Research map / Graph learning / GNN architectures
Physics-inspired GNNs
Apply equivariant and diffusion-based GNNs to physical simulation.
81 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2018–2026) · an approach in GNN architectures, keyword cluster “gnn · explanations · trained”
State History Benchmarks Tried Checklist Preprints Who Export
Where it stands
Few recent reports None of the tracked benchmarks has a report from 2025–26.
27 papers in 2023–24 and 35 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 5.7% to 6.9%.
No longer reported by papers here: Citeseer (accuracy (%), last in 2024); Cora (accuracy (%), last in 2024).
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2018 · Surface Networks (CVPR 2018 · 56 citations)
- 2019 · Universal Invariant and Equivariant Graph Neural Networks (NeurIPS 2019 · 130 citations)
- 2020 · Discovering Symbolic Models from Deep Learning with Inductive Biases (NeurIPS 2020 · 264 citations)
- 2021 · Learning Parametrised Graph Shift Operators (ICLR 2021 · 1 citation)
- 2022 · Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs (NeurIPS 2022 · 27 citations)
- 2023 · Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs (ICML 2023 · 28 citations)
- 2024 · Graph Neural Networks for Learning Equivariant Representations of Neural Networks (ICLR 2024 · 3 citations)
- 2025 · Dynamics-Based Feature Augmentation of Graph Neural Networks for Variant Emergence Prediction (AAAI 2025 · 1 citation)
- 2026 · Rapid Training of Hamiltonian Graph Networks Using Random Features (ICLR 2026 · 1 citation)
Earliest papers here
- Surface Networks (CVPR 2018 · 56 citations)
- Universal Invariant and Equivariant Graph Neural Networks (NeurIPS 2019 · 130 citations)
- Hyperbolic Graph Neural Networks (NeurIPS 2019 · 77 citations)
Benchmark records
The best number each year that beat every earlier one, among papers of this approach reporting their own method. Numbers are extracted by AI from each paper's text; check the paper before citing.
Citeseer · accuracy (%) (higher is better)
4 papers, 2021–2024 · not reported since 2024
| Year | Best so far | Set by |
|---|---|---|
| 2021 | 73.1 | Learning Parametrised Graph Shift Operators (ICLR 2021 · 1 citation) |
| 2022 | 77.14 | Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs (NeurIPS 2022 · 27 citations) |
Cora · accuracy (%) (higher is better)
4 papers, 2021–2024 · not reported since 2024
| Year | Best so far | Set by |
|---|---|---|
| 2021 | 84.3 | Learning Parametrised Graph Shift Operators (ICLR 2021 · 1 citation) |
| 2022 | 87.3 | Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs (NeurIPS 2022 · 27 citations) |
| 2023 | 88.31 | Implicit Graph Neural Networks: A Monotone Operator Viewpoint (ICML 2023 · 0 citations) |
What has been tried
52 papers here report 512 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 9%, hurt 20%, mixed 4%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Add pressure relaxation | 2D TGV · Sinkhorn | 5.4e-7 -> 1.7e-8 | Helped | Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics (ICML 2024 · 2 citations) |
| increase the number of mesh points | OE62 · energy MAE | Hurt | Neural P$^3$M: A Long-Range Interaction Modeling Enhancer for Geometric GNNs (NeurIPS 2024 · 2 citations) | |
| add global growth rate S to prevalence-ratio time-series features r | Delay Prediction · MedMedAE | 3.0 -> 3.48 | Hurt | Dynamics-Based Feature Augmentation of Graph Neural Networks for Variant Emergence Prediction (AAAI 2025 · 1 citation) |
| use tensor-product coloring instead of distance-to-center coloring | Chirality test · graph distinction | Helped | Universally Invariant Learning in Equivariant GNNs (NeurIPS 2025 · 1 citation) | |
| remove the learnable Laplace block | Cylinder flow, Re [440, 480, 520] · MSE | Hurt | PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems (ICLR 2025 · 1 citation) | |
| add rotation augmentation to CGC | 1imp · L_comp | 8.37 -> 4.47 | Helped | Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials (ICLR 2024 · 1 citation) |
| add PDE constraints to the difference-matrix model | River Network, Forward · MSE | 0.0898 -> 0.0801 | Helped | Topology-aware Neural Flux Prediction Guided by Physics (ICML 2025 · 0 citations) |
| add virtual nodes and edges to preserve connectivity across partition boundaries | a-HfO2 test structure 3 · ϵn and ϵe | 5.39 -> 2.16 mEh; 0.55 -> 0.16 mEh | Helped | Learning the Electronic Hamiltonian of Large Atomic Structures (ICML 2025 · 0 citations) |
| Add Fused inference optimization | ITC99 · inference time | 2.496 -> 1.463 | Helped | DeepGate4: Efficient and Effective Representation Learning for Circuit Design at Scale (ICLR 2025 · 0 citations) |
| Use pressure instead of velocity to select rewiring nodes | CylinderFlow · Velocity RMSE (×10^3) | 41.6\scriptsize{\;±\;}{3.9} -> 80.9\scriptsize{\;±\;}{13.4} | Hurt | PIORF: Physics-Informed Ollivier-Ricci Flow for Long–Range Interactions in Mesh Graph Neural Networks (ICLR 2025 · 0 citations) |
| Use Orbit+ instead of Orbit augmentation | BPP · Top-70% error | 1.3 -> 0.9 | Helped | When GNNs meet symmetry in ILPs: an orbit-based feature augmentation approach (ICLR 2025 · 0 citations) |
| use incremental rather than fixed grouping | Peptides-struct test · MAE | 0.2582 ± 0.0011 -> 0.3239 ± 0.0014 | Hurt | Neural Atoms: Propagating Long-range Interaction in Molecular Graphs through Efficient Communication Channel (ICLR 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 19 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- Pubmed · 2 of 19 papers
Baselines
- GCN · 5 of 19 papers
- GAT · 4 of 19 papers
- GraphSAGE · 3 of 19 papers
- MLP · 2 of 19 papers
- Graph Transformer · 2 of 19 papers
- MGN · 2 of 19 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 62 papers; from OpenAlex and the papers' affiliations).
- Microsoft · 3 papers
- Google · 3 papers
- Renmin University of China · 2 papers
- Tencent · 2 papers
- Mila · 2 papers
- University of Cambridge · 2 papers
- Nanyang Technological University · 2 papers
- Anhui University · 2 papers
- Singapore University of Social Sciences · 2 papers
- University of California, Los Angeles · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- GNN generalization theory (187 papers)
- Simple and scalable GNNs (131 papers)
- Robustness, privacy, and fairness of GNNs (94 papers)
- GNN explainability (64 papers)
- Graph structure learning (201 papers)
Elsewhere in the topic
- Expressive equivariant message passing (109 papers)
- Theory of graph convolutional networks (83 papers)
- Deep graph convolution and simplification (82 papers)
- Graph rewiring and scalable message passing (72 papers)
- Weisfeiler-Leman expressivity hierarchies (66 papers)
- Structural GNN variants (65 papers)
- Oversmoothing and heterophily (60 papers)
- Substructure-aware GNN expressivity (50 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).