Machine Learning and Coupled Cluster Theory Applied to Infinite Matter

\textit{An initio} many-body methods, such as coupled cluster theory, are able to make accurate predictions on systems, even if no experimental data for the system exists. This makes them an invaluable tool for studying exotic nuclei or systems, such as infinite matter, where experimental results are sparse. However, the performance and accuracy of a coupled cluster calculation suffer from truncations of the cluster operator and basis truncations, both of which are needed to reduce the scale of the problem such that it is computationally feasible. Additionally, when coupled cluster theory is applied to systems of infinite matter (the homogeneous electron gas and infinite nuclear matter), the number of particles in the system must also be truncated to a finite number, this introduces another source of error in the calculations. Finally, when modeling all nuclear systems, including infinite nuclear matter, the choice of nuclear interaction can greatly affect both the results and the computational run time. Simple nuclear interactions, such as the Minnesota potential, have comparatively small run times but lack the accuracy of computationally more complex interactions which are derived from effective field theory.The goal of this thesis is to improve the accuracy of coupled cluster calculations applied to two infinite matter systems: the homogeneous electron gas and two infinite nuclear matter system (pure neutron matter and symmetric nuclear matter). Coupled cluster calculations at the doubles and triples levels will be compared to determine if the increase in computational time is worth the increase in accuracy. Additionally, two different nuclear interactions will be tested on calculations of pure neutron matter: a toy model called the Minnesota potential, which is computationally simple, and a much more complex set of optimized interactions which are derived from effective field theory, which increase the accuracy but also the computational run time.Finally, the main part of this thesis is devoted to the development of a simple machine learning algorithm that can accurately extrapolate coupled cluster calculations of infinite systems separately to the complete basis limit and the thermodynamic limit. This algorithm, known as sequential regression extrapolation, combines a Bayesian machine learning algorithm with a unique way of formatting the training data to create a powerful and accurate extrapolate that can be trained on very little data, does not require hyperparameter tuning, and can automatically produce uncertainties on its predictions. With this method, we are able to accurately predict the coupled cluster correlation energies of infinite matter systems accurately in the complete basis and thermodynamic limits while savings months of computational time in the process.