Using Bayesian Machine Learning to Extend the Range of Ab Initio Many-Body Calculations of Infinite Matter Systems

Many-body perturbation theory and coupled cluster theory provide many-body perspectives for studying infinite matter systems (homogeneous electron gas and infinite nuclear matter). However, these calculations can suffer from long computational times due to the complexity of the many-body problem, thus hindering large-scale studies. This work presents several novel algorithms based on Bayesian machine learning, which can drastically decrease the computational time needed to perform these calculations by making accurate predictions of the correlation energies of the system. This work includes predicting the converged (with respect to basis size) correlation energy of an infinite matter system using only calculation at small basis sizes and predicting the correlation energies at all densities in a relevant range using only a few fully converged data points in the region. The accuracy of the predictions and the time saved over performing traditional calculations will be presented as a motivation for using these novel Bayesian algorithms.