  Normalizing flows are a class of machine learning models used to construct a
complex distribution through a bijective mapping of a simple base distribution.
We demonstrate that normalizing flows are particularly well suited as a Monte
Carlo integration framework for quantum many-body calculations that require the
repeated evaluation of high-dimensional integrals across smoothly varying
integrands and integration regions. As an example, we consider the
finite-temperature nuclear equation of state. An important advantage of
normalizing flows is the ability to build highly expressive models of the
target integrand, which we demonstrate enables precise evaluations of the
nuclear free energy and its derivatives. Furthermore, we show that a
normalizing flow model trained on one target integrand can be used to
efficiently calculate related integrals when the temperature, density, or
nuclear force is varied. This work will support future efforts to build
microscopic equations of state for numerical simulations of supernovae and
neutron star mergers that employ state-of-the-art nuclear forces and many-body
methods.
