sage-lab/PreGen-NavierStokes-2D

PreGen Navier-Stokes 2D Dataset

Dataset Description

This dataset accompanies the research paper "Pre-Generating Multi-Difficulty PDE Data For Few-Shot Neural PDE Solvers" (under review at ICLR 2026). It contains systematically generated 2D incompressible Navier-Stokes fluid flow simulations designed to study difficulty transfer in neural PDE solvers.

The key insight: by pre-generating many low and medium difficulty examples and including them with a small number of hard examples, neural PDE solvers can learn high-difficulty physics from far fewer samples.

Dataset Summary

• Format: NumPy arrays (.npy files)
• Number of Files: 9
• Simulations per file: 6,400 trajectories
• Timesteps: 20 per trajectory
• Spatial Resolution: 128 × 128 grid
• Solver: OpenFOAM (icoFoam)
• Domain: 2D Incompressible Navier-Stokes equations

Difficulty Axes

The dataset systematically varies complexity along three axes:

1. Geometry Axis (Number of Obstacles)

Simulations in flow-past-object (FPO) configuration with varying obstacle complexity:

• Easy: No obstacles (open channel flow)
• Medium: Single square obstacle
• Hard: 2-10 randomly placed square obstacles

Files:

• Geometry_Axis/FPO_Geometry_Easy_NoObstacle.npy (47 GB)
• Geometry_Axis/FPO_Geometry_Medium_SingleObstacle.npy (47 GB)
• Geometry_Axis/FPO_Geometry_Hard_MultiObstacle.npy (47 GB)

2. Physics Axis (Reynolds Number)

Simulations with varying flow complexity via Reynolds number:

Multi-Obstacle Flows:

• Easy: Re ∈ [100, 1000] - laminar regime
• Medium: Re ∈ [2000, 4000] - transitional regime
• Hard: Re ∈ [8000, 10000] - turbulent regime

Files:

• Physics_Axis/MultiObstacle/FPO_Physics_MultiObstacle_Easy_Re100-1000.npy (47 GB)
• Physics_Axis/MultiObstacle/FPO_Physics_MultiObstacle_Medium_Re2000-4000.npy (47 GB)
• Physics_Axis/MultiObstacle/FPO_Physics_MultiObstacle_Hard_Re8000-10000.npy (47 GB)

No-Obstacle Flows:

• Physics_Axis/NoObstacle/FPO_Physics_NoObstacle_Easy_Re100-1000.npy (47 GB)

3. Combined Axis (Geometry + Physics)

Combined variations in both geometry and Reynolds number:

• Easy: No obstacles + low Re ([100, 1000])
• Medium: Single obstacle + medium Re ([2000, 4000])
• Hard: Multiple obstacles + high Re ([8000, 10000])

File:

• Combined_Axis/FPO_Combined_Medium_SingleObstacle_MedRe.npy (47 GB)

4. Special Configuration

• Special/FPO_Cylinder_Hole_Location_6284.npy (47 GB) - Cylinder with hole at specific location

Data Format

Each .npy file contains a NumPy array with shape: (6400, 20, 128, 128, 6)

Dimensions:

• 6400: Number of simulation trajectories
• 20: Timesteps per trajectory
• 128 × 128: Spatial grid resolution
• 6: Channels (features)

Channels (in order):

1. u - Horizontal velocity component (m/s)
2. v - Vertical velocity component (m/s)
3. p - Kinematic pressure (m²/s²)
4. Re_normalized - Normalized Reynolds number
5. Binary mask - Geometry encoding (1 = obstacle, 0 = fluid)
6. SDF - Signed distance field to nearest obstacle boundary

Usage

import numpy as np
from huggingface_hub import hf_hub_download

# Download a specific difficulty level
file_path = hf_hub_download(
    repo_id="sage-lab/PreGen-NavierStokes-2D",
    filename="Geometry_Axis/FPO_Geometry_Easy_NoObstacle.npy",
    repo_type="dataset"
)

# Load the data
data = np.load(file_path)
print(f"Data shape: {data.shape}")  # (6400, 20, 128, 128, 6)

# Extract individual trajectories
trajectory_0 = data[0]  # Shape: (20, 128, 128, 6)

# Extract velocity and pressure
u = trajectory_0[:, :, :, 0]  # Horizontal velocity
v = trajectory_0[:, :, :, 1]  # Vertical velocity
p = trajectory_0[:, :, :, 2]  # Pressure
mask = trajectory_0[:, :, :, 4]  # Binary geometry mask
sdf = trajectory_0[:, :, :, 5]  # Signed distance field

Citation

If you use this dataset, please cite:

@inproceedings{pregen2026,
  title={Pre-Generating Multi-Difficulty {PDE} Data For Few-Shot Neural {PDE} Solvers},
  author={Anonymous},
  booktitle={Under review at International Conference on Learning Representations (ICLR)},
  year={2026},
  url={https://openreview.net}
}

Note: Citation will be updated once the paper is published.

License

MIT License

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Dataset Version: 1.0 Last Updated: 2024 Status: Research dataset under peer review