Machine learning the deuteron

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.