Deep learning: Extrapolation tool for ab initio nuclear theory

TL;DR

This paper introduces a neural network-based extrapolation method for ab initio nuclear physics calculations, improving the estimation of ground state energies and radii from finite basis space results with quantified uncertainties.

Contribution

It presents a novel ANN approach for extrapolating nuclear observables, providing a unified tool with uncertainty assessment for different quantities.

Findings

ANN accurately extrapolates $^6$Li ground state energy.

ANN provides reliable radius estimates with uncertainty quantification.

Comparison shows ANN outperforms traditional methods.

Abstract

Ab initio approaches in nuclear theory, such as the no-core shell model (NCSM), have been developed for approximately solving finite nuclei with realistic strong interactions. The NCSM and other approaches require an extrapolation of the results obtained in a finite basis space to the infinite basis space limit and assessment of the uncertainty of those extrapolations. Each observable requires a separate extrapolation and most observables have no proven extrapolation method. We propose a feed-forward artificial neural network (ANN) method as an extrapolation tool to obtain the ground state energy and the ground state point-proton root-mean-square (rms) radius along with their extrapolation uncertainties. The designed ANNs are sufficient to produce results for these two very different observables in $^6$Li from the ab initio NCSM results in small basis spaces that satisfy the following theoretical physics condition: independence of basis space parameters in the limit of extremely large matrices. Comparisons of the ANN results with other extrapolation methods are also provided.