https://doi.org/10.1140/epjd/s10053-024-00841-7
Regular Article - Cold Matter and Quantum Gases
Discovering hidden physical mechanisms in Bose–Einstein condensates via deep-learning
1
Department of Mathematics and Theories, Peng Cheng Laboratory, 518000, Shenzhen, People’s Republic of China
2
BIC-ESAT, ERE, and SKLTCS, College of Engineering, Peking University, 100871, Beijing, People’s Republic of China
3
National Center for Applied Mathematics Shenzhen (NCAMS), Southern University of Science and Technology, 518055, Shenzhen, People’s Republic of China
Received:
18
December
2023
Accepted:
3
April
2024
Published online:
3
September
2024
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 
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.
Xiao-Dong Bai, Hao Xu and Dongxiao Zhang have contributed equally to this paper.
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