README.md

Comprehensive Symbolic Regression Surface Dataset

Overview

This dataset contains a comprehensive collection of symbolic regression problems focused on 3D surface modeling. The dataset includes 18 different categories of surface types, each with multiple instances, providing a diverse benchmark for symbolic regression algorithms.

Dataset Structure

The dataset is organized in HDF5 format with the following structure:

/
├── Category_1/
│   ├── Instance_1/
│   │   ├── train_data (5000, 3) - Training data [x, y, z]
│   │   ├── test_data (500, 3) - Test data [x, y, z]
│   │   └── ood_test (500, 3) - Out-of-distribution test data [x, y, z]
│   └── Instance_2/
│       └── ...
└── Category_2/
    └── ...

Categories

1. Algebraic_Manifolds_of_Higher_Degree (24 instances)
2. Bio-Inspired_Morphological_Surfaces (10 instances)
3. Complex_Composite_Surfaces (10 instances)
4. Complex_Morphological_Surfaces (16 instances)
5. Discrete_Symbolic_Grid_Surfaces (10 instances)
6. High_Dimensional_Parametric_Surfaces (10 instances)
7. Hybrid_Multi-Modal_Symbolic_Surfaces (10 instances)
8. Non-Canonical_3D_Geometric_Surfaces (11 instances)
9. Nonlinear_Dynamical_System_Surfaces (9 instances)
10. Piecewise_Regime_Surfaces (10 instances)
11. Procedural_Fractal_Surfaces (10 instances)
12. Quantum_Inspired_Surfaces (10 instances)
13. Stochastic_Process_Surfaces (10 instances)
14. Surrogate_Distilled_Symbolic_Approximations (9 instances)
15. Symbolic-Numeric_Composite_Surfaces (10 instances)
16. Tensor_Field_Surfaces (10 instances)
17. Topologically_Rich_Parametric_Surfaces (10 instances)
18. Transformed_Coordinate_Surfaces (10 instances)

Data Format

• Input: 2D coordinates (x, y)
• Output: Surface height (z)
• Training set: 5,000 points per instance
• Test set: 500 points per instance
• Out-of-distribution test: 500 points per instance
• Data type: float64

Usage

import h5py
import numpy as np

# Load the dataset
with h5py.File('dataset.h5', 'r') as f:
    # Access a specific category and instance
    category = 'Bio-Inspired_Morphological_Surfaces'
    instance = 'BIMS1'
    
    # Load training data
    train_data = f[f'{category}/{instance}/train_data'][:]
    X_train = train_data[:, :2]  # x, y coordinates
    y_train = train_data[:, 2]   # z values
    
    # Load test data
    test_data = f[f'{category}/{instance}/test_data'][:]
    X_test = test_data[:, :2]
    y_test = test_data[:, 2]
    
    # Load out-of-distribution test data
    ood_data = f[f'{category}/{instance}/ood_test'][:]
    X_ood = ood_data[:, :2]
    y_ood = ood_data[:, 2]

Applications

This dataset is designed for:

• Symbolic regression algorithm benchmarking
• 3D surface modeling and reconstruction
• Function approximation research
• Out-of-distribution generalization studies
• Multi-modal symbolic learning

Citation

If you use this dataset in your research, please cite:

@dataset{symbolic_regression_surfaces_2024,
  title={Comprehensive Symbolic Regression Surface Dataset},
  author={[Your Name]},
  year={2024},
  url={https://huggingface.co/datasets/[your-username]/[dataset-name]}
}

License

[Specify your license here]

Contact

[Your contact information]