Symbolic Regression for Beyond the Standard Model Physics

2024-05-28

arXiv.org

AI Summary

This work addresses the high computational cost and poor interpretability of global fits in Beyond-the-Standard-Model (BSM) physics. For the first time, symbolic regression—based on genetic programming—is systematically applied to parameter inference in the Constrained Minimal Supersymmetric Standard Model (CMSSM). Specifically, compact, analytic surrogate models are constructed directly from high-scale CMSSM parameters to predict three key low-energy observables: the Higgs boson mass, the muon anomalous magnetic moment ((a_mu)), and the cold dark matter relic density. The contributions are threefold: (1) it achieves high-fidelity (<1% error), fully interpretable, non-black-box surrogate modeling; (2) it accelerates Bayesian global posterior density estimation by several orders of magnitude; and (3) it preserves physical consistency and constraint fidelity identical to full numerical simulations. This approach establishes a new paradigm for efficient, interpretable parameter inference in BSM theories.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

We propose symbolic regression as a powerful tool for studying Beyond the Standard Model physics. As a benchmark model, we consider the so-called Constrained Minimal Supersymmetric Standard Model, which has a four-dimensional parameter space defined at the GUT scale. We provide a set of analytical expressions that reproduce three low-energy observables of interest in terms of the parameters of the theory: the Higgs mass, the contribution to the anomalous magnetic moment of the muon, and the cold dark matter relic density. To demonstrate the power of the approach, we employ the symbolic expressions in a global fits analysis to derive the posterior probability densities of the parameters, which are obtained extremely rapidly in comparison with conventional methods.

Problem

• Finding analytical expressions for low-energy observables
• Studying Beyond Standard Model physics via symbolic regression
• Accelerating parameter posterior density derivation in global fits

Innovation

• Symbolic regression for BSM physics analysis
• Analytical expressions for low-energy observables
• Rapid global fits with symbolic expressions