Update dataset card: Add paper, project page, code links, and update citation

This PR improves the dataset card by:
- Adding `language: en` to the metadata for better discoverability.
- Adding explicit links to the paper (`https://huggingface.co/papers/2512.00564`), project page (`https://naman-choudhary-ai-ml.github.io/pde-difficulty-transfer/`), and code repository (`https://github.com/Naman-Choudhary-AI-ML/pregenerating-pde`) at the top of the README.
- Updating the paper link within the "Dataset Description" to point to the official Hugging Face paper page.
- Updating the BibTeX citation to include the authors: Naman Choudhary, Vedant Singh, Ameet Talwalkar, Nicholas Matthew Boffi, Mikhail Khodak, Tanya Marwah, and linking to the Hugging Face paper URL, along with updating the publication year to 2025.

These changes enhance the completeness and navigability of the dataset card.

README.md

@@ -1,154 +1,156 @@
----
-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.
-
-### 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
-
-```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
-```
-
-## 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.
-
-## License
-
-MIT License
-
----
-
-**Dataset Version:** 1.0
-**Last Updated:** 2024
-**Status:** Research dataset under peer review
+---
+license: mit
+size_categories:
+- 100K<n<1M
+task_categories:
+- other
+pretty_name: PreGen Navier-Stokes 2D Dataset
+tags:
+- physics
+- fluid-dynamics
+- navier-stokes
+- pde
+- scientific-computing
+- neural-operators
+- foundation-models
+- difficulty-transfer
+- reynolds-number
+- openfoam
+language:
+- en
+---
+
+# PreGen Navier-Stokes 2D Dataset
+
+[Paper](https://huggingface.co/papers/2512.00564) | [Project Page](https://naman-choudhary-ai-ml.github.io/pde-difficulty-transfer/) | [Code](https://github.com/Naman-Choudhary-AI-ML/pregenerating-pde)
+
+## Dataset Description
+
+This dataset accompanies the research paper **[Pre-Generating Multi-Difficulty PDE Data For Few-Shot Neural PDE Solvers](https://huggingface.co/papers/2512.00564)** (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
+
+```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
+```
+
+## Citation
+
+If you use this dataset, please cite:
+
+```bibtex
+@article{pregen2025,
+  title={Pre-Generating Multi-Difficulty PDE Data For Few-Shot Neural PDE Solvers},
+  author={Choudhary, Naman and Singh, Vedant and Talwalkar, Ameet and Boffi, Nicholas Matthew and Khodak, Mikhail and Marwah, Tanya},
+  journal={arXiv preprint},
+  year={2025},
+  url={https://huggingface.co/papers/2512.00564}
+}
+```
+
+## License
+
+MIT License
+
+---
+
+**Dataset Version:** 1.0
+**Last Updated:** 2024
+**Status:** Research dataset under peer review