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
MHD_64	3D Magnetohydrodynamics	3D	7 (density + velocity + magnetic)	64×64×64	The Well
P3D	3D Periodic Channel Flow	3D	4 (velocity + pressure)	96×96×96	DNS Simulation

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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; velocity conversion was performed using Generate_velocity.py from the ReViT repository

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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 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

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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

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Usage

Quick Download

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:

# 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

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)

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Citation

If you use these datasets, please cite:

@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.

Acknowledgments

• KF2D: Generated using the APEBench benchmark framework
• MHD_64: Subset from The Well benchmark
• P3D: Direct numerical simulation data