Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional neural networks, deep graph networks do not necessarily yield better performance than shallow graph networks. This behavior usually stems from the over-smoothing phenomenon. In this work, we propose a family of architectures to control this behavior by design. Our networks are motivated by numerical methods for solving Partial Differential Equations (PDEs) on manifolds, and as such, their behavior can be explained by similar analysis. Moreover, as we demonstrate using an extensive set of experiments, our PDE-motivated networks can generalize and be effective for various types of problems from different fields. Our architectures obtain better or on par with the current state-of-the-art results for problems that are typically approached using different architectures.

本文提出了一类基于偏微分方程数值方法的图神经网络架构来解决传统卷积神经网络可能存在的过度平滑问题，通过实验证明该方法可以处理不同领域的问题并在某些领域获得优于或相当于当前最先进结果。

PDE-GCN:基于偏微分方程驱动的图神经网络的创新结构