Supervised machine learning of ultracold atoms with speckle disorder

TL;DR

This paper demonstrates that deep neural networks can accurately predict energy levels of ultracold atoms in speckle disorder, showing potential for efficient quantum system analysis.

Contribution

It introduces a supervised learning approach using neural networks to predict energy levels in disordered quantum systems, highlighting the importance of network architecture and training data.

Findings

Neural networks can predict ground state energies with high accuracy.

Prediction accuracy decreases slightly for excited states.

Network depth and training set size significantly affect performance.

Abstract

We analyze how accurately supervised machine learning techniques can predict the lowest energy levels of one-dimensional noninteracting ultracold atoms subject to the correlated disorder due to an optical speckle field. Deep neural networks with different numbers of hidden layers and neurons per layer are trained on large sets of instances of the speckle field, whose energy levels have been preventively determined via a high-order finite difference technique. The Fourier components of the speckle field are used as feature vector to represent the speckle-field instances. A comprehensive analysis of the details that determine the possible success of supervised machine learning tasks, namely the depth and the width of the neural network, the size of the training set, and the magnitude of the regularization parameter, is presented. It is found that ground state energies of previously unseen instances can be predicted with essentially arbitrary accuracy. First and second excited state energies can be predicted too, albeit with slightly lower accuracy and using more layers of hidden neurons.