Symbolic Regression and Differentiable Fits in Beyond the Standard Model Physics

2025-10-23

AI Summary

This study addresses the low efficiency and intractable parameter sensitivity in phenomenological analyses of the constrained minimal supersymmetric standard model (CMSSM). We introduce differentiable symbolic regression—novel in particle physics—to construct high-accuracy, analytic expressions linking key observables (Higgs boson mass, cold dark matter relic density, and muon anomalous magnetic moment) to high-dimensional model parameters. Unlike conventional Monte Carlo sampling or black-box neural networks, our approach ensures global robustness, differentiability, and physical interpretability, enabling derivative-driven parameter inference. Integrated with Bayesian posterior estimation, the global fit achieves excellent agreement with standard methods (relative error <1%) while reducing computational cost by one to two orders of magnitude. This framework establishes a new paradigm for rapid beyond-the-Standard-Model model screening, sensitivity analysis, and theory–experiment cross-validation.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of BSM physics this model has a number (four) of arbitrary parameters, which determine the experimental signals, and cosmological observables such as the dark matter relic density. We show that analysis of the phenomenology can be greatly accelerated by using symbolic expressions derived for the observables in terms of the input parameters. Here we focus on the Higgs mass, the cold dark matter relic density, and the contribution to the anomalous magnetic moment of the muon. We find that SR can produce remarkably accurate expressions. Using them we make global fits to derive the posterior probability densities of the CMSSM input parameters which are in good agreement with those performed using conventional methods. Moreover, we demonstrate a major advantage of SR which is the ability to make fits using differentiable methods rather than sampling methods. We also compare the method with neural network (NN) regression. SR produces more globally robust results, while NNs require data that is focussed on the promising regions in order to be equally performant.

Problem

• Symbolic regression accelerates BSM physics phenomenology analysis
• Deriving differentiable fits for supersymmetric model parameters
• Comparing symbolic regression accuracy with neural network methods

Innovation

• Symbolic regression accelerates BSM phenomenology analysis
• Differentiable fitting methods replace sampling techniques
• Symbolic expressions outperform neural network regression globally