Sloppy nuclear energy density functionals: effective model reduction

TL;DR

This paper applies information geometry to analyze the sensitivity of nuclear energy density functionals, revealing their inherent sloppiness and demonstrating a systematic method to reduce model complexity by focusing on stiff parameter combinations.

Contribution

It introduces a geometric approach to identify and reduce sloppiness in nuclear density functionals, enabling the construction of simpler, more effective models.

Findings

Nuclear energy density functionals are characterized by exponential sensitivity ranges.

Most parameters are soft, influencing the model minimally.

Systematic reduction of parameters eliminates sloppiness, retaining only stiff combinations.

Abstract

Concepts from information geometry are used to analyse parameter sensitivity for a nuclear energy density functional, representative of a class of semi-empirical functionals that start from a microscopically motivated ansatz for the density dependence of the energy of a system of protons and neutrons. It is shown that such functionals are sloppy, characterized by an exponential range of sensitivity to parameter variations. Responsive to only a few stiff parameter combinations, they exhibit an exponential decrease of sensitivity to variations of the remaining soft parameters. By interpreting the space of model predictions as a manifold embedded in the data space, with the parameters of the functional as coordinates on the manifold, it is also shown that the exponential distribution of model manifold widths corresponds to the distribution of parameter sensitivity. Using the Manifold Boundary Approximation Method, we illustrate how to systematically construct effective nuclear density functionals of successively lower dimension in parameter space until sloppiness is eventually eliminated and the resulting functional contains only stiff combinations of parameters.