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.

翻译：物理启发的图神经网络通过学习图结构数据，在缓解过平滑、过挤压和异质性适应等常见图神经网络挑战方面取得了显著性能。尽管已有这些进展，但如何开发一种简单有效的范式来恰当整合先前方法以应对所有这些挑战仍在探索中。本文将图神经网络的传播与物理中的粒子系统进行类比，提出了一种模型无关的增强框架。该框架通过引入额外节点并依据节点标签信息，用正负权重重新连接边来丰富图结构。我们从理论上证明，经此方法增强的图神经网络能有效规避过平滑问题，并对过挤压具有鲁棒性。此外，我们对重连后的图进行谱分析，表明对应的图神经网络既能拟合同质图也能拟合异质图。在同质图、异质图和长程图基准数据集上的实证验证表明，经本方法增强的图神经网络显著优于原始版本。