[ICLR26 Oral] RealPDEBench: A Benchmark for Complex Physical Systems with Paired Real-World and Simulated Data

Peiyan Hu^∗†1,3, Haodong Feng^*1, Hongyuan Liu^*1, Tongtong Yan², Wenhao Deng¹, Tianrun Gao^†1,4, Rong Zheng^†1,5, Haoren Zheng^†1,2, Chenglei Yu¹, Chuanrui Wang¹, Kaiwen Li^†1,2, Zhi-Ming Ma³, Dezhi Zhou², Xingcai Lu⁶, Dixia Fan¹, Tailin Wu^†1.

¹School of Engineering, Westlake University; ²Global College, Shanghai Jiao Tong University; ³Academy of Mathematics and Systems Science, Chinese Academy of Sciences; ⁴Department of Geotechnical Engineering, Tongji University; ⁵School of Physics, Peking University; ⁶Key Laboratory for Power Machinery and Engineering of M. O. E., Shanghai Jiao Tong University

*Equal contribution, †Work done as an intern at Westlake University, †Corresponding authors

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‼️ News

[2026.07] The NeurIPS RealPDE Competition is now live! Join us to tackle real-world physical systems, with generous prizes for winning teams.

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💧🔥 Overview

RealPDEBench is the first scientific ML benchmark with paired real-world measurements and matched numerical simulations for complex physical systems, designed for spatiotemporal forecasting and sim-to-real transfer.

At a glance 👀

• 5 Datasets: cylinder, fsi, controlled_cylinder, foil, combustion
• 700+ Trajectories
• 10 Baseline models: U-Net, FNO, CNO, WDNO, DeepONet, MWT, GK-Transformer, Transolver, DPOT, DMD
• 9 Evaluation metrics: RMSE, MAE, Rel L₂, R², Update Ratio, fRMSE, FE, KE, MVPE

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🎬 Installation (pip)

This repo is packaged with pyproject.toml and can be installed via pip (requires Python ≥ 3.10):

git clone https://github.com/AI4Science-WestlakeU/RealPDEBench.git
cd RealPDEBench
pip install -e .

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⏬ Dataset download

Hugging Face dataset:

The repo id AI4Science-WestlakeU/RealPDEBench.

We provide a small pattern-based downloader:

# safe default: download metadata JSONs only
realpdebench download --dataset-root /path/to/data --scenario cylinder --what metadata

# to download Arrow shards (LARGE), explicitly set --what=hf_dataset or --what=all
# splits are stored in index JSONs under hf_dataset/ (no split directories)
realpdebench download --dataset-root /path/to/data --scenario cylinder --what hf_dataset --dataset-type real

Tips:

• Set --endpoint https://hf-mirror.com (or env HF_ENDPOINT) to get acesss.
• If you hit rate limits (HTTP 429) or need auth, login and set env HF_TOKEN=....
• We recommend setting env HF_HUB_DISABLE_XET=1.

HDF5-format dataset

Note: The Hugging Face dataset above is still the recommended way to download data (faster, and integrates with the realpdebench loaders). The raw HDF5 distribution below is provided for completeness, e.g., if you want to inspect the original simulation outputs or use them outside the RealPDEBench codebase.

Raw HDF5 trajectories are hosted on the Westlake data distribution server: https://realpdebench.westlake.edu.cn/

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📝 Checkpoint download

We release trained checkpoints for all 10 models × 5 scenarios × 3 training paradigms (numerical / real / finetune) on HuggingFace.

from huggingface_hub import hf_hub_download

# Download a single checkpoint
path = hf_hub_download(
    repo_id="AI4Science-WestlakeU/RealPDEBench-models",
    filename="cylinder/fno/finetune.pth",
)

from huggingface_hub import snapshot_download

# Download all checkpoints for a scenario
snapshot_download(
    repo_id="AI4Science-WestlakeU/RealPDEBench-models",
    allow_patterns="cylinder/**",
    local_dir="./checkpoints",
)

DPOT models require pretrained backbone weights (not included). Download via python -m realpdebench.utils.dpot_ckpts_dl or from hzk17/DPOT.

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📥 Training

# Simulated training (train on numerical data)
python -m realpdebench.train --config configs/cylinder/fno.yaml --train_data_type numerical

# Real-world training (train on real data from scratch)
python -m realpdebench.train --config configs/cylinder/fno.yaml --train_data_type real

# Real-world finetuning (finetune on real data)
python -m realpdebench.train --config configs/cylinder/fno.yaml --train_data_type real --is_finetune

Using HF Arrow-backed datasets

HF Arrow datasets are stored under {dataset_root}/{scenario}/hf_dataset/{real,numerical}/ with split index files {split}_index_{type}.json. To use them, enable:

• --use_hf_dataset: load Arrow trajectories + index files (lazy slicing, dynamic N_autoregressive)
• --hf_auto_download: download missing artifacts from HF automatically (use --hf_endpoint https://hf-mirror.com for easy accessing)

Example:

python -m realpdebench.train --config configs/cylinder/fno.yaml --use_hf_dataset --hf_auto_download --hf_endpoint https://hf-mirror.com

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📤 Inference

python -m realpdebench.eval --config configs/cylinder/fno.yaml --checkpoint_path /path/to/checkpoint.pth

Using HF Arrow-backed datasets

python -m realpdebench.eval --config configs/cylinder/fno.yaml --checkpoint_path /path/to/checkpoint.pth --use_hf_dataset

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👩‍💻 Contribute

We welcome contributions from the community! Please feel free to

• Add your models
• Contact us to submit to the leaderboard
• Contribute code improvements
• Improve documentation

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❓ FAQ

Why do the number of .arrow files differ from the trajectory count?

Arrow format packs multiple rows into one shard up to a size limit (~500 MB), but never splits a single row across shards. Real trajectories are smaller (fewer channels, ~130–260 MB each), so 2–4 are packed per shard; numerical trajectories are larger (extra channels such as pressure or 15 simulated fields, ~1.5–2.1 GB each), so each one already exceeds the shard limit, resulting in a 1:1 mapping.

Scenario	Trajectories (real / numerical)	Arrow shards (real / numerical)
cylinder	92 / 92	73 / 92
controlled_cylinder	96 / 96	51 / 96
fsi	51 / 51	51 / 51
foil	98 / 99	98 / 99
combustion	30 / 30	8 / 30

What do remain_params, in_dist_test_params, and out_dist_test_params mean?

These JSON files partition trajectories by physical parameter regime. The three groups sum to the total trajectory count for each scenario:

• in_dist_test_params: trajectories with in-distribution parameters, entirely reserved for testing.
• out_dist_test_params: trajectories with out-of-distribution (edge/extreme) parameters, entirely reserved for testing.
• remain_params: all other trajectories — part of each trajectory's time axis is used for training, the rest for validation/testing.

At evaluation time, test_mode can be set to "seen" (remain), "in_dist", "out_dist", "unseen" (in_dist + out_dist), or "all".

Scenario	Type	remain	in_dist_test	out_dist_test	Total
cylinder	real	72	10	10	92
cylinder	numerical	92	0	0	92
controlled_cylinder	real	76	10	10	96
controlled_cylinder	numerical	96	0	0	96
fsi	real	39	0	12	51
fsi	numerical	51	0	0	51
foil	real	78	10	10	98
foil	numerical	99	0	0	99
combustion	real	30	0	0	30
combustion	numerical	30	0	0	30

Where are the field / channel names for each scenario documented?

Each scenario folder on the HF dataset ships a machine-readable {scenario}/channels.json listing every field (Arrow column) with its shape.

Scenario	Real fields	Numerical fields
cylinder	u, v	u, v, p
controlled_cylinder	u, v	u, v, p
fsi	u, v	u, v, p
foil	u, v	u, v, p
combustion	observed	observed + numerical (packed 15 channels, see below)

For combustion, the numerical column has shape (T, H, W, 15); the 15 channels along the last axis are, in order:

Idx	Channel	Idx	Channel
0	Absolute_Pressure	8	Mole_Fraction_of_OH
1	Chemistry_Heat_Release_Rate	9	Pressure
2	Mole_Fraction_of_CH4	10	Temperature
3	Mole_Fraction_of_CO	11	Velocity[i]
4	Mole_Fraction_of_CO2	12	Velocity[j]
5	Mole_Fraction_of_H2O	13	Velocity[k]
6	Mole_Fraction_of_NH2	14	Velocity_Magnitude
7	Mole_Fraction_of_NH3

A machine-readable copy of the same list lives in combustion/channels.json.

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🫡 Citation

If you find our work and/or our code useful, please cite us via:

@inproceedings{hu2026realpdebench,
    title={RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data}, 
    author={Peiyan Hu and Haodong Feng and Hongyuan Liu and Tongtong Yan and Wenhao Deng and Tianrun Gao and Rong Zheng and Haoren Zheng and Chenglei Yu and Chuanrui Wang and Kaiwen Li and Zhi-Ming Ma and Dezhi Zhou and Xingcai Lu and Dixia Fan and Tailin Wu},
    booktitle={The Fourteenth International Conference on Learning Representations},
    year={2026},
    url={https://openreview.net/forum?id=y3oHMcoItR},
    note={Oral Presentation}
}

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📚 Related Resources

• AI for Scientific Simulation and Discovery Lab: https://github.com/AI4Science-WestlakeU
• NeurIPS 2026 RealPDE Competition: https://realpdecompetition.github.io
• REALM: https://github.com/deepflame-ai/REALM/tree/main
• PDEBench: https://github.com/pdebench/PDEBench