# Extrapolation of nuclear structure observables with artificial neural networks

## TL;DR

This paper introduces neural network-based extrapolation methods to accurately predict nuclear structure observables like energy and radius from finite model space calculations, improving stability and uncertainty estimation.

## Contribution

It presents a novel neural network approach for extrapolating nuclear observables, addressing multiple solutions and enhancing reliability over traditional methods.

## Key findings

- Neural networks can effectively extrapolate energies and radii to infinite model spaces.
- Preprocessing and correlation inclusion improve stability and consistency.
- Results agree with traditional infrared extrapolations for tested nuclei.

## Abstract

Calculations of nuclei are often carried out in finite model spaces. Thus, finite-size corrections enter, and it is necessary to extrapolate the computed observables to infinite model spaces. In this work, we employ extrapolation methods based on artificial neural networks for observables such as the ground-state energy and the point-proton radius. We extrapolate results from no-core shell model and coupled-cluster calculations to very large model spaces and estimate uncertainties. Training the network on different data typically yields extrapolation results that cluster around distinct values. We show that a preprocessing of input data, and the inclusion of correlations among the input data, reduces the problem of multiple solutions and yields more stable extrapolated results and consistent uncertainty estimates. We perform extrapolations for ground-state energies and radii in $^{4}$He, $^{6}$Li, and $^{16}$O, and compare the predictions from neural networks with results from infrared extrapolations.