Coupled-Cluster Calculations of Infinite Nuclear Matter in the Complete Basis Limit Using Bayesian Machine Learning

TL;DR

This paper introduces a Bayesian machine learning method, the SRE algorithm, to accurately predict coupled-cluster energies of infinite nuclear matter, significantly reducing computational time while maintaining high accuracy.

Contribution

The study presents a novel Gaussian process-based extrapolation technique that predicts nuclear matter energies from smaller basis set data, enabling faster calculations.

Findings

Achieved average error of 0.0083 MeV/N in neutron matter energies

Reduced computational time by over 80% for neutron matter calculations

Predicted symmetry energy with an average error of 0.031 MeV/A

Abstract

Infinite nuclear matter provides valuable insights into the behavior of nuclear systems and aids our understanding of atomic nuclei and large-scale stellar objects such as neutron stars. However, partly due to the large basis needed to converge the system's binding energy, size-extensive methods such as coupled-cluster theory struggle with long computational run times, even using the nation's largest high-performance computing facilities. This research introduces a novel approach to the problem. We propose using a machine learning method to predict the coupled-cluster energies of infinite matter systems in the complete basis limit, leveraging only data collected using smaller basis sets. This method promises to deliver high-accuracy results with significantly reduced run times. The sequential regression extrapolation (SRE) algorithm, based on Gaussian processes, was created to perform these extrapolations. By combining Bayesian machine learning with a unique method of formatting the training data, we can create a powerful extrapolator that can make accurate predictions given very little data. The SRE algorithm successfully predicted the CCD(T) energies for pure neutron matter across six densities near nuclear saturation density, with an average error of 0.0083 MeV/N. The algorithm achieved an average error of 0.038 MeV/A for symmetric nuclear matter. These predictions were made with a time savings of 83.8 node hours for pure neutron matter and 284 node hours for symmetric nuclear matter. Additionally, the symmetry energy at these six densities was predicted with an average error of 0.031 MeV/A and a total time savings of 368 node hours compared to the traditional converged coupled-cluster calculations performed without the SRE algorithm.