Optimization of the Normalizing Flow Machine Learning Method for Microscopic Calculations of the Nuclear Equation of State*

Analyzing neutron stars, neutron star mergers, and core-collapse supernovae using a microscopic description of the nuclear equation of state offers many advantages over the dominant mean-field theory models, such as maintained connections to fundamental nuclear many-body forces, improved descriptions of thermodynamic quantities, and the ability to better track systematic uncertainty. However, introducing the higher-order, many-body corrections needed for such a microscopic description requires the evaluation of complicated, multi-dimensional integrals. We employ neural networks to learn and compute these integrals, using normalizing flows alongside Monte Carlo importance sampling. Using this framework, we investigate the effects of different pseudo-random number generators versus low discrepancy sequences and loss functions in the convergence of the normalizing flow model. Quasi-Monte Carlo (QMC) sampling methods studied include those based on the Halton sequence, the Korobov set, Lattice points, and the Sobol sequence. Models were compared directly against one another throughout training and evaluation for a variety of importance samplings methods and loss function implementations. We identify the optimal choices for the sampling methods and loss functions in evaluating perturbation theory contributions to the hot and dense matter equation of state.