---
language:
- en
license: mit
tags:
- dynamical-systems
- pde
- operator-learning
- fluid-dynamics
- turbulence
- benchmark
- scientific-ml
pretty_name: DyMixOp Benchmarks
homepage: https://github.com/Lai-PY/DyMixOp
paper: https://arxiv.org/abs/2508.13490
size_categories:
- 1K<n<10K  # Sample count range
---

# DyMixOp Benchmarks

**Benchmark datasets for evaluating neural operators on multi-scale spatiotemporal dynamical systems.**

Part of the **DyMixOp** ([DyMixOp: A Neural Operator Designed from a Complex Dynamics Perspective with Local-Global Mixing for Solving PDEs](https://arxiv.org/abs/2508.13490)) framework for learning complex PDE solutions.

[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)
[![Paper](https://img.shields.io/badge/arXiv-2508.13490-b31b1b.svg)](https://arxiv.org/abs/2508.13490)
[![Dataset Size](https://img.shields.io/badge/Total_Size-~20GB-blue.svg)]()

## 📊 Available Datasets

| Dataset | PDE System | Spatial Dim | Resolution | Samples | Time Span | File Size | Key Parameters |
|---------|------------|-------------|------------|---------|-----------|-----------|----------------|
| [`1dKS`](./1dKS_1200x22x1x4096_dt1_t[100_120].mat) | Kuramoto-Sivashinsky | 1D | 4096 | 1,200 | t∈[100,120] | 845 MB | 1 channel(Scalar $u$), dt=1 |
| [`2dBurgers`](./2dBurgers_1200x20x2x64x64_dt0.0025_t[0_0.5]_nu0.005.mat) | Burgers | 2D | 64×64 | 1,200 | t∈[0,0.5] | 1.6 GB | 2 channel(X-Velocity $u$, Y-Velocity $v$), ν=0.005, dt=0.0025 |
| [`2dCE-CRP`](./2dCE-CRP_1430x21x5x128x128_dt0.05_t[0_1].nc) | Compressible Euler Curved Riemann Problem | 2D | 128×128 | 1,430 | t∈[0,1] | 9.6 GB | 5 channels(Density $\rho$, X-Velocity $u$, Y-Velocity $v$, Pressure $p$, Energy $E$), dt=0.05 |
| [`2dDarcy`](./2dDarcy_5keys_2048x1x1x241x241.mat) | Darcy Flow | 2D | 241×241 | 2,048 | Steady-state | 3.7 GB | 1 channel(Scalar $u$) |
| [`2dNS`](./2dNS_1200x20x1x64x64_dt1_t[10_30]_nu1e-05.mat) | Navier-Stokes | 2D | 64×64 | 1,200 | t∈[10,30] | 2.2 GB | 1 channel(Vorticity $\omega$), ν=1e-5, dt=1 |
| [`3dShallowWater`](./3dShallowWater_1200x30x2x64x32.mat) | Shallow Water | 3D (2D in Spherical) | 64×32 (Spherical) | 1,200 | 30 timesteps | 1.2 GB | 2 channels(Heigt $h$, Vorticity $\omega$) |
| [`3dBrusselator`](./3dBrusselator_1000x2x1x39x28x28_dt0.5_t[0_19].mat) | Brusselator | 2D + 1D (Time) | 39×28×28 | 1,000 | t∈[0,19] | 478 MB | 1 channel(Spatiotemporal Trajectory of Concentration $u(x,y,t)$), dt=0.5|


**Total: ~20GB across 7 benchmark datasets**

## 🚀 Quick Start

### Installation

```bash
pip install huggingface-hub scipy
```

### Direct Download

```python
from huggingface_hub import hf_hub_download
import scipy.io as sio

# Download a specific dataset
file_path = hf_hub_download(
    repo_id="Lai-PY/DyMixOp-Benchmarks",
    filename="2dNS_1200x20x1x64x64_dt1_t[10_30]_nu1e-05.mat",
    repo_type="dataset"
)

# Load the data
data = sio.loadmat(file_path)
print(data.keys())  # View available variables
```

### Batch Download Script

```python
from huggingface_hub import snapshot_download
import os

# Download all datasets
local_dir = "./DyMixOp_datasets"
os.makedirs(local_dir, exist_ok=True)

snapshot_download(
    repo_id="Lai-PY/DyMixOp-Benchmarks",
    repo_type="dataset",
    local_dir=local_dir,
    max_workers=4
)
```

## 📖 Data Format Documentation

### File Naming Convention

```
{dimension}{system}_{samples}x{time_steps}x{channels}x{spatial_dims}_{params}.ext
```

### NetCDF Format (2dCE-CRP)

The 2dCE-CRP dataset uses NetCDF format:

```python
import netCDF4 as nc

dataset = nc.Dataset('2dCE-CRP_1430x21x5x128x128_dt0.05_t[0_1].nc')
print(dataset.keys())  # View available variables
```

## 🔬 Benchmark Applications

These datasets are designed for evaluating:

- **Neural Operators**: FNO, DeepONet, etc.
- **Operator Learning**: Mapping between function spaces
- **Multi-scale Dynamics**: Capturing phenomena across scales
- **Long-term Prediction**: Temporal extrapolation capability
- **Uncertainty Quantification**: Robustness to parameter variations

## 📚 Citation

If you use these benchmarks in your research, please cite:

```bibtex
@article{lai2025dymixop,
  title={DyMixOp: Guiding Neural Operator Design for PDEs from a Complex Dynamics Perspective with Local-Global-Mixing},
  author={Lai, Pengyu and Chen, Yixiao and Xu, Hui},
  journal={arXiv preprint arXiv:2508.13490},
  year={2025}
}
```

## 🤝 Contributing

We welcome contributions! Please see our [GitHub repository](https://github.com/Lai-PY/DyMixOp) for guidelines.

## 📄 License

This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details.