Machine learning the deuteron

J.W.T Keeble,A Rios

doi:10.1016/j.physletb.2020.135743

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.

Highlights

Machine learning (ML) techniques are ubiquitous within and outside the scientific domain
We explore the bias and variance of our minimal VANN model, the out-of-sample error, in two different ways
For the first time, that VANN techniques can be used successfully in solving bound-state nuclear physics problems

Summary

Introduction

Machine learning (ML) techniques are ubiquitous within and outside the scientific domain. A more recent development of ML techniques is their application to solve specific physics problems in the quantum domain [13, 14, 15]. More sophisticated techniques based on deep neural networks have been recently developed to tackle realistic quantum chemistry problems [20, 21, 22] In all these cases, the problem is set up as a variational one, and the solution is fully ab initio. The deuteron is a natural starting point to explore the feasibility of ab initio methods [25] While this is far from being a relevant many-body application, it allows for an exploratory analysis of the quality of ANN ansatze to the deuteron wavefunction

Methods

Results

Conclusions