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Bayesian symbolic regression: automated equation discovery from a physicist's perspective.

Roger Guimerà1,2,3, Marta Sales-Pardo1,2

  • 1Department of Chemical Engineering, Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|April 9, 2026
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The probabilistic approach to symbolic regression offers a principled alternative to heuristic methods for learning mathematical models. This data-driven approach provides performance guarantees and emphasizes model ensembles for robust scientific discovery.

Keywords:
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Area of Science:

  • * Computational Physics
  • * Machine Learning
  • * Information Theory

Background:

  • * Symbolic regression aims to discover closed-form mathematical models from data.
  • * Current methods often use heuristics for model selection, regularization, and exploration.
  • * These heuristic approaches lack performance guarantees.

Purpose of the Study:

  • * To introduce and discuss the probabilistic approach to symbolic regression.
  • * To highlight its advantages over heuristic methods in model discovery.
  • * To explore its connections to information theory and statistical physics.

Main Methods:

  • * Utilizing a probabilistic framework for symbolic regression.
  • * Establishing model plausibility through fundamental considerations and approximations.
  • * Connecting the approach to information theory and statistical physics principles.

Main Results:

  • * The probabilistic approach provides performance guarantees absent in heuristic methods.
  • * It offers a principled way to assess model plausibility.
  • * The framework naturally leads to the consideration of model ensembles.

Conclusions:

  • * The probabilistic approach offers a robust and theoretically grounded alternative for symbolic regression.
  • * It enhances the reliability and interpretability of discovered mathematical models.
  • * This methodology is particularly relevant for applications in the physical sciences.