Bayesian model mixing with multi-reference energy density functional

Abstract

Reliably predicting nuclear properties across the entire chart of isotopes is important for applications ranging from nuclear astrophysics to superheavy science to nuclear technology. To this day, however, all the theoretical models that can scale at the level of the chart of isotopes remain semi phenomenological. Because they are fitted locally, their predictive power can vary significantly; different versions of the same theory provide different predictions. Bayesian model mixing takes advantage of such imperfect models to build a local mixture of a set of models to make improved predictions. Earlier attempts to use Bayesian model mixing for mass table calculations relied on models treated at single-reference energy density functional level, which fail to capture some of the correlations caused by configuration mixing or the restoration of broken symmetries. In this study we have applied Bayesian model mixing techniques within a multi-reference energy density functional (MR-EDF) framework. We considered predictions of two-particle separation energies from particle number projection or angular momentum projection with four different energy density functionals - a total of eight different MR-EDF models. We used a hierarchical Bayesian stacking framework with a Dirichlet prior distribution over weights together with an inverse log-ratio transform to enable positive correlations between different models. We found that Bayesian model mixing provide significantly improved predictions over results from single MR-EDF calculations.

References in corpus (28)

• The impact of individual nuclear properties on $r$-process nucleosynthesis
• Nuclear energy density optimization: Large deformations
• Bayesian model averaging: A systematic review and conceptual classification
• Machine Learning in Nuclear Physics
• Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects
• Global study of quadrupole correlation effects
• Neutron drip line in the Ca region from Bayesian model averaging
• Predictions of nuclear $\beta$-decay half-lives with machine learning and their impacts on $r$ process
• Nuclear charge radii: Density functional theory meets Bayesian neural networks
• Bayesian Evaluation of Incomplete Fission Yields
• Nuclear mass predictions with machine learning reaching the accuracy required by $r$-process studies
• Quantified limits of the nuclear landscape
• Get on the BAND Wagon: A Bayesian Framework for Quantifying Model Uncertainties in Nuclear Dynamics
• Refining mass formulas for astrophysical applications: a Bayesian neural network approach
• Novel Bayesian neural network based approach for nuclear charge radii
• Nuclear masses learned from a probabilistic neural network
• Physically Interpretable Machine Learning for nuclear masses
• Validating neural-network refinements of nuclear mass models
• Horizons: Nuclear Astrophysics in the 2020s and Beyond
• Error Analysis in Nuclear Density Functional Theory
• Propagation of Statistical Uncertainties of Skyrme Mass Models to Simulations of $r$-Process Nucleosynthesis
• Nuclear mass predictions using machine learning models
• Axially-deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (IV) hfbtho (v4.0): A new version of the program
• Detailed illustration of accuracy of presently used nuclear-mass models
• Correlation energies by the generator coordinate method: computational aspects for quadrupolar deformations
• Bayesian model averaging for nuclear symmetry energy from effective proton-neutron chemical potential difference of neutron-rich nuclei
• Controlling extrapolations of nuclear properties with feature selection
• Interpolating between small- and large-$g$ expansions using Bayesian Model Mixing