Add dataset card

README.md

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+---
+license: mit
+task_categories:
+  - time-series-forecasting
+tags:
+  - physics
+  - simulation
+  - PDE
+  - fluid-dynamics
+  - equivariance
+  - Navier-Stokes
+  - MHD
+  - turbulence
+language:
+  - en
+pretty_name: ReViT - Datasets for Rotationally Equivariant Vision Transformers
+size_categories:
+  - 10G<n<100G
+---
+
+# ReViT: Datasets for Rotationally Equivariant Vision Transformers
+
+This repository contains the datasets used in the **ReViT** project, which develops rotationally equivariant vision transformers for learning PDE dynamics.
+
+## Datasets
+
+We provide three benchmark datasets spanning 2D and 3D physics simulations:
+
+| Dataset | Task | Dimensionality | Channels | Spatial Resolution | Source |
+|---------|------|---------------|----------|-------------------|--------|
+| **KF2D** | 2D Kolmogorov Flow | 2D | 2 (velocity) | 160×160 | [APEBench](https://github.com/Ceyron/apebench) |
+| **MHD_64** | 3D Magnetohydrodynamics | 3D | 7 (density + velocity + magnetic) | 64×64×64 | [The Well](https://github.com/PolymathicAI/the_well) |
+| **P3D** | 3D Periodic Channel Flow | 3D | 4 (velocity + pressure) | 96×96×96 | DNS Simulation |
+
+---
+
+## KF2D — 2D Kolmogorov Flow
+
+**Physical scenario:** Forced 2D turbulence governed by the incompressible Navier-Stokes equations with sinusoidal forcing (Kolmogorov flow). The external forcing sustains turbulence, producing statistically stationary vortex dynamics.
+
+### Files
+
+| File | Shape | dtype | Size | Description |
+|------|-------|-------|------|-------------|
+| `KF2D/train_V.npy` | `(50, 51, 2, 160, 160)` | float64 | ~1.0 GB | Training trajectories |
+| `KF2D/test_V.npy` | `(30, 201, 2, 160, 160)` | float64 | ~2.4 GB | Test trajectories |
+
+### Data Layout
+- **Axis 0** (`N`): Number of independent trajectory samples
+- **Axis 1** (`T`): Time steps per trajectory (51 train / 201 test)
+- **Axis 2** (`C=2`): Velocity channels `[u, v]`
+- **Axes 3-4** (`H, W`): Spatial grid (160×160, periodic boundary conditions)
+
+### Notes
+- Data is stored as **velocity** fields (converted from vorticity via stream function inversion)
+- Domain: `[0, 1]²` with periodic boundaries
+- The original vorticity data was generated using [APEBench](https://github.com/Ceyron/apebench); velocity conversion was performed using `Generate_velocity.py` from the ReViT repository
+
+---
+
+## MHD_64 — 3D Magnetohydrodynamics
+
+**Physical scenario:** Compressible ideal magnetohydrodynamics (MHD) simulation with Mach number Ma=0.7 and sonic Mach number Ms=0.5. The simulation evolves coupled density, velocity, and magnetic fields on a 3D periodic domain.
+
+### Files
+
+| File | Description |
+|------|-------------|
+| `MHD_64/data/train/MHD_Ma_0.7_Ms_0.5.hdf5` | Training data (~5.8 GB) |
+| `MHD_64/data/valid/MHD_Ma_0.7_Ms_0.5.hdf5` | Validation data (~734 MB) |
+| `MHD_64/stats.yaml` | Normalization statistics |
+
+### HDF5 Structure
+
+```
+├── boundary_conditions/
+│   ├── x_periodic/mask   (64,)  bool
+│   ├── y_periodic/mask   (64,)  bool
+│   └── z_periodic/mask   (64,)  bool
+├── dimensions/
+│   ├── time              (100,) float32
+│   ├── x                 (64,)  float64
+│   ├── y                 (64,)  float64
+│   └── z                 (64,)  float64
+├── scalars/
+│   ├── Ma                ()     float32  (= 0.7)
+│   └── Ms                ()     float32  (= 0.5)
+├── t0_fields/
+│   └── density           (5, 100, 64, 64, 64)       float32
+└── t1_fields/
+    ├── magnetic_field     (5, 100, 64, 64, 64, 3)    float32
+    └── velocity           (5, 100, 64, 64, 64, 3)    float32
+```
+
+### Data Layout
+- **5 trajectories** × **100 time steps** each
+- **Density**: scalar field `(5, 100, 64, 64, 64)`
+- **Velocity**: 3-component vector field `(5, 100, 64, 64, 64, 3)`
+- **Magnetic field**: 3-component vector field `(5, 100, 64, 64, 64, 3)`
+- All spatial dimensions are periodic
+
+### Notes
+- This dataset is a subset of [The Well](https://github.com/PolymathicAI/the_well) benchmark
+- Only the `MHD_Ma_0.7_Ms_0.5` parameter combination is included (used in experiments)
+- The model consumes channels in order: `[velocity(3), magnetic(3), density(1)]` = 7 channels total
+- Note: the HDF5 stores fields in order `[density, velocity, magnetic]`; the data loader reorders them
+
+---
+
+## P3D — 3D Periodic Channel Flow
+
+**Physical scenario:** Direct numerical simulation (DNS) of incompressible turbulent flow in a 3D periodic channel. The simulation resolves velocity and pressure fields at high resolution.
+
+### Files
+
+| File | Shape (velocity) | Shape (pressure) | Size | Description |
+|------|-------------------|-------------------|------|-------------|
+| `P3D/sim0_data_train.h5` | `(1, 180, 3, 96, 96, 96)` | `(1, 180, 1, 96, 96, 96)` | ~1.4 GB | Training |
+| `P3D/sim0_data_test.h5` | `(1, 20, 3, 96, 96, 96)` | `(1, 20, 1, 96, 96, 96)` | ~157 MB | Test |
+
+### HDF5 Structure
+
+```
+├── velocity    (1, T, 3, 96, 96, 96)  float32
+├── pressure    (1, T, 1, 96, 96, 96)  float32
+└── timesteps   (T,)                    int64
+```
+
+### Data Layout
+- **Axis 0** (`B=1`): Batch dimension (single simulation)
+- **Axis 1** (`T`): Time steps (180 train / 20 test)
+- **Axis 2** (`C`): Channels — 3 for velocity `[u, v, w]`, 1 for pressure `[p]`
+- **Axes 3-5** (`D, H, W`): Spatial grid (96×96×96)
+
+### Notes
+- The model uses 4 channels total: `[u, v, w, p]` (velocity + pressure)
+- Only `sim0` is included (used in the default experiments)
+- Spatial domain is periodic in all three directions
+
+---
+
+## Usage
+
+### Quick Download
+
+```python
+from huggingface_hub import hf_hub_download, snapshot_download
+
+# Download the entire repository
+snapshot_download(
+    repo_id="thuerey-group/ReViT",
+    repo_type="dataset",
+    local_dir="./Dataset"
+)
+
+# Or download a specific dataset
+hf_hub_download(
+    repo_id="thuerey-group/ReViT",
+    repo_type="dataset",
+    filename="KF2D/train_V.npy",
+    local_dir="./Dataset"
+)
+```
+
+### Using the Download Script
+
+A convenience script is provided in the [ReViT repository](https://github.com/thuerey-group/ReViT):
+
+```bash
+# Download all datasets
+python scripts/download_from_hf.py --output_dir ./Dataset
+
+# Download specific dataset
+python scripts/download_from_hf.py --dataset KF2D --output_dir ./Dataset
+
+# List available datasets
+python scripts/download_from_hf.py --list
+```
+
+### Loading Data in Python
+
+```python
+import numpy as np
+import h5py
+
+# === KF2D ===
+train_data = np.load("Dataset/KF2D/train_V.npy")
+# shape: (50, 51, 2, 160, 160) — [samples, timesteps, channels, H, W]
+
+# === MHD_64 ===
+with h5py.File("Dataset/MHD_64/data/train/MHD_Ma_0.7_Ms_0.5.hdf5", "r") as f:
+    velocity = f["t1_fields/velocity"][:]       # (5, 100, 64, 64, 64, 3)
+    magnetic = f["t1_fields/magnetic_field"][:]  # (5, 100, 64, 64, 64, 3)
+    density  = f["t0_fields/density"][:]         # (5, 100, 64, 64, 64)
+
+# === P3D ===
+with h5py.File("Dataset/P3D/sim0_data_train.h5", "r") as f:
+    velocity = f["velocity"][:]   # (1, 180, 3, 96, 96, 96)
+    pressure = f["pressure"][:]   # (1, 180, 1, 96, 96, 96)
+```
+
+---
+
+## Citation
+
+If you use these datasets, please cite:
+
+```bibtex
+@article{revit2025,
+    title={ReViT: Rotationally Equivariant Vision Transformers for PDE Dynamics},
+    author={Thuerey Group},
+    year={2025}
+}
+```
+
+## License
+
+This dataset is released under the [MIT License](https://opensource.org/licenses/MIT).
+
+## Acknowledgments
+
+- **KF2D**: Generated using the [APEBench](https://github.com/Ceyron/apebench) benchmark framework
+- **MHD_64**: Subset from [The Well](https://github.com/PolymathicAI/the_well) benchmark
+- **P3D**: Direct numerical simulation data