Normalizing flows for microscopic many-body calculations: an application to the nuclear equation of state

TL;DR

This paper introduces the use of normalizing flows as an efficient Monte Carlo integration tool for quantum many-body calculations, specifically applied to the nuclear equation of state at finite temperature, enabling precise and adaptable evaluations.

Contribution

It demonstrates the suitability of normalizing flows for high-dimensional integrals in nuclear physics and shows their ability to adapt to parameter changes with a single trained model.

Findings

Normalizing flows enable precise evaluation of nuclear free energy.

A trained flow model can efficiently adapt to different temperatures and densities.

The approach supports future microscopic nuclear equation of state calculations.

Abstract

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.