Generation of Bose-Einstein Condensates' Ground State Through Machine Learning

TL;DR

This paper demonstrates that deep convolutional neural networks can efficiently simulate and predict the ground states and eigen-energies of Bose-Einstein condensates, outperforming traditional methods in speed while maintaining high accuracy.

Contribution

The study introduces a neural network approach to simulate BEC ground states, achieving faster predictions with high precision, a novel application in quantum many-body physics.

Findings

Neural networks predict BEC ground states faster than imaginary time evolution.

Predicted states have a mean-square-error between 10^{-5} and 10^{-4}.

Eigen-energies are accurately predicted by the neural network.

Abstract

We show that both single-component and two-component Bose-Einstein condensates' (BECs) ground states can be simulated by deep convolutional neural networks of the same structure. We trained the neural network via inputting the coupling strength in the dimensionless Gross-Pitaevskii equation (GPE) and outputting the ground state wave-function. After training, the neural network generates ground states faster than the method of imaginary time evolution, while the relative mean-square-error between predicted states and original states is in the magnitude between $10^{-5}$ and $10^{-4}$. We compared the eigen-energies based on predicted states and original states, it is shown that the neural network can predict eigen-energies in high precisions. Therefore, the BEC ground states, which are continuous wave-functions, can be represented by deep convolution neural networks.