Research map / Architectures and efficiency / Attention and transformers
Transformer neural operators for PDEs
Uses attention-based neural operators to simulate and pre-train on partial differential equations.
69 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2019–2026) · an approach in Attention and transformers, keyword cluster “kv · cache · long context”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
22 papers in 2023–24 and 35 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 3.8% to 3.0%.
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
- 2019 · Template-Based Math Word Problem Solvers with Recursive Neural Networks (AAAI 2019)
- 2020 · Transformer Hawkes Process (ICML 2020 · 21 citations)
- 2021 · Transformer Tracking (CVPR 2021 · 1,440 citations)
- 2022 · CTIN: Robust Contextual Transformer Network for Inertial Navigation (AAAI 2022 · 53 citations)
- 2023 · AirFormer: Predicting Nationwide Air Quality in China with Transformers (AAAI 2023 · 170 citations)
- 2024 · PMET: Precise Model Editing in a Transformer (AAAI 2024 · 37 citations)
- 2025 · BSDB-Net: Band-Split Dual-Branch Network with Selective State Spaces Mechanism for Monaural Speech Enhancement (AAAI 2025 · 4 citations)
- 2026 · Transolver Is a Linear Transformer: Revisiting Physics-Attention Through the Lens of Linear Attention (AAAI 2026 · 2 citations)
Earliest papers here
- Template-Based Math Word Problem Solvers with Recursive Neural Networks (AAAI 2019)
- Transformer Hawkes Process (ICML 2020 · 21 citations)
- Transformer Tracking (CVPR 2021 · 1,440 citations)
What has been tried
47 papers here report 526 measured changes (a component added, removed or swapped, compared with a baseline): helped 69%, no clear effect 8%, hurt 20%, mixed 3%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Add MHSA hidden-state optimization | CounterFact, 1K–10K edits · Generalization | 96.6 -> 96.1; 95.0 -> 94.5; 89.0 -> 92.8 | Mixed | PMET: Precise Model Editing in a Transformer (AAAI 2024 · 37 citations) |
| replace the targeted AJB/AJBM adjacency matrices with I + Aske for both fusion streams | NTU RGB+D 60 Cross-Subject · accuracy | 91.29 -> 90.19 | Hurt | Behavioral Recognition of Skeletal Data Based on Targeted Dual Fusion Strategy (AAAI 2024 · 18 citations) |
| Increase wavelet decomposition layers | Brusselator · training time | Hurt | Multiscale Attention Wavelet Neural Operator for Capturing Steep Trajectories in Biochemical Systems (AAAI 2024 · 15 citations) | |
| Add auto-regressive denoising pre-training | PDEBench test subsets (average) · L2RE | 0.0178 -> 0.0152 | Helped | DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training (ICML 2024 · 6 citations) |
| add value position encoding ψ | JARVIS-DFT 3D 2021, formation energy · MAE | 0.0541 -> 0.0301 | Helped | Crystalformer: Infinitely Connected Attention for Periodic Structure Encoding (ICLR 2024 · 5 citations) |
| Remove layer normalization | PPA-All · Pearson | 0.366± 0.024 -> 0.514± 0.011 | Hurt | Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning (ICML 2024 · 5 citations) |
| use parallel magnitude and complex-spectrum branches instead of either branch alone | WSJ0-SI84 · PESQ | 2.67 / 2.76 -> 2.92 | Helped | BSDB-Net: Band-Split Dual-Branch Network with Selective State Spaces Mechanism for Monaural Speech Enhancement (AAAI 2025 · 4 citations) |
| Replace MCPA with vanilla attention | Housing · R² | 0.911 -> 0.906 | Hurt | GeoAggregator: An Efficient Transformer Model for Geo-Spatial Tabular Data (AAAI 2025 · 4 citations) |
| add attention-value estimator only | GLUE dev · average score | 69.2 -> 69.9 | Helped | BiPFT: Binary Pre-trained Foundation Transformer with Low-Rank Estimation of Binarization Residual Polynomials (AAAI 2024 · 3 citations) |
| Add graph embedding (GE) | Satellite traffic datasets across varying sampling rates · Estimation performance | Helped | Satformer: Accurate and Robust Traffic Data Estimation for Satellite Networks (NeurIPS 2024 · 3 citations) | |
| add orthogonalization instead of using no orthogonalization | Elasticity limited-data experiment · l2 relative error | ONO: 0.0114 -> 0.0181; ONO^{-}: 0.0352 -> 0.0694 | Helped | Improved Operator Learning by Orthogonal Attention (ICML 2024 · 2 citations) |
| replace all position-attention layers with vanilla self-attention | InviscidBurgers · relative l1 error | 0.0136 -> 0.016 | Hurt | Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learning (ICML 2024 · 2 citations) |
What reviewers will expect
Datasets and baselines named in the 18 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- LSTM · 3 of 18 papers
- FNO · 3 of 18 papers
- OFormer · 3 of 18 papers
- XGBoost · 2 of 18 papers
- Informer · 2 of 18 papers
- FactFormer · 2 of 18 papers
- UNet · 2 of 18 papers
- UNO · 2 of 18 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 57 papers; from OpenAlex and the papers' affiliations).
- Tsinghua University · 5 papers
- Shanghai Jiao Tong University · 3 papers
- Huazhong University of Science and Technology · 2 papers
- The University of Sydney · 2 papers
- Beihang University · 2 papers
- Renmin University of China · 2 papers
- Brookhaven National Laboratory · 2 papers
Use it
Download BibTeX of 35 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Sparse and structured attention (163 papers)
- Attention head and block redesign (127 papers)
- Efficient image transformers (84 papers)
- Long-context KV and memory attention (88 papers)
Elsewhere in the topic
- Transformer expressivity and learnability (217 papers)
- State space and recurrent sequence models (172 papers)
- Sparse attention for long-context LLMs (147 papers)
- Efficient and robust vision transformers (124 papers)
- Efficient language transformers (105 papers)
- Language model pretraining and induction (99 papers)
- Hybrid and interpretable ViT designs (94 papers)
- KV cache eviction and compression (92 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).