RealPDEBench

RealPDEBench is a benchmark of paired real-world measurements and matched numerical simulations for complex physical systems. It is designed for spatiotemporal forecasting and sim-to-real transfer evaluation on real data.

This Hub repository (AI4Science-WestlakeU/RealPDEBench) is the release repo for RealPDEBench.

• Website & documentation: realpdebench.github.io
• Raw HDF5 distribution: realpdebench.westlake.edu.cn
• Benchmark codebase: AI4Science-WestlakeU/RealPDEBench

Figure 1. RealPDEBench provides paired real-world measurements and matched numerical simulations for sim-to-real evaluation.

What makes RealPDEBench different?

• Paired real + simulated data: each scenario provides experimental measurements and corresponding CFD/LES simulations.
• Real-world evaluation: models are evaluated on real trajectories to quantify the sim-to-real gap.
• Multi-modal mismatch: simulations include additional unmeasured modalities (e.g., pressure, species fields), enabling modality-masking and transfer strategies.

Data sources (high level)

• Fluid systems (cylinder, controlled_cylinder, fsi, foil):
  • Real: Particle Image Velocimetry (PIV) in a circulating water tunnel
  • Sim: CFD (2D finite-volume + immersed-boundary; 3D GPU solvers depending on scenario)
• Combustion (combustion):
  • Real: OH* chemiluminescence imaging (high-speed)
  • Sim: Large Eddy Simulation (LES) with detailed chemistry (NH3/CH4/air co-firing)

Scenarios (5)

Scenario	Real data (measured)	Numerical data (simulated)	Frames / trajectory	Spatial grid (full resolution)	Trajectories (real / numerical)
cylinder	velocity (u,v)	(u,v,p)	3990	128×256	92 / 92
controlled_cylinder	(u,v)	(u,v,p) (+ control params in filenames)	3990	128×256	96 / 96
fsi	(u,v)	(u,v,p)	2173	128×128	51 / 51
foil	(u,v)	(u,v,p)	3990	128×256	98 / 99
combustion	OH* chemiluminescence intensity (1 channel)	intensity surrogate (1) + 15 simulated fields	2001	128×128	30 / 30

Total trajectories (HDF5 files): ~735 (≈364 real + ≈368 numerical).

Physical parameter ranges (real experiments)

Scenario	Key parameters (real)
cylinder	Reynolds number (Re): 1800–12000
controlled_cylinder	(Re): 1781–9843; control frequency (f): 0.5–1.4 Hz
fsi	(Re): 3272–9068; mass ratio (m^*): 18.2–20.8
foil	angle of attack (\alpha): 0°–20°; (Re): 2968–17031
combustion	CH4 ratio: 20–100%; equivalence ratio (\phi): 0.75–1.3

Data format on the Hub

RealPDEBench stores complete trajectories in HuggingFace Arrow format, with separate JSON index files for train/val/test splits. This enables dynamic N_autoregressive support at runtime.

Each scenario contains:

• Trajectory data: hf_dataset/{real,numerical}/ — Arrow files with complete time series
• Index files: hf_dataset/{split}_index_{type}.json — maps sample indices to (sim_id, time_id)
• test_mode metadata: {in_dist,out_dist,remain}_params_{type}.json

Arrow shard files vs. trajectory counts

Important clarification: The number of .arrow shard files does not equal the number of trajectories. HuggingFace Arrow format packs multiple rows into one shard up to a size limit (~500 MB by default), but never splits a single row across shards. Real trajectories are smaller (fewer channels, ~130–260 MB each), so 2–4 trajectories are packed per shard, resulting in fewer shards than trajectories. 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 on its own, resulting in a 1:1 mapping between shards and trajectories.

Dataset version: 2.0.0 (see version.json at repo root; released 2026-01-24, format lazy_slicing_v2).

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

Notes:

• The Trajectories column is the ground-truth count (each row in the Arrow dataset = one complete trajectory). The Arrow shards column is the number of .arrow files on disk — a storage-level detail that depends on per-trajectory size.

• The {remain,in_dist_test,out_dist_test}_params_{real,numerical}.json files partition trajectories by physical parameter regime. Each entry is keyed by HDF5 filename and maps to its parameter tuple (e.g., (Re, control_freq)). The three groups sum to the total trajectory count:

  • 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".

  Per-scenario split counts

  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

Repository layout:

{repo_root}/
  cylinder/
    channels.json                     # Field / channel schema for this scenario
    in_dist_test_params_real.json
    out_dist_test_params_real.json
    remain_params_real.json
    in_dist_test_params_numerical.json
    out_dist_test_params_numerical.json
    remain_params_numerical.json
    hf_dataset/
      real/                           # Arrow: complete trajectories (92 files)
        data-*.arrow
        dataset_info.json
        state.json
      numerical/                      # Arrow: complete trajectories
        data-*.arrow
        dataset_info.json
        state.json
      train_index_real.json           # Index: [{"sim_id": "xxx.h5", "time_id": 0}, ...]
      val_index_real.json
      test_index_real.json
      train_index_numerical.json
      val_index_numerical.json
      test_index_numerical.json
  fsi/
    ...  (same structure)
  controlled_cylinder/
    ...  (same structure)
  foil/
    ...  (same structure)
  combustion/
    ...  (same structure)

How to download only what you need

For large data, use snapshot_download(..., allow_patterns=...) to avoid pulling the full repository.

import os
from huggingface_hub import snapshot_download
from datasets import load_from_disk

repo_id = "AI4Science-WestlakeU/RealPDEBench"
os.environ["HF_HUB_DISABLE_XET"] = "1"
local_dir = snapshot_download(
    repo_id=repo_id,
    repo_type="dataset",
    allow_patterns=["fsi/**"],  # example: download only the FSI folder
    endpoint="https://hf-mirror.com",
)

# Load trajectory data
trajectories = load_from_disk(os.path.join(local_dir, "fsi", "hf_dataset", "real"))
print(f"Loaded {len(trajectories)} trajectories")
print(trajectories[0].keys())  # sim_id, u, v, vo, x, y, t, shape_t, shape_h, shape_w, ...

Using the RealPDEBench loaders (recommended)

For automatic train/val/test splitting and dynamic N_autoregressive support, use the provided dataset loaders:

from realpdebench.data.fluid_hf_dataset import FSIHFDataset

dataset = FSIHFDataset(
    dataset_name="fsi",
    dataset_root="/path/to/data",
    dataset_type="real",
    mode="test",
    N_autoregressive=10,  # Dynamic! Works with any value
)

input_tensor, output_tensor = dataset[0]
print(f"Input shape: {input_tensor.shape}")   # (20, H, W, 2)
print(f"Output shape: {output_tensor.shape}") # (200, H, W, 2) = 20 × 10

Schema (columns)

Fluid datasets (cylinder, controlled_cylinder, fsi, foil)

• Keys (each row = one complete trajectory):
  • sim_id (string): trajectory file name (e.g., 10031.h5)
  • u, v (bytes): float32 arrays of shape (T_full, H, W) — complete time series
  • p (bytes): float32 array (T_full, H, W) (numerical splits only)
  • vo (bytes): float32 array (T_full, H, W) — vorticity
  • x (bytes): float32 array (H, W) — spatial x-coordinate grid (time-invariant)
  • y (bytes): float32 array (H, W) — spatial y-coordinate grid (time-invariant)
  • t (bytes): float32 array (T_full,) — time stamps
  • shape_t (int): complete trajectory length (e.g., 3990, 2173)
  • shape_h, shape_w (int): spatial dimensions
• Field names for each scenario are also documented machine-readably in {scenario}/channels.json (with their Arrow keys and shapes).

Note on spatial grids: x and y are identical across all time frames, so they are stored once as (H, W) instead of (T, H, W). For methods that require per-frame coordinate grids (e.g., PINNs), broadcast at runtime: x_grid = np.broadcast_to(x[np.newaxis, :, :], (T, H, W)). This is a zero-copy view with no memory overhead.

Combustion dataset (combustion)

• Keys (each row = one complete trajectory):
  • sim_id (string): e.g., 40NH3_1.1.h5
  • observed (bytes): float32 array (T_full, H, W) — complete time series
  • numerical (bytes): float32 array (T_full, H, W, 15) (numerical splits only)
  • numerical_channels (int): number of numerical channels (15)
  • x (bytes): float32 array (H, W) — spatial x-coordinate grid (time-invariant)
  • y (bytes): float32 array (H, W) — spatial y-coordinate grid (time-invariant)
  • t (bytes): float32 array (T_full,) — time stamps
  • shape_t (int): complete trajectory length (e.g., 2001)
  • shape_h, shape_w (int): spatial dimensions
• Channel order of the 15 fields packed in numerical (along the last axis) is listed in combustion/channels.json under numerical.numerical_axis_names (index → name).

Index files (JSON)

Each split has an index file mapping sample indices to trajectory positions:

[
  {"sim_id": "10031.h5", "time_id": 0},
  {"sim_id": "10031.h5", "time_id": 20},
  {"sim_id": "10031.h5", "time_id": 40},
  ...
]

Data size

• Total: ~783GB across all scenarios (full resolution, all fields)
• Largest shard file: ~2.1GB (well below the Hub's recommended <50GB per file)
• Total Arrow file count: 649 files (well below the Hub's recommended <100k files per repo)

Per-scenario totals:

Scenario	real	numerical	Total
cylinder	36GB	144GB	180GB
controlled_cylinder	25GB	151GB	176GB
fsi	44GB	58GB	102GB
foil	103GB	155GB	258GB
combustion	4GB	63GB	67GB
Total	212GB	571GB	~783GB

Recommended benchmark protocols

RealPDEBench supports three standard training paradigms (all evaluated on real-world data):

• Simulated training (numerical only)
• Real-world training (real only)
• Simulated pretraining + real finetuning

License

This dataset is released under CC BY‑NC 4.0 (non‑commercial). Please credit the authors and the benchmark paper when using the dataset.

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}
}

Contact

AI for Scientific Simulation and Discovery Lab, Westlake University Maintainer: westlake-ai4s (Hugging Face) Org: AI4Science-WestlakeU