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AI Feynman: a Physics-Inspired Method for Symbolic Regression

arXiv 1905.11481 ↗First posted 27 May 2019physics.comp-ph cs.AI cs.LGcited by 536

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Abstract (arXiv)

A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the Feynman Lectures on Physics, and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult test set, we improve the state of the art success rate from 15% to 90%.

Key facts. Cited by 536 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 May 2019.

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Citing papers per year: 2021: 42; 2022: 71; 2023: 94; 2024: 75; 2025: 128; 2026: 126.

536 papers.

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  1. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  2. 2022End-to-end symbolic regression with transformerscited by 195
  3. 2021Neural Symbolic Regression that Scalescited by 185
  4. 2024LLM-SR: Scientific Equation Discovery via Programming with Large Language Modelscited by 117
  5. 2022Interpretable Scientific Discovery with Symbolic Regression: A Reviewcited by 105
  6. 2021SymbolicGPT: A Generative Transformer Model for Symbolic Regressioncited by 101
  7. 2021Symbolic Regression via Neural-Guided Genetic Programming Population Seedingcited by 97
  8. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 87
  9. 2025From Automation to Autonomy: A Survey on Large Language Models in Scientific Discoverycited by 86
  10. 2024Symbolic Regression with a Learned Concept Librarycited by 76
  11. 2023A Mathematical Guide to Operator Learningcited by 74
  12. 2023Transformer-based Planning for Symbolic Regressioncited by 72
38 more
  1. 2022Rediscovering orbital mechanics with machine learningcited by 71
  2. 2022On scientific understanding with artificial intelligencecited by 68
  3. 2022Symbolic Regression is NP-hardcited by 68
  4. 2022Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modelingcited by 65
  5. 2021Encoding physics to learn reaction-diffusion processescited by 61
  6. 2022Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree searchcited by 61
  7. 2025LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Modelscited by 61
  8. 2023ODEFormer: Symbolic Regression of Dynamical Systems with Transformerscited by 58
  9. 2023Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical lawscited by 55
  10. 2025What Has a Foundation Model Found? Using Inductive Bias to Probe for World Modelscited by 46
  11. 2024Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolationcited by 45
  12. 2022Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discoverycited by 44
  13. 2021Data-driven discovery of Green's functions with human-understandable deep learningcited by 43
  14. 2023SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-trainingcited by 41
  15. 2024Towards Scientific Discovery with Generative AI: Progress, Opportunities, and Challengescited by 41
  16. 2023Deep Generative Symbolic Regression with Monte-Carlo-Tree-Searchcited by 40
  17. 2023Seeing is Believing: Brain-Inspired Modular Training for Mechanistic Interpretabilitycited by 38
  18. 2023Interpretable Machine Learning for Science with PySR and SymbolicRegression.jlcited by 36
  19. 2024A review on data-driven constitutive laws for solidscited by 35
  20. 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 34
  21. 2023Discovering Causal Relations and Equations from Datacited by 33
  22. 2025NewtonBench: Benchmarking Generalizable Scientific Law Discovery in LLM Agentscited by 32
  23. 2021Machine-learning hidden symmetriescited by 31
  24. 2022A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledgecited by 31
  25. 2022Exhaustive Symbolic Regressioncited by 29
  26. 2023AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identificationcited by 29
  27. 2024In-Context Symbolic Regression: Leveraging Large Language Models for Function Discoverycited by 29
  28. 2021Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledgecited by 27
  29. 2023Deep Generative Symbolic Regressioncited by 27
  30. 2021Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networkscited by 26
  31. 2021Noether Networks: Meta-Learning Useful Conserved Quantitiescited by 26
  32. 2021Machine-Learning Mathematical Structurescited by 25
  33. 2021Discovering Sparse Interpretable Dynamics from Partial Observationscited by 25
  34. 2022Learning Green's functions associated with time-dependent partial differential equationscited by 25
  35. 2023Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regressioncited by 25
  36. 2024SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learningcited by 24
  37. 2022Deep Learning and Symbolic Regression for Discovering Parametric Equationscited by 22
  38. 2023Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principlescited by 22

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