Our second physics paper using Picat for symbolic regression and data analysis has been published

[Hakan Kjellerstrand]

Our second physics paper (preprint) is now available at arXiv: S. V. Chekanov (, H. Kjellerstrand: "Evidence of Relationships Among Fundamental Constants of the Standard Model": https://arxiv.org/abs/2509.07713 .

Abstract: This paper presents an approach to reducing the number of fundamental parameters in the Standard Model (SM) using genetic programming, a machine learning technique based on evolutionary algorithms. We outline the core principles of our method and identify the simplest analytic relationships among SM parameters. Our results suggest that the SM parameters associated with quark and boson masses are not randomly distributed, but instead follow a hierarchical structure within a high-dimensional functional space. The found analytic solution depends on only two input parameters, representing the simplest mathematical model that could provide a foundation for developing a future theoretical framework to address the SM.

This paper is based (and extended) on the findings and data from our first physics paper (preprint): S. V. Chekanov, H. Kjellerstrand: "Discovering the underlying analytic structure within Standard Model constants using artificial intelligence"(https://arxiv.org/abs/2507.00225 )

For some more background, see my post on the first paper https://groups.google.com/g/picat-lang/c/-cZVKYuuCdQ .

For the second paper, I again wrote most of programs, and often only using Picat's excellent feature of backtracking to generate all possible solutions given some restrictions (which we played a lot with during our experiments). So it was actually mostly plain logic programming. It would be great to use constraint modeling, but we needed a powerful MIP solver that supports floats on non linear constraints and trigonometric functions, which - alas - Picat's MIP solver does not support.

It was really fun and I learned a lot. For example I wrote a module doing dimensionality analysis (i.e. that the dimensions at the left side of an equation should be the same as the right side) since it is required when dealing with this kind of physics research. This dimensionality analysis module was used for checking the equations that was generated by my symbolic regression program, but - in a moment of play - I did just a few changes in the code and could then generate equations that are dimensional correct; but we decided not to use that data for the paper.

/Hakan