This thesis contains two topics related to strongly interacting neutron matter. The first considers the effective mass, described in Landau Fermi liquid theory, which aims to capture many-body physics in terms of a single parameter. Monte Carlo algorithms were used to determine energies for finite particle simulations. Studying the deviations from the thermodynamic limit for the non-interacting gas allows for claims about the macroscopic scale. Following this systematic investigation, the density dependence was determined to be less than one for the considered densities. The second topic focuses on machine learning algorithms which have proliferated into many fields, with an emerging popularity in nuclear physics. These algorithms work by learning patterns found in datasets to develop their predictive power. After identifying and resolving issues introduced by a small dataset, they were used to extrapolate finite calculations to zero effective-range in the thermodynamic limit, which best approximates neutron matter.