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 the 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 an essentially negligible error given a computationally feasible number of training instances. First and second excited state energies can be predicted too, albeit with slightly lower accuracy and using more layers of hidden neurons. We also find that a three-layer neural network is remarkably resilient to Gaussian noise added to the training-set data (up to 10% noise level), suggesting that cold-atom quantum simulators could be used to train artificial neural networks.
Highlights
Machine learning techniques are at the heart of various technologies used in every day life, like e-mail spam filtering, voice recognition software, and web-text analysis tools
We evaluate the performance of the trained neural network in predicting the energy levels of a set of Np = 40000 speckle-field instances not included in the training set
The last aspect we investigate is the resilience of the neural network to the noise eventually present in the data representing the energy levels of the training set
Summary
Machine learning techniques are at the heart of various technologies used in every day life, like e-mail spam filtering, voice recognition software, and web-text analysis tools. Computational physicists and chemists have already demonstrated that supervised machine learning can be used, in particular, to determine the potential energy surfaces for molecular dynamics simulations of materials, of chemical compounds, and of biological systems[20,21,22,23,24,25,26] This allows one to avoid on-the-fly quantum mechanical electronic-structure computations, providing a dramatic speed-up that makes larger scale simulations of complex systems as, e.g., liquid and solid water, feasible[27]. These systems have emerged in recent years as an ideal platform to investigate quantum many-body phenomena[31,32] They allowed experimentalists to implement archetypal Hubbard-type models of condensed matter physics[33] and even the realization of www.nature.com/scientificreports/. The speckle-field correlations determine the transport properties and even the emergence of so-called effective mobility edge, i.e. energy thresholds where the localization length changes abruptly[52,53,54]
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