Physics-informed Graph Neural Networks have achieved remarkable performance in learning through graph-structured data by mitigating common GNN challenges such as over-smoothing, over-squashing, and heterophily adaption. Despite these advancements, the development of a simple yet effective paradigm that appropriately integrates previous methods for handling all these challenges is still underway. In this paper, we draw an analogy between the propagation of GNNs and particle systems in physics, proposing a model-agnostic enhancement framework. This framework enriches the graph structure by introducing additional nodes and rewiring connections with both positive and negative weights, guided by node labeling information. We theoretically verify that GNNs enhanced through our approach can effectively circumvent the over-smoothing issue and exhibit robustness against over-squashing. Moreover, we conduct a spectral analysis on the rewired graph to demonstrate that the corresponding GNNs can fit both homophilic and heterophilic graphs. Empirical validations on benchmarks for homophilic, heterophilic graphs, and long-term graph datasets show that GNNs enhanced by our method significantly outperform their original counterparts.

通过在图结构数据中学习，物理启发图神经网络在解决常见图神经网络挑战（如平滑过度、压缩过度和异质适应）方面取得了显著的性能。本文通过在传播过程中引入额外的节点和重新连接具有正负权重的连接来丰富图结构，在理论上验证了通过我们的方法增强的图神经网络可以有效地解决平滑过度问题，并对压缩过度具有鲁棒性。此外，我们对重连后的图进行谱分析，证明相应的图神经网络可以适应同质化和异质化的图。在同质化、异质化图以及长期图数据集的基准验证中，我们通过我们的方法增强的图神经网络显著优于原始版本。

设计您自己的宇宙：一种增强图神经网络的物理知识无偏方法