mlsanityData to 7 Oct 2026

Interpretable Scientific Discovery with Symbolic Regression: A Review

arXiv 2211.10873 ↗First posted 20 Nov 2022cs.LG cs.AI hep-phcited by 105

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Abstract (arXiv)

Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has recently gained a growing interest in deep learning as a data-driven model discovery method, achieving significant advances in various application domains ranging from fundamental to applied sciences. This survey presents a structured and comprehensive overview of symbolic regression methods and discusses their strengths and limitations.

Key facts. Cited by 105 papers in the map (data through 7 Oct 2026). Builds on 21 of its 73 references that are in the map. First posted on arXiv 20 Nov 2022.

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21 of 73 references.

References · 21

  1. 2017Attention Is All You Needcited by 59,932
  2. 2022Emergent Abilities of Large Language Modelscited by 2,483
  3. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 536
  4. 2014OpenML: networked science in machine learningcited by 523
  5. 2020Discovering Symbolic Models from Deep Learning with Inductive Biasescited by 335
  6. 2021Contemporary Symbolic Regression Methods and their Relative Performancecited by 209
  7. 2022End-to-end symbolic regression with transformerscited by 195
  8. 2021Neural Symbolic Regression that Scalescited by 185
  9. 2018Learning Equations for Extrapolation and Controlcited by 151
  10. 2017PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparisoncited by 139
  11. 2016Extrapolation and learning equationscited by 106
  12. 2021SymbolicGPT: A Generative Transformer Model for Symbolic Regressioncited by 101
9 more
  1. 2021Symbolic Regression via Neural-Guided Genetic Programming Population Seedingcited by 97
  2. 2019Bayesian Symbolic Regressioncited by 77
  3. 2022Rediscovering orbital mechanics with machine learningcited by 71
  4. 2022Symbolic Regression is NP-hardcited by 68
  5. 2019Learning Internal Representations (COLT 1995)cited by 25
  6. 2019Fast, accurate, and transferable many-body interatomic potentials by symbolic regressioncited by 23
  7. 2021Symbolic regression for scientific discovery: an application to wind speed forecastingcited by 16
  8. 2021Discovering State Variables Hidden in Experimental Datacited by 12
  9. 2019Improving Model-based Genetic Programming for Symbolic Regression of Small Expressionscited by 3

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Citing papers per year: 2023: 7; 2024: 22; 2025: 45; 2026: 31.

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  1. 2024Symbolic Regression with a Learned Concept Librarycited by 76
  2. 2023ODEFormer: Symbolic Regression of Dynamical Systems with Transformerscited by 58
  3. 2025SR-Scientist: Scientific Equation Discovery With Agentic AIcited by 30
  4. 2023Predicting Ordinary Differential Equations with Transformerscited by 26
  5. 2025DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experiencecited by 20
  6. 2023Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systemscited by 18
  7. 2024Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstructioncited by 18
  8. 2024Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description lengthcited by 16
  9. 2025Call for Action: towards the next generation of symbolic regression benchmarkcited by 16
  10. 2024Zero-shot Imputation with Foundation Inference Models for Dynamical Systemscited by 13
  11. 2025Generative Discovery of Partial Differential Equations by Learning from Math Handbookscited by 12
  12. 2025Interpretable Machine Learning in Physics: A Reviewcited by 11
38 more
  1. 2025Comprehension Without Competence: Architectural Limits of LLMs in Symbolic Computation and Reasoningcited by 7
  2. 2025Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Modelscited by 7
  3. 2025SyMANTIC: An Efficient Symbolic Regression Method for Interpretable and Parsimonious Model Discovery in Science and Beyondcited by 6
  4. 2024A Comparison of Recent Algorithms for Symbolic Regression to Genetic Programmingcited by 5
  5. 2025Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networkscited by 5
  6. 2025On the definition and importance of interpretability in scientific machine learningcited by 5
  7. 2024Learning Interpretable Network Dynamics via Universal Neural Symbolic Regressioncited by 4
  8. 2026LLM-Based Scientific Equation Discovery via Physics-Informed Token-Regularized Policy Optimizationcited by 4
  9. 2024Closed-Form Interpretation of Neural Network Classifiers with Symbolic Gradientscited by 3
  10. 2024TorchSISSO: A PyTorch-Based Implementation of the Sure Independence Screening and Sparsifying Operator for Efficient and Interpretable Model Discoverycited by 3
  11. 2024Ab Initio Nonparametric Variable Selection for Scalable Symbolic Regression with Large pcited by 3
  12. 2025Enabling Population-Level Parallelism in Tree-Based Genetic Programming for GPU Accelerationcited by 3
  13. 2025Forecasting VIX using interpretable Kolmogorov-Arnold networkscited by 3
  14. 2025DiSciPLE: Learning Interpretable Programs for Scientific Visual Discoverycited by 3
  15. 2025A Perspective on Symbolic Machine Learning in Physical Sciencescited by 3
  16. 2025SatelliteFormula: Multi-Modal Symbolic Regression from Remote Sensing Imagery for Physics Discoverycited by 3
  17. 2025Iterated Agent for Symbolic Regressioncited by 3
  18. 2023Scalable Neural Symbolic Regression using Control Variablescited by 2
  19. 2023Celestial Machine Learning: From Data to Mars and Beyond with AI Feynmancited by 2
  20. 2024Bootstrapping OTS-Funcimg Pre-training Model (Botfip) -- A Comprehensive Symbolic Regression Frameworkcited by 2
  21. 2024Hyperdimensional computing: a fast, robust and interpretable paradigm for biological datacited by 2
  22. 2024Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical modelscited by 2
  23. 2024Generalizing the SINDy approach with nested neural networkscited by 2
  24. 2024Discovering an interpretable mathematical expression for a full wind-turbine wake with artificial intelligence enhanced symbolic regressioncited by 2
  25. 2024An Efficient and Generalizable Symbolic Regression Method for Time Series Analysiscited by 2
  26. 2025Interpretable neural network system identification method for two families of second-order systems based on characteristic curvescited by 2
  27. 2025Beyond empirical models: Discovering new constitutive laws in solids with graph-based equation discoverycited by 2
  28. 2025Building Trustworthy AI for Materials Discovery: From Autonomous Laboratories to Z-scorescited by 2
  29. 2026Alpha Discovery via Grammar-Guided Learning and Searchcited by 2
  30. 2026STRIDE: A Self-Reflective Agent Framework for Reliable Automatic Equation Discoverycited by 2
  31. 2024A Personalised Learning Tool for Physics Undergraduate Students Built On a Large Language Model for Symbolic Regressioncited by 1
  32. 2024Closed-Form Interpretation of Neural Network Latent Spaces with Symbolic Gradientscited by 1
  33. 2024Ranking Perspective for Tree-based Methods with Applications to Symbolic Feature Selectioncited by 1
  34. 2024AI-Powered CPS-Enabled Vulnerable-User-Aware Urban Transportation Digital Twin: Methods and Applicationscited by 1
  35. 2025Interpretable Multimodal Learning for Tumor Protein-Metal Binding: Progress, Challenges, and Perspectivescited by 1
  36. 2025CTSR: Cartesian tensor-based sparse regression for data-driven discovery of high-dimensional invariant governing equationscited by 1
  37. 2025Automated Modeling Method for Pathloss Model Discoverycited by 1
  38. 2025SymFlux: deep symbolic regression of Hamiltonian vector fieldscited by 1

50 most cited of 105 All 105 (JSON)