PIMPC-GNN: Physics-Informed Multiphase Consensus Learning for Enhancing Imbalanced Node Classification in Graph Neural Networks

Graph neural networks (GNNs) often struggle in class-imbalanced settings, where minority classes are underrepresented, and predictions are biased toward the majority. We propose PIMPC-GNN, a physics-informed multiphase consensus framework for imbalanced node classification. Our method integrates three complementary dynamics: 1) thermodynamic diffusion, which spreads minority labels to capture long-range dependencies; 2) Kuramoto synchronization, which aligns minority nodes through oscillatory consensus; and 3) spectral embedding, which separates classes via structural regularization. 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 to 100, PIMPC-GNN outperforms 14 state-of-the-art (SOTA) baselines, achieving notable gains in minority-class recall and balanced accuracy. Beyond empirical improvements, the framework also provides interpretable insights into consensus dynamics in graph learning. The implementation code is available at https://github.com/afofanah/PIMPC-GNN.