SurfaceBench: Benchmark for Scientific Surface Discovery

This dataset contains a comprehensive collection of symbolic regression problems focused on 3D surface modeling. The dataset includes 15 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. Nonlinear_Analytic_Composition_Surfaces (11 instances)
2. Piecewise-Defined_Surfaces (10 instances)
3. Mixed_Transcendental_Analytic_Surfaces (9 instances)
4. Conditional_Multi-Regime_Surfaces (9 instances)
5. Oscillatory_Composite_Surfaces (11 instances)
6. Trigonometric–Exponential_Composition_Surfaces (10 instances)
7. Multi-Operator_Composite_Surfaces (10 instances)
8. Elementary_Bivariate_Surfaces (10 instances)
9. Discrete_Integer-Grid_Surfaces (10 instances)
10. Nonlinear_Coupled_Surfaces (10 instances)
11. Exponentially-Modulated_Trigonometric_Surfaces (10 instances)
12. Localized_and_Radially-Decaying_Surfaces (10 instances)
13. Polynomial–Transcendental_Mixtures (9 instances)
14. High-Degree_Implicit_Surfaces (24 instances)
15. Parametric_Multi-Output_Surfaces (30 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 = 'Elementary_Bivariate_Surfaces'
    instance = 'EBS1'
    
    # 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 find our code and data useful, please cite our paper:

@article{kabra2026surfacebenchgeometryawarebenchmarksymbolic,
      title={SURFACEBENCH: A Geometry-Aware Benchmark for Symbolic Surface Discovery}, 
      author={Sanchit Kabra and Shobhnik Kriplani and Parshin Shojaee and Chandan K. Reddy},
      journal={arXiv preprint arXiv:2511.10833},
      year={2026}
}

License

MIT License