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Extrapolation to infinite model space of no-core shell model calculations using machine learning

Aleksandr Mazur, Roman Sharypov, Andrey Shirokov

TL;DR

The paper addresses extrapolating No-Core Shell Model results to infinite model space for light nuclei. It proposes an ensemble of fully connected neural networks that take model-space parameters $N_{ m max}$ and $\hbar\Omega$ as inputs to predict energies and rms radii, with uncertainty quantified via the ensemble. Applied to light nuclei with the Daejeon16 interaction, the method yields ground-state energies within a few hundred keV of experiment and convergent radii for bound states, while radii for unbound states do not stabilize. This approach offers a principled, uncertainty-aware pathway to extend ab initio predictions and can be adapted to additional observables, potentially enabling broader predictive reach.

Abstract

An ensemble of neural networks is employed to extrapolate no-core shell model (NCSM) results to infinite model space for light nuclei. We present a review of our neural network extrapolations of the NCSM results obtained with the Daejeon16 NN interaction in different model spaces and with different values of the NCSM basis parameter $\hbarΩ$ for energies of nuclear states and root-mean-square (rms) radii of proton, neutron and matter distributions in light nuclei. The method yields convergent predictions with quantifiable uncertainties. Ground-state energies for $^{6}$Li, $^{6}$He, and the unbound $^{6}$Be, as well as the excited $(3^{+},0)$ and $(0^{+},1)$ states of $^{6}$Li, are obtained within a few hundred keV of experiment. The extrapolated radii of bound states converge well. In contrast, radii of unbound states in $^{6}$Be and $^{6}$Li do not stabilize.

Extrapolation to infinite model space of no-core shell model calculations using machine learning

TL;DR

The paper addresses extrapolating No-Core Shell Model results to infinite model space for light nuclei. It proposes an ensemble of fully connected neural networks that take model-space parameters and as inputs to predict energies and rms radii, with uncertainty quantified via the ensemble. Applied to light nuclei with the Daejeon16 interaction, the method yields ground-state energies within a few hundred keV of experiment and convergent radii for bound states, while radii for unbound states do not stabilize. This approach offers a principled, uncertainty-aware pathway to extend ab initio predictions and can be adapted to additional observables, potentially enabling broader predictive reach.

Abstract

An ensemble of neural networks is employed to extrapolate no-core shell model (NCSM) results to infinite model space for light nuclei. We present a review of our neural network extrapolations of the NCSM results obtained with the Daejeon16 NN interaction in different model spaces and with different values of the NCSM basis parameter for energies of nuclear states and root-mean-square (rms) radii of proton, neutron and matter distributions in light nuclei. The method yields convergent predictions with quantifiable uncertainties. Ground-state energies for Li, He, and the unbound Be, as well as the excited and states of Li, are obtained within a few hundred keV of experiment. The extrapolated radii of bound states converge well. In contrast, radii of unbound states in Be and Li do not stabilize.

Paper Structure

This paper contains 4 sections, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Results
  4. Discussion

Figures (3)

  • Figure 1: Convergence of the extrapolated ground-state energy (left) and rms radii (right) of $^{6}$Li. Symbols are explained in the legend.
  • Figure 2: Convergence of the extrapolated energies (top) and rms radii (bottom) for the ground states $^{6}$He (left) and $^{6}$Be (right) nuclei.
  • Figure 3: Convergence of the extrapolated energies (top) and rms radii (bottom) for the excited states of $^{6}$Li($3^{+},0$) (left), $^{6}$Li($0^{+},1$) (right).