Graph neural networks (GNNs) often struggle in class-imbalanced settings, where minority classes are under-represented and predictions are biased toward majorities. We propose \textbf{PIMPC-GNN}, a physics-informed multi-phase consensus framework for imbalanced node classification. Our method integrates three complementary dynamics: (i) thermodynamic diffusion, which spreads minority labels to capture long-range dependencies, (ii) Kuramoto synchronisation, which aligns minority nodes through oscillatory consensus, and (iii) spectral embedding, which separates classes via structural regularisation. These perspectives are combined through class-adaptive ensemble weighting and trained with an imbalance-aware loss that couples balanced cross-entropy with physics-based constraints. Across five benchmark datasets and imbalance ratios from 5-100, PIMPC-GNN outperforms 16 state-of-the-art baselines, achieving notable gains in minority-class recall (up to +12.7\%) and balanced accuracy (up to +8.3\%). Beyond empirical improvements, the framework also provides interpretable insights into consensus dynamics in graph learning. The code is available at \texttt{https://github.com/afofanah/PIMPC-GNN}.

翻译：图神经网络（GNNs）在类别不平衡的场景中常常表现不佳，其中少数类样本代表性不足，预测结果偏向多数类。我们提出了 **PIMPC-GNN**，一种用于不平衡节点分类的基于物理信息的多相共识框架。我们的方法整合了三种互补的动力学机制：（i）热力学扩散，通过传播少数类标签以捕获长程依赖关系；（ii）Kuramoto 同步，通过振荡共识对齐少数类节点；（iii）谱嵌入，通过结构正则化实现类别分离。这些视角通过类别自适应的集成加权进行结合，并采用一种不平衡感知损失函数进行训练，该损失将平衡交叉熵与基于物理的约束相耦合。在五个基准数据集以及 5 到 100 的不平衡比例范围内，PIMPC-GNN 在 16 个先进基线方法中表现优异，在少数类召回率（最高提升 +12.7%）和平衡准确率（最高提升 +8.3%）方面取得了显著提升。除了经验性改进之外，该框架还为图学习中的共识动力学提供了可解释的见解。代码发布于 \texttt{https://github.com/afofanah/PIMPC-GNN}。