Stability of the manifold boundary approximation method for reductions of nuclear structure models

TL;DR

This paper investigates the stability of the manifold boundary approximation method (MBAM) in nuclear models, showing that key conclusions are stable under parameter variations and identifying a geometric criterion for parameter space separation.

Contribution

The study applies MBAM to nuclear energy density functional models, demonstrating stability of model reductions and linking geodesic termination to Fisher information metric properties.

Findings

MBAM conclusions are stable under parameter variation

Geodesic ends when Fisher information determinant vanishes

Parameter space splits into disconnected regions

Abstract

The framework of nuclear energy density functionals has been employed to describe nuclear structure phenomena for a wide range of nuclei. Recently, statistical properties of a given nuclear model, such as parameter confidence intervals and correlations, have received much attention, particularly when one tries to fit complex models. We apply information-theoretic methods to investigate stability of model reductions by the manifold boundary approximation method (MBAM). In an illustrative example of the density-dependent point-coupling model of the relativistic energy density functional, utilizing Monte Carlo simulations, it is found that main conclusions obtained from the MBAM procedure are stable under variation of the model parameters. Furthermore, we find that the end of the geodesic occurs when the determinant of the Fisher information metric vanishes, thus effectively separating the parameter space into two disconnected regions.