Optimization of generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double-beta decay: ridge regression for nuclei with axial deformation

TL;DR

This paper introduces a machine learning-based subspace reduction technique for the generator coordinate method in nuclear physics, significantly improving computational efficiency while maintaining accuracy in modeling nuclear spectra and neutrinoless double-beta decay.

Contribution

It proposes a novel ML-assisted subspace reduction algorithm using ridge regression to efficiently approximate GCM calculations for deformed nuclei.

Findings

Accurately reproduces low-energy spectra of 76Ge and 76Se.

Calculates $0 uetaeta$ decay NME with high precision.

Reduces computational cost of GCM significantly.

Abstract

The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. In this work, we propose a subspace-reduction algorithm that employs optimal statistical ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra and the NME of ground state to ground state $0\nu\beta\beta$ decay based on the orthogonality condition (OC) and the energy-transition-orthogonality procedure (ENTROP), respectively. For simplicity, the polynomial ridge regression (RR) algorithm is used to learn the norm and Hamiltonian kernels of axially deformed configurations. The efficiency and accuracy of this algorithm are illustrated for 76Ge and 76Se by comparing results obtained using the optimal RR models to direct GCM calculations. The low-lying energy spectra of $^{76}$Ge and $^{76}$Se, as well as the $0\nu\beta\beta$-decay NME between their ground states, are computed. The results show that the performance of the GCM+OC/ENTROP+RR is more robust than that of the GCM+RR alone, and the former can reproduce the results of the original GCM calculation accurately with a significantly reduced computational cost.