Machine Learning in the Problem of Extrapolating Variational Calculations in Nuclear Physics

Abstract

A modified machine learning method is proposed, utilizing an ensemble of artificial neural networks for the extrapolation of energies obtained in variational calculations, specifically in the no-core shell model (NCSM), to the case of the infinite basis. A new neural network topology is employed, and criteria for selecting both the data used for training and the trained neural networks for statistical analysis of the results are formulated. The approach is tested by extrapolating the deutron ground state energy in calculations with the Nijmegen II \(NN\) interaction and provides statistically significant results. This technique is applied to obtain extrapolated ground state energies of \({}^{6}\)Li and \({}^{6}\)He nuclei based on the NCSM calculations with Daejeon16 \(NN\) interaction.