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

Xiao Liang, Sheng Liu, Yan Li, Yong-Sheng Zhang
(Submitted on 29 Dec 2017)

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.

https://arxiv.org/abs/1712.10093