Discovering hidden physical mechanisms in Bose–Einstein condensates via deep-learning

Discovering hidden physical mechanisms of a system, such as underlying partial differential equations (PDEs), is an intriguing subject that has not yet been fully explored. In particular, how to go beyond the traditional method to obtain the PDEs of complex systems is currently under active debate. In this work, we propose a deep-learning approach to discover the underlying Gross-Pitaevskii equations (GPEs) of one-dimensional Bose–Einstein condensates (BECs). The results show that such method is markedly superior to the traditional method due to advantages of the deep neural network. The former possesses the ability to obtain a parsimonious model with high accuracy and insensitivity to data noise, and can successfully discover the underlying GPEs that BECs should obey directly from the data even in the absence of a knowledge structure. More importantly, we find that such method is able to work well even for data with \(15\%\) noise. Although the cases studied are proof-of-concept, the method provides a promising technique for unveiling hidden novel physical mechanisms in quantum systems from observations.