Add comprehensive dataset card

README.md

@@ -0,0 +1,327 @@
+---
+license: mit
+task_categories:
+- other
+pretty_name: PreGen Navier-Stokes 2D Dataset
+size_categories:
+- 100K<n<1M
+tags:
+- physics
+- fluid-dynamics
+- navier-stokes
+- pde
+- scientific-computing
+- neural-operators
+- foundation-models
+- difficulty-transfer
+- reynolds-number
+- openfoam
+---
+
+# 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. This dataset enables **8.9× reduction in compute time** while achieving comparable performance.
+
+### Dataset Summary
+
+- **Total Size:** ~421 GB
+- **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
+
+### Problem Setting
+
+The dataset solves the 2D incompressible Navier-Stokes equations:
+
+```
+∂u/∂t + (u · ∇)u + ∇p = ν∆u
+∇ · u = 0
+```
+
+where:
+- `u(x,t)` is the velocity field
+- `p(x,t)` is the kinematic pressure
+- `ν` is the kinematic viscosity (1.5 × 10⁻⁵ m²/s)
+- Domain: Ω ⊂ [0,1]²
+
+## 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
+
+## Simulation Details
+
+### Boundary Conditions
+
+**Flow Past Object (FPO):**
+- **Left (inlet):** Parabolic velocity profile with peak velocity Umax
+- **Right (outlet):** Zero-gradient pressure outlet
+- **Top/Bottom:** No-slip walls (u = 0)
+- **Obstacles:** No-slip walls (u = 0)
+
+### Reynolds Number Sampling
+Re is sampled from a truncated Gaussian distribution N(5000, 2000²) with support [100, 10000]. The inlet velocity is scaled to achieve the target Re:
+
+```
+Re = (U_avg × L) / ν
+U_avg = (2/3) × U_max
+```
+
+### Time Integration
+- **Scheme:** Backward Euler (1st order implicit)
+- **Spatial discretization:** Finite volume method
+- **Gradient terms:** Gauss linear (central differencing)
+- **Convection:** Gauss linearUpwind with gradient reconstruction
+- **Diffusion:** Gauss linear orthogonal
+
+### Simulation Duration
+Adaptive time scheduling based on Reynolds number to ensure flow development:
+- **Low Re (10-100):** Fixed 2700s
+- **Medium Re (100-1000):** 1-10× characteristic diffusion time
+- **High Re (1000-10000):** 10-40× characteristic diffusion time
+
+### Computational Cost
+The harder the simulation, the more expensive to generate:
+
+| Configuration | Average Time (seconds) |
+|--------------|----------------------|
+| No obstacle, Low Re | 176.7 |
+| No obstacle, Medium Re | 261.1 |
+| No obstacle, High Re | 350.4 |
+| One obstacle, Low Re | 609.5 |
+| One obstacle, Medium Re | 731.1 |
+| One obstacle, High Re | 942.8 |
+| Multiple obstacles, Low Re | 1550.9 |
+| Multiple obstacles, Medium Re | 1599.2 |
+| Multiple obstacles, High Re | 1653.3 |
+
+## Key Research Findings
+
+This dataset was specifically designed to study **difficulty transfer** in neural PDE solvers:
+
+1. **Sample Efficiency**: Training on 10% hard data + 90% easy/medium data recovers ~96-98% of the performance of training on 100% hard data
+
+2. **Compute Efficiency**: By mixing difficulties optimally, you can achieve the same error with **8.9× less compute** spent on data generation
+
+3. **Medium > Easy**: For most budgets, generating fewer medium-difficulty examples outperforms generating more easy examples
+
+4. **Foundation Dataset Potential**: Medium-difficulty data (single obstacle) improves few-shot performance on complex geometries (NURBS shapes from FlowBench)
+
+## Usage
+
+### Basic Loading
+
+```python
+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
+```
+
+### Difficulty Mixing for Training
+
+```python
+import numpy as np
+from huggingface_hub import hf_hub_download
+
+# Load different difficulty levels
+easy_data = np.load(hf_hub_download(
+    repo_id="sage-lab/PreGen-NavierStokes-2D",
+    filename="Geometry_Axis/FPO_Geometry_Easy_NoObstacle.npy",
+    repo_type="dataset"
+))
+
+medium_data = np.load(hf_hub_download(
+    repo_id="sage-lab/PreGen-NavierStokes-2D",
+    filename="Geometry_Axis/FPO_Geometry_Medium_SingleObstacle.npy",
+    repo_type="dataset"
+))
+
+hard_data = np.load(hf_hub_download(
+    repo_id="sage-lab/PreGen-NavierStokes-2D",
+    filename="Geometry_Axis/FPO_Geometry_Hard_MultiObstacle.npy",
+    repo_type="dataset"
+))
+
+# Recommended: Use 10% hard + 90% medium for cost-effective training
+n_hard = 80
+n_medium = 720
+
+train_data = np.concatenate([
+    hard_data[:n_hard],
+    medium_data[:n_medium]
+], axis=0)
+
+# Hold out 100 hard examples for testing
+test_data = hard_data[-100:]
+```
+
+### Computing Metrics
+
+```python
+def compute_nmae(y_true, y_pred):
+    """
+    Compute normalized Mean Absolute Error (nMAE)
+    as used in the paper.
+
+    Args:
+        y_true: Ground truth, shape (N, T, H, W, C)
+        y_pred: Predictions, shape (N, T, H, W, C)
+
+    Returns:
+        nMAE: Normalized mean absolute error
+    """
+    numerator = np.abs(y_true - y_pred).sum()
+    denominator = np.abs(y_true).sum()
+    return numerator / (denominator + 1e-10)
+```
+
+## Tested Models
+
+The paper evaluates this dataset on:
+
+### Supervised Neural Operators (trained from scratch)
+- **CNO** (Convolutional Neural Operator) - 18M parameters
+- **F-FNO** (Factorized Fourier Neural Operator) - 5-layer
+
+### Foundation Models (fine-tuned)
+- **Poseidon-T** (Tiny) - 21M parameters
+- **Poseidon-B** (Base) - 158M parameters
+- **Poseidon-L** (Large) - 629M parameters
+
+All models are trained autoregressively with one-step-ahead prediction (t → t+1) using relative L1 loss.
+
+## Citation
+
+If you use this dataset, please cite:
+
+```bibtex
+@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.
+
+## Related Datasets
+
+- **The Well** - Large-scale multi-physics PDE dataset
+- **PDEBench** - Benchmark for scientific machine learning
+- **FlowBench** - Flow simulation over complex geometries (NURBS shapes)
+
+## License
+
+MIT License
+
+## Acknowledgments
+
+This dataset was generated using:
+- **OpenFOAM** (v2406) for CFD simulations
+- Simulations performed on computational clusters
+- Total compute time: Several thousand GPU/CPU hours
+
+## Contact
+
+For questions or issues:
+- Open an issue in the dataset repository
+- Contact the sage-lab organization on Hugging Face
+- See the paper for additional contact information (once published)
+
+## Dataset Maintainers
+
+sage-lab organization
+
+---
+
+**Dataset Version:** 1.0
+**Last Updated:** 2024
+**Status:** Research dataset under peer review