Picat used in paper in High Energy Physics and Symbolic Regression
Hakan Kjellerstrand
Today our paper “Discovering the underlying analytic structure within Standard Model constants using artificial intelligence” by Sergey Chekanov (scientist working in the field of high-energy particle physics at the Large Hadron Collider, https://www.anl.gov/profile/sergei-chekanov) and myself was published at arXiv: https://arxiv.org/abs/2507.00225, in the category hep-ph. The report number is: HEP-ANL-197373, June 26, (2025).
The paper is about finding (mathematical) relationships between certain physical constants that are important in the so-called Standard Model (https://en.wikipedia.org/wiki/Standard_Model ) of particle physics, which is about those very tiny stuff of everything.
Sergei is the expert in the physics domain and behind the idea of this paper. I wrote the software that generated these relationships (expressions) using Symbolic Regression (https://en.wikipedia.org/wiki/Symbolic_regression ), here implemented based on Genetic Programming (https://en.wikipedia.org/wiki/Genetic_programming ); that’s the AI part mentioned in the title. The specific version of symbolic regression we used is “constant identification”, since it tries to discover mathematical formulas for mathematical constants (not mathematical expressions given a huge number of datapoints that symbolic regression tends to be used for). The paper describes more details of the program.
The program that generated the formulas (expressions) is my Picat program https://hakank.org/picat/symbolic_regression.pi . It’s a general framework for symbolic regression and works together with a configuration file. The special way of doing constant identification can be seen in this configuration file: https://hakank.org/picat/symbolic_regression_identify_constant_force_constant.pi .
For more examples what can be done with the symbolic regression program, see https://hakank.org/picat/#symbolic_regression .
This has been a very fun project. So far, I’ve previously written papers related to constraint programming/modeling, Picat and logic programming, see Google Scholar: https://scholar.google.se/citations?user=Z4xfQ9cAAAAJ . Thus this is my very first paper in the realm of physics, and first paper related to genetic programming/symbolic regression.
Best,
Hakan