feat: DyMixOp benchmarks (small files)

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README.md

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+---
+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
+
+**High-fidelity benchmark datasets for evaluating neural operators on multi-scale spatiotemporal dynamical systems.**
+
+Part of the **DyMixOp** (Dynamical Mixture of Operators) 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 | dt=1 |
+| [`2dBurgers`](./2dBurgers_1200x20x2x64x64_dt0.0025_t[0_0.5]_nu0.005.mat) | 2D Burgers | 2D | 64×64 | 1,200 | t∈[0,0.5] | 1.6 GB | ν=0.005, dt=0.0025 |
+| [`2dCE-CRP`](./2dCE-CRP_1430x21x5x128x128_dt0.05_t[0_1].nc) | Cahn-Hilliard + Reaction-Diffusion | 2D | 128×128 | 1,430 | t∈[0,1] | 9.6 GB | 5 channels, dt=0.05 |
+| [`2dDarcy`](./2dDarcy_5keys_2048x1x1x241x241.mat) | Darcy Flow | 2D | 241×241 | 2,048 | Steady-state | 3.7 GB | 5 permeability fields |
+| [`2dNS`](./2dNS_1200x20x1x64x64_dt1_t[10_30]_nu1e-05.mat) | 2D Navier-Stokes | 2D | 64×64 | 1,200 | t∈[10,30] | 2.2 GB | ν=1e-5, dt=1 |
+| [`3dBrusselator`](./3dBrusselator_1000x2x1x39x28x28_dt0.5_t[0_19].mat) | 3D Brusselator | 3D | 39×28×28 | 1,000 | t∈[0,19] | 478 MB | dt=0.5 |
+| [`3dShallowWater`](./3dShallowWater_1200x30x2x64x32.mat) | Shallow Water | 3D | 64×32 | 1,200 | 30 timesteps | 1.2 GB | 2 variables |
+
+**Total: ~20GB across 7 benchmark datasets**
+
+## 🚀 Quick Start
+
+### Installation
+
+```bash
+pip install huggingface-hub numpy 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
+```
+
+### Data Structure
+
+Most datasets are stored in MATLAB `.mat` format with the following structure:
+
+```python
+{
+    'u': array([...]),      # Solution fields (main data)
+    't': array([...]),      # Time coordinates
+    'x': array([...]),      # Spatial coordinates
+    'params': {...},        # System parameters
+    '__header__': bytes,    # MATLAB header
+    '__version__': str,     # MATLAB version
+    '__globals__': []       # Global variables
+}
+```
+
+### NetCDF Format (2dCE-CRP)
+
+The Cahn-Hilliard dataset uses NetCDF format:
+
+```python
+import netCDF4 as nc
+
+dataset = nc.Dataset('2dCE-CRP_1430x21x5x128x128_dt0.05_t[0_1].nc')
+print(dataset.variables.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.