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Discovering the Underlying Analytic Structure Within Standard Model Constants Using Artificial Intelligence

S. V. Chekanov, H. Kjellerstrand

TL;DR

This work introduces a genetic-programming-driven symbolic regression framework to search for simple analytic relations among Standard Model constants. By deploying constant-identification GP in Picat and by constructing both unitful and dimensionless input schemes (the latter via $m_\rho$ normalization), the authors generate and filter large catalogs of candidate relations, reporting numerous dimensionless snippets with sub-percent precision and a smaller set of unitful relations. They validate the approach on known mathematical benchmarks and discuss the prevalence of coincidental patterns, advocating a second, physics-based filtering step to extract physically meaningful connections. The resulting collection of analytic snippets and the methodological pipeline provide a resource for model builders and AI-driven analyses aiming to uncover potential unifying structures among SM parameters. The work also outlines clear avenues for methodological enhancements and extensions to other scientific domains with many free parameters.

Abstract

This paper presents a method for uncovering hidden analytic relationships among the fundamental parameters of the Standard Model (SM), a foundational theory in physics that describes the fundamental particles and their interactions, using symbolic regression and genetic programming. Using this approach, we identify the simplest analytic relationships connecting pairs of these constants and report several notable expressions obtained with relative precision better than 1%. These results may serve as valuable inputs for model builders and artificial intelligence methods aimed at uncovering hidden patterns among the SM constants, or potentially used as building blocks for a deeper underlying law that connects all parameters of the SM through a small set of fundamental constants.

Discovering the Underlying Analytic Structure Within Standard Model Constants Using Artificial Intelligence

TL;DR

This work introduces a genetic-programming-driven symbolic regression framework to search for simple analytic relations among Standard Model constants. By deploying constant-identification GP in Picat and by constructing both unitful and dimensionless input schemes (the latter via normalization), the authors generate and filter large catalogs of candidate relations, reporting numerous dimensionless snippets with sub-percent precision and a smaller set of unitful relations. They validate the approach on known mathematical benchmarks and discuss the prevalence of coincidental patterns, advocating a second, physics-based filtering step to extract physically meaningful connections. The resulting collection of analytic snippets and the methodological pipeline provide a resource for model builders and AI-driven analyses aiming to uncover potential unifying structures among SM parameters. The work also outlines clear avenues for methodological enhancements and extensions to other scientific domains with many free parameters.

Abstract

This paper presents a method for uncovering hidden analytic relationships among the fundamental parameters of the Standard Model (SM), a foundational theory in physics that describes the fundamental particles and their interactions, using symbolic regression and genetic programming. Using this approach, we identify the simplest analytic relationships connecting pairs of these constants and report several notable expressions obtained with relative precision better than 1%. These results may serve as valuable inputs for model builders and artificial intelligence methods aimed at uncovering hidden patterns among the SM constants, or potentially used as building blocks for a deeper underlying law that connects all parameters of the SM through a small set of fundamental constants.

Paper Structure

This paper contains 14 sections, 3 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. The Method
  3. Technical details
  4. Inputs for the genetic algorithm
  5. Inputs with Units
  6. Inputs Without Physical Units
  7. The GP Search Algorithm
  8. Validation of the GP Algorithm
  9. Results of the GP Algorithm
  10. Output for Inputs with Physical Units
  11. Output for Dimensionless Inputs
  12. Discussion of the Results
  13. Next Steps
  14. Conclusions

Figures (1)

  • Figure 1: The distribution of $\Delta D= 100\% \times |y-y_{t}|/y_t$ (see the text) for the expressions without mass scaling (the filled histogram), and after scaling by the $\rho$ and $\phi$ meson masses. Only expressions with analytic rank smaller than 40 are shown.