael Poli and Stefano Massaroli and Clayton M. Rabideau and Junyoung Park and Atsushi Yamashita and Hajime Asama and Jinkyoo Park},
journal= {arXiv preprint arXiv:2106.11581},
year = {2021}
}
Comments
Extended version of the workshop paper "Graph Neural Ordinary Differential Equations". arXiv admin note: substantial text overlap with arXiv:1911.07532