Feature Transportation Improves Graph Neural Networks
Abstract
Graph neural networks (GNNs) have shown remarkable success in learning representations for graph-structured data. However, GNNs still face challenges in modeling complex phenomena that involve feature transportation. In this paper, we propose a novel GNN architecture inspired by Advection-Diffusion-Reaction systems, called ADR-GNN. Advection models feature transportation, while diffusion captures the local smoothing of features, and reaction represents the non-linear transformation between feature channels. We provide an analysis of the qualitative behavior of ADR-GNN, that shows the benefit of combining advection, diffusion, and reaction. To demonstrate its efficacy, we evaluate ADR-GNN on real-world node classification and spatio-temporal datasets, and show that it improves or offers competitive performance compared to state-of-the-art networks.
Benchmark Results
Tested on 8 datasets 30 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
Classic
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphSAGE+CNA | 0.9418
±0.0033 | |
| 2 | GCN+CNA | 0.9366
±0.0048 | |
| 3 | TransformerConv | 0.9350
±0.0058 | |
| 21 | GCN | 0.9004 best reported | best at pub: SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels (2017) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| 32 | ADR-GNN_S | 0.8943 | This paper |
| 39 | SAGE | 0.8911
±0.0012 | |
| 42 | C&S | 0.8905 | This paper |
| 44 | GAT | 0.8897
±0.0014 best reported | best at pub: Learned Low Precision Graph Neural Networks (2020) |
| 45 | GCNII | 0.8893
±0.0137 best reported | best at pub: Orthogonal Graph Neural Networks (AAAI 2021) best today: Large Language Model Meets Graph Neural Network in Knowledge Distillation (AAAI 2024) Difference within reported uncertainty; not counted as underperformance. |
| 51 | H2GCN | 0.8787 | prev best: Block Modeling-Guided Graph Convolutional Neural Networks (AAAI 2021) best today: Adaptive Tokenization: On the Hop-Overpriority Problem in Tokenized Graph Learning Models (2025) Improvement within reported uncertainty; not highlighted. |
| 55 | JKNet | 0.8870 best reported | best at pub: Learned Low Precision Graph Neural Networks (2020) |
| 60 | PDE-GCN | 0.8860 | This paper |
| 62 | GREAD | 0.8857 | This paper |
| 80 | ACMII | 0.8825 | This paper |
| 82 | WRGAT | 0.8820 | prev best: From Node Interaction to Hop Interaction: New Effective and Scalable Graph Learning Paradigm (2022) Improvement within reported uncertainty; not highlighted. |
| 87 | GRAND | 0.8815 | prev best: Graph-Coupled Oscillator Networks (ICML 2022) |
| 96 | GRAFF | 0.8801 | This paper |
| 103 | GGCN | 0.8795 | This paper |
| 108 | APPNP | 0.8787 | This paper |
| 113 | MixHop | 0.8761 | This paper |
| 138 | NSD | 0.8714 | This paper |
| 168 | DMP | 0.8652 | This paper |
| 170 | FLODE | 0.8644
±0.0117 best reported | |
| 207 | Geom-GCN | 0.8540
±0.0040 best reported | best at pub: Non-Local Graph Neural Networks (2020) best today: The Expressive Power of Graph Neural Networks: A Survey (2023) |
| 243 | LINKX | 0.8464 | This paper |
| 724 | MLP | 0.7768 | |
| 734 | Ord. GNN | 0.7731 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | CNA | 0.9575
±0.0058 | |
| 2 | IS-GIB | 0.9390
±0.0187 | |
| 3 | EERM | 0.9112
±0.0145 | |
| 8 | Ord. GNN | 0.9015 | This paper |
| 12 | FLODE | 0.8902 | This paper |
| 20 | APPNP | 0.8142
±0.0026 best reported | best at pub: Feature Expansion for Graph Neural Networks (ICML 2023) |
| 35 | GAT | 0.8080
±0.0026 best reported | best at pub: Feature Expansion for Graph Neural Networks (ICML 2023) |
| 36 | GCNII | 0.8076
±0.0030 best reported | best at pub: Feature Expansion for Graph Neural Networks (ICML 2023) |
| 44 | GCN | 0.8033
±0.0088 best reported | best at pub: Gophormer: Ego-Graph Transformer for Node Classification (2021) |
| 61 | GraphSAGE | 0.7923
±0.0053 | |
| 62 | JKNet | 0.7920 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 79 | PDE-GCN | 0.7848 | This paper |
| 83 | ADR-GNN | 0.7836 | This paper |
| 88 | Geom-GCN | 0.7799 | prev best: GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophily (WWW 2021) Improvement within reported uncertainty; not highlighted. |
| 99 | GREAD | 0.7760 | This paper |
| 104 | GRAFF | 0.7730 | This paper |
| 107 | NSD | 0.7714 | This paper |
| 108 | GGCN | 0.7714 | This paper |
| 109 | ACMII | 0.7712 | This paper |
| 111 | H2GCN | 0.7711 | This paper |
| 117 | DMP | 0.7687 | This paper |
| 119 | WRGAT | 0.7681 | This paper |
| 122 | GRAND | 0.7657 | prev best: Discovering Data Geometry: Energy-Driven Neural Diffusion (ICLR 2023) |
| 126 | MixHop | 0.7626 | prev best: Structural Entropy Guided Graph Hierarchical Pooling (ICML 2022) |
| 127 | C&S | 0.7622 | This paper |
| 312 | LINKX | 0.7319 | prev best: Uplifting Message Passing Neural Network with Graph Original Information (2022) |
| 350 | MLP | 0.7289
±0.0010 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | LGTL | 0.9518
±0.0011 | |
| 2 | MixHop (LO) | 0.9513
±0.0038 | |
| 3 | GraphSAGE (LO) | 0.9511
±0.0036 | |
| 16 | H2GCN | 0.9361
±0.0013 best reported | best at pub: Optimization-Induced Graph Implicit Nonlinear Diffusion (ICML 2022) |
| 17 | APPNP | 0.9355
±0.0060 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 18 | GCN | 0.9296
±0.0015 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 20 | GAT | 0.9233
±0.0018 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 24 | JKNet | 0.9160 best reported | best at pub: Tackling Over-Smoothing for General Graph Convolutional Networks (2020) |
| 52 | ADR-GNN_S | 0.9055 | This paper |
| 58 | GCNII | 0.9030 | prev best: Graph Neural Networks Inspired by Classical Iterative Algorithms (ICML 2021) |
| 62 | GREAD | 0.9023 | This paper |
| 69 | Geom-GCN | 0.9005 | This paper |
| 70 | MixHop | 0.8531 | prev best: Graph Contrastive Learning under Heterophily via Graph Filters (2023) best today: Language is All a Graph Needs (2023) Improvement within reported uncertainty; not highlighted. |
| 71 | GRAFF | 0.9004 | This paper |
| 74 | PDE-GCN | 0.8993 | This paper |
| 81 | C&S | 0.8974 | This paper |
| 82 | ACMII | 0.8971 | This paper |
| 88 | NSD | 0.8949 | This paper |
| 96 | DMP | 0.8927 | This paper |
| 98 | GGCN | 0.8915 | This paper |
| 109 | GRAND | 0.8902 | prev best: Framelet Message Passing (2023) |
| 116 | SAGE | 0.8881
±0.0015 | |
| 129 | WRGAT | 0.8852 | This paper |
| 138 | Ord. GNN | 0.8837 | This paper |
| 162 | LINKX | 0.8786 | prev best: Uplifting Message Passing Neural Network with Graph Original Information (2022) |
| 210 | MLP | 0.8690
±0.0074 | |
| 224 | FLODE | 0.8644 | This paper |
Heterophilic Graphs
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | P^2GNN | 0.9672
±0.0147 | |
| 2 | DoG | 0.9660
±0.0210 | |
| 3 | GPF-plus | 0.9583
±0.0419 | |
| 18 | ADR-GNN_S | 0.9361
±0.0426 | This paper |
| 34 | MLP | 0.9230
±0.0070 | |
| 39 | GGCN | 0.9213
±0.0305 best reported | best at pub: Understanding convolution on graphs via energies (TMLR 2022) best today: Graph Wave Networks (WWW 2025) |
| 40 | H2GCN | 0.9189
±0.0393 best reported | best at pub: How Curvature Enhance the Adaptation Power of Framelet GCNs (2023) best today: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) Difference within reported uncertainty; not counted as underperformance. |
| 53 | GraphSAGE | 0.9000
±0.0365 | |
| 61 | FAGCN | 0.8961
±0.0152 best reported | best at pub: Node-oriented Spectral Filtering for Graph Neural Networks (2022) |
| 70 | GCNII | 0.8918
±0.0443 best reported | best at pub: Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited (NeurIPS 2022) best today: Piecewise Constant Spectral Graph Neural Network (TMLR 2025) |
| 82 | GRAFF | 0.8838
±0.0453 | This paper |
| 83 | ACMII-GCN | 0.8838
±0.0343 | This paper |
| 96 | G^2 | 0.8757
±0.0386 | This paper |
| 115 | ACMP-GCN | 0.8620
±0.0300 | This paper |
| 121 | NSD | 0.8595
±0.0551 | This paper |
| 181 | MagNet | 0.8330
±0.0610 | prev best: PyTorch Geometric Signed Directed: A Software Package on Graph Neural Networks for Signed and Directed Graphs (LoG 2022) Improvement within reported uncertainty; not highlighted. |
| 211 | GAT | 0.8162
±0.0645 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) best today: Equivariance Everywhere All At Once: A Recipe for Graph Foundation Models (2025) |
| 217 | GRAND | 0.8140
±0.0350 best reported | best at pub: Understanding convolution on graphs via energies (TMLR 2022) best today: When Graph Neural Networks Meet Dynamic Mode Decomposition (ICLR 2024) Difference within reported uncertainty; not counted as underperformance. |
| 257 | GCN | 0.7933
±0.0447 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) best today: Graph Wave Networks (WWW 2025) |
| 325 | LINKX | 0.7460
±0.0837 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DiGGR | 0.4535
±0.0353 | |
| 2 | TRIGON | 0.4402
±0.0028 | |
| 3 | DoG | 0.4320
±0.0120 | |
| 38 | GCNII | 0.4082
±0.0179 best reported | best at pub: Feature Expansion for Graph Neural Networks (ICML 2023) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) |
| 42 | MLP | 0.4026
±0.0108 | |
| 52 | GPRGNN | 0.3992
±0.0067 best reported | best at pub: LON-GNN: Spectral GNNs with Learnable Orthonormal Basis (2023) best today: GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers (ICML 2024) |
| 56 | FAGCN | 0.3970 best reported | best at pub: Beyond Low-frequency Information in Graph Convolutional Networks (AAAI 2021) |
| 62 | GGCN | 0.3781
±0.0156 | prev best: Understanding convolution on graphs via energies (TMLR 2022) Improvement within reported uncertainty; not highlighted. |
| 65 | ADR-GNN_S | 0.3916
±0.0113 | This paper |
| 68 | GraphSAGE | 0.3899
±0.0085 | |
| 71 | H2GCN | 0.3885
±0.0117 best reported | best at pub: ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting (2022) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) |
| 75 | WRGAT | 0.3860
±0.0110 best reported | best at pub: ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting (2022) |
| 87 | Geom-GCN | 0.3810 best reported | best at pub: Beyond Low-frequency Information in Graph Convolutional Networks (AAAI 2021) |
| 100 | NSD | 0.3781
±0.0115 best reported | best today: Graph Parsing Networks (ICLR 2024) Difference within reported uncertainty; not counted as underperformance. |
| 118 | G^2 | 0.3730
±0.0101 | This paper |
| 129 | GRAFF | 0.3711
±0.0108 | This paper |
| 131 | ACMII-GCN | 0.3709
±0.0132 | This paper |
| 135 | GCN | 0.3690 best reported | best at pub: Beyond Low-frequency Information in Graph Convolutional Networks (AAAI 2021) |
| 162 | MixHop | 0.3648
±0.0120 best reported | best at pub: Towards Deep Attention in Graph Neural Networks: Problems and Remedies (ICML 2023) |
| 180 | LINKX | 0.3610
±0.0155 | This paper |
| 182 | GAT | 0.3605
±0.0035 best reported | best at pub: Hierarchical Graph Transformer with Adaptive Node Sampling (NeurIPS 2022) |
| 203 | GRAND | 0.3562
±0.0101 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | Hetero-S (GAT 8-layer) | 0.8693 | |
| 2 | Dir-GNN+CNA | 0.8586
±0.0180 | |
| 3 | GAT | 0.8560 | |
| 12 | A + D + R | 0.7991 | This paper |
| 52 | GCN | 0.7033 | |
| 169 | MLP | 0.5429 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | IBG-NN | 0.7763
±0.0179 | |
| 2 | Dir-GNN+CNA | 0.7747
±0.0128 | |
| 3 | DHGNN | 0.7684
±0.0161 | |
| 15 | ADR-GNN_S | 0.7254
±0.0220 | This paper |
| 26 | ACMII-GCN | 0.6740
±0.0221 | This paper |
| 31 | G^2 | 0.6426
±0.0238 | This paper |
| 39 | H2GCN | 0.6190
±0.0140 best reported | best at pub: Optimization-Induced Graph Implicit Nonlinear Diffusion (ICML 2022) best today: Efficient Learning on Large Graphs using a Densifying Regularity Lemma (2025) |
| 40 | LINKX | 0.6181
±0.0180 | This paper |
| 46 | GCN | 0.6067 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| 53 | GRAFF | 0.5901
±0.0131 | This paper |
| 65 | NSD | 0.5634
±0.0132 | This paper |
| 67 | GAT | 0.5630
±0.0220 best reported | best at pub: Restructuring Graphs for Higher Homophily via Adaptive Spectral Clustering (AAAI 2022) |
| 69 | GGCN | 0.5567
±0.0187 best reported | best at pub: GPNet: Simplifying Graph Neural Networks via Multi-channel Geometric Polynomials (2022) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) Difference within reported uncertainty; not counted as underperformance. |
| 76 | GPRGNN | 0.5435
±0.0087 best reported | best at pub: LON-GNN: Spectral GNNs with Learnable Orthonormal Basis (2023) best today: Directed Homophily-Aware Graph Neural Network (2025) |
| 96 | WRGAT | 0.4885
±0.0078 | This paper |
| 120 | SAGE | 0.4460
±0.0130 | |
| 127 | MixHop | 0.4380
±0.0148 | This paper |
| 139 | FAGCN | 0.4259
±0.0069 | This paper |
| 164 | GRAND | 0.4005
±0.0150 | This paper |
| 172 | MLP | 0.3930
±0.0079 | |
| 176 | GCNII | 0.3881
±0.0197 best reported | best at pub: GPNet: Simplifying Graph Neural Networks via Multi-channel Geometric Polynomials (2022) best today: $P^2$GNN: Two Prototype Sets to boost GNN Performance (2026) Difference within reported uncertainty; not counted as underperformance. |
| 179 | Geom-GCN | 0.3832
±0.0092 | prev best: Gradient Gating for Deep Multi-Rate Learning on Graphs (ICLR 2022) Improvement within reported uncertainty; not highlighted. |
LINKX Benchmarks
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | LargeScaleNet | 0.6582
±0.0036 | |
| 2 | S² DirGCN | 0.6495
±0.0033 | |
| 3 | FaberNet | 0.6462
±0.0101 | |
| 6 | G^2 | 0.6330
±0.0184 | This paper |
| 8 | ADR-GNN_S | 0.6117
±0.0154 | This paper |
| 30 | L Prop (2 hop) | 0.4607
±0.0015 | This paper |
| 31 | GCN | 0.4602
±0.0026 | |
| 40 | C&S (2 hop) | 0.4217
±0.0027 | This paper |
| 56 | MLP | 0.3670
±0.0021 | |
| 59 | SGC (2 hop) | 0.3227
±0.0006 | This paper |
