---
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