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Feature Transportation Improves Graph Neural Networks
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Proposes ADR-GNN, a graph neural network built from a learnable advection-diffusion-reaction PDE discretization (mass-conserving neural advection operator, implicit diffusion, MLP reaction), evaluated on node classification and spatio-temporal forecasting.
Problem
Standard GNNs (diffusion, wave, reaction-based) struggle to model feature transportation, where node information must be moved directionally across the graph; oversmoothing and limited expressiveness are also issues.
Approach
Adds a learnable, mass-preserving neural advection operator with direction-oriented learned edge weights to a learnable diffusion and reaction term, discretized via operator splitting into a GNN layer (ADR-GNN).
Key results
- ADR-GNN-S reaches 89.43% on Cora and 90.55% on Pubmed, outperforming listed baselines on those datasets.
- On heterophilic Chameleon, ADR-GNN-S achieves 79.91% vs. 74.76% for the next best (ACMII), roughly 5 points higher.
- On METR-LA horizon 12, ADR-GNN-T reduces MAE to 3.19 from 3.37 for STEP.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add advection to the full ADR-GNN_S (ablation) | ADR-GNN_S · Chameleon | accuracy (%): 73.46 -> 79.91 | Helped |
| Add diffusion to the full ADR-GNN_S (ablation) | ADR-GNN_S · Chameleon | accuracy (%): 73.33 -> 79.91 | Helped |
| Add reaction to the full ADR-GNN_S (ablation) | ADR-GNN_S · Chameleon | accuracy (%): 72.08 -> 79.91 | Helped |
| Add advection to a diffusion-and-reaction model (ablation) | ADR-GNN_S · Chameleon | accuracy (%): 72.08 -> 79.91 | Helped |
| Use all three learned terms instead of any single term (ablation) | ADR-GNN_S · Chameleon | accuracy (%): 66.79 -> 79.91; 65.08 -> 79.91; 52.28 -> 79.91 | Helped |
| Use ADR-GNN_S rather than the strongest listed baseline | ADR-GNN_S · Cora | accuracy (%): 89.05 -> 89.43 | Helped |
| Use ADR-GNN_S rather than the strongest listed baseline | ADR-GNN_S · Citeseer | accuracy (%): 78.48 -> 78.36 | Hurt |
| Use ADR-GNN_S rather than the strongest listed baseline | ADR-GNN_S · Pubmed | accuracy (%): 90.30 -> 90.55 | Helped |
| Use ADR-GNN_S rather than the strongest listed baseline | ADR-GNN_S · Chameleon | accuracy (%): 74.76 -> 79.91 | Helped |
| Use ADR-GNN_T rather than the strongest listed baseline | ADR-GNN_T · Chickenpox Hungary | MSE: 1.114 $\pm$ 0.008 -> 0.817 $\pm$ 0.012 | Helped |
| Use ADR-GNN_T rather than the strongest listed baseline | ADR-GNN_T · PedalMe | MSE: 1.455 $\pm$ 0.023 -> 0.598 $\pm$ 0.050 | Helped |
| Use ADR-GNN_T rather than STEP | ADR-GNN_T · METR-LA horizon 12 | MAE: 3.37 -> 3.19 | Helped |
Surprising findings
- Ablation on Cora shows the advection-only variant (88.92 with diffusion) gives only minor gains on homophilic data, while advection gives large gains on heterophilic and traffic datasets.
Limitations
- Gains on homophilic datasets are modest.
- Advection layer is more costly than GCN/GAT (higher runtime and complexity O((|V|+|E|)c^2)).
Experimental setup
Datasets: Cora Citeseer Pubmed Chameleon Squirrel Film Cornell Texas Wisconsin Chickenpox Hungary PedalMe London Wikipedia Math
Benchmarks: Cora Citeseer Pubmed Chameleon Squirrel Film Cornell Texas Wisconsin Chickenpox Hungary PedalMe London Wikipedia Math
Metrics: accuracy MSE MAE RMSE MAPE
Baselines: GCN GAT GCNII PDE-GCN GRAND GGCN GREAD ACMII STEP STAEformer DIFFormer Graph WaveNet
Builds on: GRAND GraphCON PDE-GCN GCNII Geom-GCN
Closest papers by meaning
- Supercharging Graph Transformers with Advective Diffusion (ICML 2025 · similarity 0.88)
- A Generalized Neural Diffusion Framework on Graphs (AAAI 2024 · similarity 0.88)
- On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning (NeurIPS 2025 · similarity 0.87)
- Diffusing to the Top: Boost Graph Neural Networks with Minimal Hyperparameter Tuning (ICLR 2025 · similarity 0.87)
- Can Classic GNNs Be Strong Baselines for Graph-level Tasks? Simple Architectures Meet Excellence (ICML 2025 · similarity 0.86)
- Towards Dynamic Message Passing on Graphs (NeurIPS 2024 · similarity 0.86)
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