Datasets

RealPDEBench contains 5 scenarios with paired real-world measurements and matched numerical simulations. Each scenario provides two branches:

  • Real-world (real): experimentally measured fields (often incomplete)
  • Simulated (numerical): CFD/LES fields (often includes unmeasured modalities, e.g. pressure)

What "paired" means in RealPDEBench

A scenario provides two branches:

  • real/: experimentally measured fields (may be incomplete)
  • numerical/: simulation fields (can include additional, unmeasured modalities)

"Paired" means that the real and numerical trajectories correspond to the same configuration (e.g., Reynolds number, control frequency, mixture ratio), enabling sim→real transfer and modality-mismatch evaluation. Note that paired trajectories are matched by configuration, but their initial frames are not necessarily aligned.

Dataset inventory

The table below summarizes dataset sizes, temporal resolution, spatial resolution, and observed modalities.

Dataset n_traj n_frame \(\Delta t\) (s) Resolution (sim) Resolution (real) Memory (GB) Modalities (sim) Modalities (real)
Cylinder 92 × 2 3990 \(2.5\times 10^{-3}\) 64×128 128×256 190.50 \(u,v,p\) \(u,v\)
Controlled Cylinder 96 × 2 3990 \(2.5\times 10^{-3}\) 64×128 128×256 187.08 \(u,v,p\) \(u,v\)
FSI 51 × 2 2173 \(2.0\times 10^{-3}\) 128×128 128×128 94.73 \(u,v,p\) \(u,v\)
Foil 99 × 2 3990 \(2.5\times 10^{-3}\) 128×256 128×256 335.64 \(u,v,p\) \(u,v\)
Combustion 30 × 2 2001 \(2.5\times 10^{-4}\) 128×128 128×128 110.12 multi-modal (15 channels) \(I\)

Note

We use n_traj = X × 2 to indicate paired trajectories: X real-world and X numerical trajectories for the same scenario.

Windowing: sim_id + time_id

RealPDEBench evaluates forecasting on short spatiotemporal windows sampled from long trajectories:

  • Trajectory ID (sim_id): trajectory identifier string (e.g., 1800, 1781_0.5, 40NH3_1.1)
  • Window start (time_id): integer time index
  • One sample: a contiguous window data[time_id : time_id + T], where \(T\) is the window length (in_step + out_step)

Public distribution format (Hugging Face snapshot)

We distribute data as Hugging Face Datasets (Arrow) shards. On disk, a downloaded snapshot is organized as:

{dataset_root}/
  {scenario}/
    hf_dataset/
      real_train/ ...
      real_val/ ...
      real_test/ ...
      numerical_train/ ...
      numerical_val/ ...
      numerical_test/ ...
    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

The *_test_params_*.json files are used for test_mode filtering ("in_dist/out_dist/seen/unseen") during validation/testing.

Evaluation subsets (JSON mappings)

The *_test_params_*.json files define evaluation subsets used by test_mode filters:

  • in_dist: in-distribution parameter settings
  • out_dist: out-of-distribution parameter settings
  • seen: settings used for training (held-out time windows)
  • unseen: settings not used for training

HF Arrow schema (high level)

  • Fluid scenarios (Cylinder / Controlled Cylinder / FSI / Foil)
  • sim_id (string), time_id (int)
  • u (bytes), v (bytes), p (bytes; numerical only)

  • shape_t, shape_h, shape_w (int)

  • Combustion

  • sim_id (string), time_id (int)
  • observed (bytes) — real-world intensity \(I\) (real) or surrogate intensity (numerical)
  • numerical (bytes; numerical only), numerical_channels (int; numerical only)
  • shape_t, shape_h, shape_w (int)