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

TL;DR

PIMPC-GNN introduces a physics-informed, multi-phase consensus framework that significantly improves imbalanced node classification in GNNs by integrating thermodynamic diffusion, Kuramoto synchronisation, and spectral embedding.

Contribution

It presents a novel multi-phase consensus approach combining physics-inspired dynamics with class-adaptive weighting for imbalanced GNN classification.

Findings

Outperforms 16 state-of-the-art baselines on five benchmarks.

Achieves up to +12.7% in minority-class recall.

Improves balanced accuracy by up to +8.3%.

Abstract

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}.