  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.
