Lai-PY/DyMixOp-Benchmarks

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) framework for learning complex PDE solutions.

📊 Available Datasets

Dataset	PDE System	Spatial Dim	Resolution	Samples	Time Span	File Size	Key Parameters
1dKS	Kuramoto-Sivashinsky	1D	4096	1,200	t∈[100,120]	845 MB	1 channel(Scalar $u$), dt=1
2dBurgers	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	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	Darcy Flow	2D	241×241	2,048	Steady-state	3.7 GB	1 channel(Scalar $u$)
2dNS	Navier-Stokes	2D	64×64	1,200	t∈[10,30]	2.2 GB	1 channel(Vorticity $\omega$), ν=1e-5, dt=1
3dShallowWater	Shallow Water	3D (2D in Spherical)	64×32 (Spherical)	1,200	30 timesteps	1.2 GB	2 channels(Heigt $h$, Vorticity $\omega$)
3dBrusselator	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

pip install huggingface-hub scipy

Direct Download

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

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:

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:

@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 for guidelines.

📄 License

This project is licensed under the MIT License - see the LICENSE file for details.