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` **Repository layout**: ``` {repo_root}/ cylinder/ 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. ```python 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: ```python 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 > **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 ### Index files (JSON) Each split has an index file mapping sample indices to trajectory positions: ```json [ {"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: ```bibtex @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`