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

arXiv: https://arxiv.org/abs/2602.01920 · HTML: https://mlsanity.com/paper/2602.01920/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 50 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 23 of 23)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Explainability in Graph Neural Networks: A Taxonomic Survey](https://mlsanity.com/paper/2012.15445/) (2020)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [A Comprehensive Survey on Graph Anomaly Detection with Deep Learning](https://mlsanity.com/paper/2106.07178/) (2021)
- [Graph-based Anomaly Detection and Description: A Survey](https://mlsanity.com/paper/1404.4679/) (2014)
- [GraphSMOTE: Imbalanced Node Classification on Graphs with Graph Neural Networks](https://mlsanity.com/paper/2103.08826/) (2021)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [Deep Over-sampling Framework for Classifying Imbalanced Data](https://mlsanity.com/paper/1704.07515/) (2017)
- [ImGAGN:Imbalanced Network Embedding via Generative Adversarial Graph Networks](https://mlsanity.com/paper/2106.02817/) (2021)
- [Learning on Attribute-Missing Graphs](https://mlsanity.com/paper/2011.01623/) (2020)
- [Rethinking Graph Neural Architecture Search from Message-passing](https://mlsanity.com/paper/2103.14282/) (2021)
- [GraphSR: A Data Augmentation Algorithm for Imbalanced Node Classification](https://mlsanity.com/paper/2302.12814/) (2023)
- [Rethinking Semi-Supervised Imbalanced Node Classification from Bias-Variance Decomposition](https://mlsanity.com/paper/2310.18765/) (2023)
- [Cluster-guided Contrastive Class-imbalanced Graph Classification](https://mlsanity.com/paper/2412.12984/) (2024)
- [Node classification in networks via simplicial interactions](https://mlsanity.com/paper/2310.10114/) (2023)

## Abstract (arXiv)

Graph neural networks (GNNs) often struggle in class-imbalanced settings, where minority classes are under-represented and predictions are biased toward majorities. We propose 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 texttthttps://github.com/afofanah/PIMPC-GNN.