Machine learning the deuteron

TL;DR

This paper demonstrates that a simple neural network can accurately model the deuteron wavefunction and binding energy, showcasing the potential of machine learning for solving nuclear physics problems.

Contribution

It introduces a minimal neural network approach to solve the deuteron bound state problem, achieving high accuracy and benchmarking against exact solutions.

Findings

Neural network with 6 hidden nodes accurately models the deuteron ground state.

Binding energy within 0.1% of exact diagonalisation results.

Proof-of-principle for machine learning in nuclear many-body problems.

Abstract

We use machine learning techniques to solve the nuclear two-body bound state problem, the deuteron. We use a minimal one-layer, feed-forward neural network to represent the deuteron S- and D-state wavefunction in momentum space, and solve the problem variationally using ready-made machine learning tools. We benchmark our results with exact diagonalisation solutions. We find that a network with 6 hidden nodes (or 24 parameters) can provide a faithful representation of the ground state wavefunction, with a binding energy that is within 0.1% of exact results. This exploratory proof-of-principle simulation may provide insight for future potential solutions of the nuclear many-body problem using variational artificial neural network techniques.