PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations

Graph neural networks are have shown their efficacy in fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike convolutional neural networks, deep graph networks do not necessarily yield better performance than shallow networks. This behaviour usually stems from the over-smoothing phenomenon. In this work, we propose a family of architecturesto control this behaviour by design. Our networks are motivated by numerical methods for solving Partial Differential Equations (PDEs) on manifolds, and as such, their behaviour can be explained by similar analysis.