HFBTHO-AD: Differentiation of a nuclear energy density functional code

TL;DR

This paper introduces the use of automatic differentiation with Tapenade to compute derivatives of the HFBTHO nuclear structure code, enabling more efficient parameter optimization and uncertainty quantification.

Contribution

It demonstrates the application of AD to a complex nuclear physics code, comparing its derivatives with finite-difference methods and analyzing performance improvements.

Findings

AD provides accurate derivatives compared to finite differences.

Automatic differentiation improves efficiency in parameter sensitivity analysis.

The approach facilitates derivative-based optimization in nuclear modeling.

Abstract

The HFBTHO code implements a nuclear energy density functional solver to model the structure of atomic nuclei. HFBTHO has previously been used to calibrate energy functionals and perform sensitivity analysis by using derivative-free methods. To enable derivative-based optimization and uncertainty quantification approaches, we must compute the derivatives of HFBTHO outputs with respect to the parameters of the energy functional, which are a subset of all input parameters of the code. We use the algorithmic/automatic differentiation (AD) tool Tapenade to differentiate HFBTHO. We compare the derivatives obtained using AD against finite-difference approximation and examine the performance of the derivative computation.