Normalizing flows for microscopic calculations of the nuclear equation of state

The nuclear equation of state (EOS) at finite temperature is fundamental to describe the properties of medium-energy heavy-ion collisions as well as the hydrodynamic evolution of core-collapse supernovae and neutron star mergers. Microscopic calculations of the hot and dense matter equation of state using state-of-the-art nuclear two-body and three-body forces in many-body perturbation theory are numerically challenging due to the repeated evaluation of high-dimensional integrals across varying density, temperature, and composition. In this talk, we demonstrate that normalizing flows provide a suitable Monte Carlo integration framework for such microscopic EOS calculations. Normalizing flows are a class of machine learning models used to construct a complex distribution from a simple base distribution and thus can be used to generate highly expressive representations of the integrands that appear in high-order many-body perturbation theory calculations. Moreover, a normalizing flow model trained on one target integrand can be easily transferred as the density, temperature, or even nuclear potential is varied.