Machine learning for correlations of electromagnetic properties in <i>ab initio</i> calculations

In nuclear structure theory, accurately predicting electromagnetic observables, such as moments and transition rates, is essential for a comprehensive understanding of nuclear properties. However, computational limitations and conceptual difficulties often hinder the precise calculation of these observables. In this work, we extend machine learning methods for model-space extrapolations to electric quadrupole moments. We further present a new machine learning approach that leverages the correlations between energies, radii, and electromagnetic observables. By learning these correlations from no-core shell model calculations in accessible model spaces, this new model enables the prediction of electromagnetic observables in the full Hilbert space from predictions of full-space energies and radii, which can be obtained with established machine learning extrapolation tools. An essential property of our approach is the capability of uncertainty quantification, allowing for reliable predictions with combined statistical error estimates for many-body and interaction uncertainties. Being solely built upon the physical correlations of different observables, it can be generalized across different methods. We demonstrate the power of this new extrapolation scheme through a precision study of electric quadrupole moments across a wide range of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>p</a:mi></a:math>-shell nuclei.