Machine learning flow-based models for nuclear many-body calculations with quantified uncertainties

Many-body perturbation theory (MBPT) enables the order-by-order calculation of nuclear properties, including the equation of state, single-particle potential, and response functions. Nuclear potentials derived from chiral effective field theory enable uncertainty quantification, however, to date a comprehensive inclusion of all sources of error remains a work in progress. In addition, the full propagation of uncertainties from EFT requires more efficient algorithms for computing high-dimensional integrals that enter in MBPT. All of this requires large amounts of computational resources, especially for the problem of fitting LECs and analyzing uncertainties in EFT, as well as repeatedly calculating high-dimensional integrals for the tabulation of the nuclear matter equation of state. In this talk, I will demonstrate the power of flow-based machine learning models that can build distributions that capture the properties of a given set of samples, and efficiently draw samples from complicated distributions. These models will be applied to Monte Carlo importance sampling and the generation of nuclear potentials.