Machine Learning for Correlations of Electromagnetic Properties in Ab Initio Calculations

TL;DR

Electromagnetic observables in ab initio nuclear structure are hindered by slow and oscillatory convergence in model spaces. The authors develop two ML extrapolation strategies: full-space prediction networks (FSPN) that learn convergence patterns from light systems to predict full-space quadrupole moments, and observable transcoder networks (OTN) that exploit correlations between energy, radius, and EM observables to map from ($E$, $R$) to the E2 moment, using FSPN outputs as inputs when needed. They quantify uncertainties with a BUQEYE-based framework combining many-body and chiral EFT uncertainties and demonstrate predictions for a range of p-shell nuclei, showing robust agreement within quantified uncertainties and potential for cross-method applicability to heavier nuclei. The work provides a unified, uncertainty-aware approach to predicting EM observables across ab initio methods and lays the groundwork for extending these techniques to additional observables and nuclear regimes.

Abstract

In ab initio nuclear structure theory, accurately predicting electromagnetic observables, such as moments and transition rates, is essential for a comprehensive understanding of nuclear properties. However, computational limitations and conceptual difficulties often hinder the precise calculation of these observables. In this work, we extend machine learning methods for model-space extrapolations to electric quadrupole moments. We further present a new machine learning approach that leverages the correlations between energies, radii, and electromagnetic observables. By learning these correlations from no-core shell model calculations in accessible model spaces, this new model enables the prediction of converged electromagnetic observables from predictions of converged energies and radii, which can be obtained with established machine learning extrapolation tools. An essential property of our approach is the capability for uncertainty quantification, allowing for reliable predictions with combined statistical error estimates for many-body and interaction uncertainties. Being solely built upon the physical correlations of different observables, it can be generalized across different ab initio methods. We demonstrate the power of this new extrapolation scheme through a precision study of electric quadrupole moments across a wide range of p-shell nuclei.

Figures (12)

• Figure 1: Example set of NCSM calculations for the E2 moment of $\isotope[2]{\mathrm{H}}$ for the EMN[500] interaction with converged value obtained at ${N_\mathrm{max}}\xspace=200$ used as FSPN training data. Inset: Loss on the training and validation data during the training of an FSPN averaged over 10 networks.
• Figure 2: Schematic topologies of an FSPN and an OTN. The numbers in the boxes indicate number and size of the hidden layers.
• Figure 3: Distributions of predictions of the ground-state E2 moment in $\isotope[6]{\mathrm{Li}}$ based on 1000 FSPNs evaluated with all possible samples at ${\curly{N}_\mathrm{max}}\xspace=12$ and a visualization of the statistical extraction of ensemble prediction and uncertainty.
• Figure 4: Input data and FSPN predictions from 1000 ANNs for the E2 momenta of the ground-states of $\isotope[6]{\mathrm{Li}}$, $\isotope[7]{\mathrm{Be}}$, and $\isotope[8]{\mathrm{B}}$ and the first $2^+$ excited state of $\isotope[12]{\mathrm{C}}$. The left hand panels show NCSM data for ${a_\mathrm{HO}}\xspace=1.2,1.3,1.4,1.5,1.6,1.7,$ and 1.8 (gray to red), while the right hand panels depict the predictions based this input data at different ${\curly{N}_\mathrm{max}}$.
• Figure 5: Correlations between the ground-state E2 moment and the ground-state energy (left) and the ground-state point-proton radius (right) in $\isotope[6]{\mathrm{Li}}$ and $\isotope[8]{\mathrm{B}}$ for EMN[500] from ${N_\mathrm{max}}\xspace=2$ (yellow) to ${N_\mathrm{max}}\xspace=12/10$ (black). The curves for each ${N_\mathrm{max}}$ are spanned by an ${a_\mathrm{HO}}$ range from 1.22.4. The red stars illustrate the FSPN predictions for the energies or radii, and the OTN predictions for the E2 moments, with their respective error bars.