---
license: mit

language:
  - en

tags:
  - symbolic-regression
  - function-approximation
  - 3d-surfaces
  - geometric-learning
  - scientific-discovery
  - equation-discovery
  - benchmark

size_categories:
  - 10K<n<100K
---
# 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.

<img src="https://github.com/deep-symbolic-mathematics/surfacebench/blob/main/images/work_flow.png?raw=true" alt="drawing" width="900"/>

## 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
```python
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:
```bibtex
@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