Comprehensive Bayesian machine learning approach to estimating the total nuclear capture rate of a negative muon

Background: A negative muon in the $1s$ orbital of a muonic atom can be captured by a nucleus, leading to subsequent nuclear decay processes. The accurate prediction of total nuclear capture rates, which could be crucial in fields such as geochemistry, nuclear astrophysics, and semiconductor device development, remains challenging with current physics models.Purpose: This study aims to develop a comprehensive machine learning (ML) model to estimate the total nuclear capture rate of a negative muon, integrating physical information and experimental data within a Bayesian framework.Methods: The study employs an ML model based on Gaussian process regression, using experimental data with evaluated uncertainties as training data. The model incorporates the Goulard-Primakoff formula as prior information and applies a transfer learning approach to improve estimations, particularly in regions where data on isotopically enriched elements are sparse.Results: The developed ML model is shown to outperform theoretical physics models in both accuracy and comprehensiveness, with key experiments identified to further refine the model performance.Conclusions: The estimates generated in this study will be incorporated into muon nuclear data and applied across a variety of research fields.