Taming nucleon density distributions with deep neural network method

TL;DR

This paper demonstrates that deep neural networks can accurately predict nucleon density distributions across the nuclear chart using limited training data, showing robustness across different models and revealing a key transition in distribution types during training.

Contribution

The study introduces a neural network approach to model nucleon densities, achieving high accuracy with minimal training data and showing weak dependence on the underlying theoretical model.

Findings

Training with about 10% of nuclei yields 2% relative error across the chart.

Training with around 200 proton/neutron densities results in 5% error.

Identification of a transition point from Fermi-like to realistic Skyrme distributions during training.

Abstract

We investigate the density distributions of finite nuclei employing a well-designed deep neural network method. We calculate the target nucleon density distributions with Skyrme density functional theories, which are used to train the networks. We find that the training with only about $10\%$ nuclei ($300-400$) is sufficient to describe the nucleon density distributions of all the nuclear chart within 2\% relative error. The relative error comes to 5\% when about 200 proton(neutron) density distributions are used for training. We obtained very similar results for different Skyrme density functional theories. Therefore the ability to train networks is weakly dependent on the theoretical model. Moreover, in the process of machine learning, there is a turning point showing the transition from the Fermi-like distribution to the realistic Skyrme distribution, which provides significant properties of convergence process.