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Where are we now? A large benchmark study of recent symbolic regression methods

arXiv 1804.09331 ↗First posted 25 Apr 2018cs.NE cs.LGcited by 44

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Abstract (arXiv)

In this paper we provide a broad benchmarking of recent genetic programming approaches to symbolic regression in the context of state of the art machine learning approaches. We use a set of nearly 100 regression benchmark problems culled from open source repositories across the web. We conduct a rigorous benchmarking of four recent symbolic regression approaches as well as nine machine learning approaches from scikit-learn. The results suggest that symbolic regression performs strongly compared to state-of-the-art gradient boosting algorithms, although in terms of running times is among the slowest of the available methodologies. We discuss the results in detail and point to future research directions that may allow symbolic regression to gain wider adoption in the machine learning community.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). First posted on arXiv 25 Apr 2018.

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Citing papers per year: 2021: 6; 2022: 9; 2023: 10; 2024: 7; 2025: 7; 2026: 5.

44 papers.

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  1. 2022Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discoverycited by 44
  2. 2022A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledgecited by 31
  3. 2021Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledgecited by 27
  4. 2024AlphaForge: A Framework to Mine and Dynamically Combine Formulaic Alpha Factorscited by 25
  5. 2023Benchmarking sparse system identification with low-dimensional chaoscited by 19
  6. 2025Call for Action: towards the next generation of symbolic regression benchmarkcited by 16
  7. 2022GSR: A Generalized Symbolic Regression Approachcited by 11
  8. 2021Problem-solving benefits of down-sampled lexicase selectioncited by 8
  9. 2022Automated Learning of Interpretable Models with Quantified Uncertaintycited by 8
  10. 2022CoNSoLe: Convex Neural Symbolic Learningcited by 7
  11. 2025Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Modelscited by 7
  12. 2023Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competitioncited by 6
32 more
  1. 2023MESSY Estimation: Maximum-Entropy based Stochastic and Symbolic densitY Estimationcited by 5
  2. 2023Symbolic Regression as Feature Engineering Method for Machine and Deep Learning Regression Taskscited by 5
  3. 2021Generative and reproducible benchmarks for comprehensive evaluation of machine learning classifierscited by 4
  4. 2022Symbolic-Regression Boostingcited by 4
  5. 2026A-SR: Self-Evolving Agentic LLMs for Symbolic Regression via Hierarchical Coordinationcited by 4
  6. 2023Particularitycited by 3
  7. 2023AutoNumerics-Zero: Automated Discovery of State-of-the-Art Mathematical Functionscited by 3
  8. 2024Interpretability in Symbolic Regression: a benchmark of Explanatory Methods using the Feynman data setcited by 3
  9. 2025Iterated Agent for Symbolic Regressioncited by 3
  10. 2022Symbolic Regression with Fast Function Extraction and Nonlinear Least Squares Optimizationcited by 2
  11. 2023Symbolic Metamodels for Interpreting Black-boxes Using Primitive Functionscited by 2
  12. 2023Differentiable Genetic Programming for High-dimensional Symbolic Regressioncited by 2
  13. 2024ISR: Invertible Symbolic Regressioncited by 2
  14. 2025TinyverseGP: Towards a Modular Cross-domain Benchmarking Framework for Genetic Programmingcited by 2
  15. 2025Data-driven Discovery of Digital Twins in Biomedical Researchcited by 2
  16. 2022Exploring Hidden Semantics in Neural Networks with Symbolic Regressioncited by 1
  17. 2023Information Fusion via Symbolic Regression: A Tutorial in the Context of Human Healthcited by 1
  18. 2024Univariate Skeleton Prediction in Multivariate Systems Using Transformerscited by 1
  19. 2024A neural network approach for solving the Monge-Amp`ere equation with transport boundary conditioncited by 1
  20. 2025Symbolic Quantile Regression for the Interpretable Prediction of Conditional Quantilescited by 1
  21. 2026Symmetry-Constrained Language-Guided Program Synthesis for Discovering Governing Equations from Noisy and Partial Observationscited by 1
  22. 2021Zoetrope Genetic Programming for Regressioncited by 0
  23. 2021EBIC.JL -- an Efficient Implementation of Evolutionary Biclustering Algorithm in Juliacited by 0
  24. 2021Pedagogical Rule Extraction to Learn Interpretable Models - an Empirical Studycited by 0
  25. 2022Iterative Genetic Improvement: Scaling Stochastic Program Synthesiscited by 0
  26. 2023Enhanced Genetic Programming Models with Multiple Equations for Accurate Semi-Autogenous Grinding Mill Throughput Predictioncited by 0
  27. 2024Evolutionary Causal Discovery with Relative Impact Stratification for Interpretable Data Analysiscited by 0
  28. 2024SPINEX_ Symbolic Regression: Similarity-based Symbolic Regression with Explainable Neighbors Explorationcited by 0
  29. 2025Impilict Runge-Kutta based sparse identification of governing equations in biologically motivated systemscited by 0
  30. 2026ERBench: A Benchmark and Testsuite for Equation Discovery Algorithmscited by 0
  31. 2026Efficient Constant Optimization for Symbolic Regression with GPU-Accelerated Tree-Based Genetic Programmingcited by 0
  32. 2026How AI Agents Discover Scientific Equations: From Hydrotope Rediscovery to New Water-Wave Amplitudescited by 0