Calibration of energy density functionals with deformed nuclei

Abstract

Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single-or multireference level), the predictive power of the theory depends strongly on how the parameters of the energy functionals have been calibrated with experimental data. Expanded algorithms and computing power have enabled recent optimization protocols to include data in deformed nuclei in order to optimize the coupling constants of the energy functional. The primary motivation of this work is to test the robustness of such protocols with respect to some of the technical and numerical details of the underlying calculations, especially when the calibration explores a large parameter space. To this end, we quantify the effect of these uncertainties on both the optimization and statistical emulation of composite objective functions. We also emphasize that Bayesian calibration can provide better estimates of the theoretical errors used to define objective functions.

A comparison of Gaussian processes and neural networks for computer model emulation and calibration

“…The DFT predictions are valuable for comparing to observed measurements of these properties in order to predict the properties of unobserved nuclei of interest, such as the possible existence of stable super-heavy nuclei. The DFT approach considered for this paper is discussed in [26] and its references. It uses 12 inputs to predict the masses for spherical and deformed nuclei (labeled Spherical and Deformed, respectively) and a set of nuclei measured at Argonne National Laboratory (labeled Argonne), the radii (labeled Radii), fission isomer energies (labeled FI), and odd-even mass differences (labeled OESp and OESn, respectively) for nuclei with various numbers of protons and neutrons.…”

“…For the cosmology example, there are no observation data with which to perform calibration. The atomic nuclei data present a difficult sampling problem (discussed in [26]) that is beyond the scope of this paper.…”

A Fast and Calibrated Computer Model Emulator: An Empirical Bayes Approach

“…GP modeling and its variants have been prominently used in the context of computationally expensive theoretical mass models for either emulation or modeling of systematic discrepancies to produce precise and quantified predictions of nuclear observables [16,31,30,39].…”

Physically Interpretable Machine Learning for nuclear masses

“…Recent efforts have included the application of Gaussian processes and Bayesian methods to better quantify the uncertainties of model parameters, particularly those of microscopic nuclear models (see Ref. [29][30][31] and references therein). Figure 2 gives some insight into how we may proceed with regards to understanding both the quality of PIML extrapolations beyond available data, as well as how these predictions can assist in our understanding of total (statistical, systematic, and/or model) uncertainties of nuclear mass predictions.…”