Normalizing flows for Monte Carlo importance sampling and quantum many-body calculations

We demonstrate that normalizing flows, a class of machine learning models used to construct a complex distribution through a bijective mapping of a simple base distribution, are particularly well suited as a Monte Carlo integration framework for quantum many-body calculations. This is especially true for 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.