Application of normalizing flows to nuclear many-body perturbation theory

TL;DR

This paper explores how normalizing flows, a machine learning technique, can improve Monte Carlo sampling in nuclear many-body perturbation theory, enabling more efficient calculations of complex integrals relevant to nuclear physics.

Contribution

It demonstrates the application of normalizing flows to nuclear many-body perturbation theory, facilitating efficient importance sampling and transferability across different physical conditions.

Findings

Normalizing flows effectively sample complex nuclear integrals.

Models can be transferred to related integrals with different conditions.

Enhanced efficiency in tabulating nuclear physics inputs for astrophysical simulations.

Abstract

Many-body perturbation theory provides a powerful framework to study the ground state and thermodynamic properties of nuclear matter as well as associated single-particle potentials and response functions within a systematic order-by-order expansion. However, computational challenges can emerge beyond the lowest orders of perturbation theory, especially when computing both single-particle potentials and response functions, which in general are complex-valued and require Cauchy principal value calculations of high-dimensional integrals. We demonstrate that normalizing flows are suitable for Monte Carlo importance sampling of both regular and irregular functions appearing in nuclear many-body calculations. Normalizing flows are a class of machine learning models that can be used to build and sample from complicated distributions through a bijective mapping from a simple base distribution. Furthermore, a well-trained model for a certain target integrand can be efficiently transferred to calculate related integrals with varying physical conditions. These features can enable more efficient tabulations of nuclear physics inputs to numerical simulations of supernovae and neutron star mergers across varying physical conditions and nuclear force models.