Machine Can Automatically Discover Parametric Functions to Model HEP Data

2026-07-22

AI Summary

This work addresses the inefficiency and subjectivity of traditional trial-and-error approaches in high-energy physics (HEP) data analysis by introducing symbolic regression to HEP fitting tasks for the first time. Coupled with uncertainty modeling, the proposed method automatically discovers optimal parametric forms without requiring prior knowledge. The authors implement this approach in the SymbolFit software package and perform extensive parallel explorations across multiple configurations on dijet invariant mass spectra from CMS and ATLAS. From 560 independent runs, over 1,000 high-quality fitting functions achieving χ²/NDF ≈ 1 are generated, including 111 instances that successfully reproduce established dijet and UA2 functional forms found in the literature. This demonstrates a fully automated, data-driven framework for discovering physically meaningful fitting functions in HEP.

Abstract

In HEP data analyses, finding an adequate function to model binned data has largely relied on a manual process: guess a functional form by intuition, fit, examine, then repeat until successful. We show that this iterative process can be automated by a machine using symbolic regression, which performs a data-driven search over function space without requiring prior knowledge of what an adequate function should look like. We present the SymbolFit package, which pairs symbolic regression with uncertainty modeling to target HEP analysis use cases, and demonstrate it on the CMS and ATLAS Run 2 dijet spectra: 560 independent seeded runs across seven simple fit configurations generated over 1000 functions fitting the spectra with $χ^2/\text{NDF}\approx 1$, and 111 of the runs rediscovered the very dijet and UA2 functions used in published dijet searches.

Problem

• HEP data modeling
• function discovery
• binned data
• manual fitting
• symbolic regression

Innovation

• symbolic regression
• automated function discovery
• HEP data modeling
• uncertainty modeling
• SymbolFit