Optimization of generator coordinate method with machine-learning algorithms for nuclear spectra and neutrinoless double-beta decay

X. Zhang, W. Lin, J. M. Yao, C. F. Jiao, A. M. Romero, T. R. Rodríguez, H. Hergert

Published 2022-11-05Version 1

The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. Recently, it has attracted increasing interest as it can be exploited to extend ab initio methods to the description of collective excitations of medium-mass and heavy deformed nuclei, as well as the nuclear matrix elements (NME) of candidates for neutrinoless double-beta (NLDBD) decay. 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. We aim to exploit machine learning (ML) algorithms to speed up GCM calculations and ultimately provide a more efficient description of nuclear energy spectra and other observables such as the NME of NLDBD decay without loss of accuracy. To speed up GCM calculations, we propose a subspace reduction algorithm that employs optimized 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, a polynomial regression algorithm is used to learn the norm and Hamiltonian kernels. The efficiency and accuracy of this algorithm are illustrated for 76Ge and 76Se by comparing results obtained using the ML models to direct GCM calculations. The results show that the performance of the GCM+OC/ENTROP+ML is more robust than that of the GCM+ML alone, and the former can reproduce the results of the original GCM calculation rather accurately with a significantly reduced computational cost.