Baseline Methods

This folder contains implementations of baseline methods used for comparison in our paper. These methods were selected based on their relevance, effectiveness, and established recognition within the symbolic regression community. Implementations closely follow the original papers to ensure a fair and rigorous evaluation of our proposed approach.

Citations

@inproceedings{TPSR_Shojaee2023,
  author = {Shojaee, Parshin and Meidani, Kazem and Barati Farimani, Amir and Reddy, Chandan},
  title = {Transformer-based Planning for Symbolic Regression},
  booktitle = {Advances in Neural Information Processing Systems},
  volume = {36},
  pages = {45907--45919},
  year = {2023}
}

@article{wAIC_Gao2022,
  title = {Autonomous inference of complex network dynamics from incomplete and noisy data},
  author = {Gao, Ting-Ting and Yan, Gang},
  journal = {Nature Computational Science},
  volume = {2},
  number = {3},
  pages = {160--168},
  year = {2022},
  publisher = {Nature Publishing Group US New York}
}

@inproceedings{DGSR_Holt2023,
  title = {Deep Generative Symbolic Regression},
  author = {Holt, Samuel and Qian, Zhaozhi and van der Schaar, Mihaela},
  booktitle = {The Eleventh International Conference on Learning Representations},
  year = {2023},
  url = {https://openreview.net/forum?id=o7koEEMA1bR}
}

@article{NGGP_Mundhenk2021,
  title = {Symbolic regression via deep reinforcement learning enhanced genetic programming seeding},
  author = {Mundhenk, Terrell and Landajuela, Mikel and Glatt, Ruben and Santiago, Claudio P and Petersen, Brenden K and others},
  journal = {Advances in Neural Information Processing Systems},
  volume = {34},
  pages = {24912--24923},
  year = {2021}
}

@article{PySR_Cranmer2023,
  title = {Interpretable machine learning for science with {PySR and SymbolicRegression.jl}},
  author = {Cranmer, Miles},
  journal = {arXiv preprint arXiv:2305.01582},
  year = {2023}
}

@inproceedings{uDSR_Landajuela2022,
  title = {A Unified Framework for Deep Symbolic Regression},
  author = {Landajuela, Mikel and Lee, Chak and Yang, Jiachen and Glatt, Ruben and Santiago, Claudio P and Aravena, Ignacio and Mundhenk, Terrell N and Mulcahy, Garrett and Petersen, Brenden K},
  booktitle = {Advances in Neural Information Processing Systems},
  pages = {33985--33998},
  volume = {35},
  year = {2022}
}

@inproceedings{SPL_Sun2023,
  title = {Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search},
  author = {Sun, Fangzheng and Liu, Yang and Wang, Jian-Xun and Sun, Hao},
  booktitle = {The Eleventh International Conference on Learning Representations},
  year = {2023},
  url = {https://openreview.net/forum?id=ZTK3SefE8_Z}
}

@article{BMS_Guimera2020,
  title = {A {Bayesian} machine scientist to aid in the solution of challenging scientific problems},
  author = {Guimer{\`a}, Roger and Reichardt, Ignasi and Aguilar-Mogas, Antoni and Massucci, Francesco A and Miranda, Manuel and Pallar{\`e}s, Jordi and Sales-Pardo, Marta},
  journal = {Science Advances},
  volume = {6},
  number = {5},
  pages = {eaav6971},
  year = {2020},
  publisher = {American Association for the Advancement of Science}
}

Method Descriptions

1. TPSR (Transformer-based Planning for Symbolic Regression): An innovative approach by Shojaee et al. that effectively leverages transformer architectures to create a principled planning framework for symbolic regression. This method represents a notable advancement in the field, demonstrating strong capabilities in discovering interpretable equations while maintaining computational efficiency.

2. wAIC (Autonomous inference with AIC): A sophisticated method published in Nature Computational Science by Gao and Yan that addresses the challenging problem of inferring complex network dynamics from incomplete and noisy data. This method's theoretical foundation and empirical results have established it as an important benchmark in scientific discovery.

3. DGSR (Deep Generative Symbolic Regression): An approach by Holt et al. that utilizes deep generative modeling to produce symbolic expressions, offering interesting capabilities for equation discovery.

4. NGGP (Neural-Guided Genetic Programming): A method by Mundhenk et al. that combines deep reinforcement learning with genetic programming, creating an enhanced symbolic regression framework.

5. PySR: A practical and widely-used interpretable machine learning library developed by Cranmer that provides efficient symbolic regression capabilities.

6. uDSR (unified Deep Symbolic Regression): A framework by Landajuela et al. that attempts to unify different aspects of deep symbolic regression into a cohesive approach.

7. SPL (Symbolic Physics Learner): A search-based approach by Sun et al. that employs Monte Carlo tree search techniques to discover governing equations in physical systems.

8. BMS (Bayesian Machine Scientist): A method by Guimerà et al. published in Science Advances that uses Bayesian inference to discover mathematical expressions from data, providing both accurate models and uncertainty quantification.

Acknowledgments

We thank the authors of these methods for their contributions to the field of symbolic regression and scientific discovery.