{"title":"Discovering hidden physical mechanisms in Bose–Einstein condensates via deep-learning","authors":"Xiao-Dong Bai, Hao Xu, Dongxiao Zhang","doi":"10.1140/epjd/s10053-024-00841-7","DOIUrl":null,"url":null,"abstract":"<p>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 <span>\\(15\\%\\)</span> 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.</p>","PeriodicalId":789,"journal":{"name":"The European Physical Journal D","volume":"78 9","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal D","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjd/s10053-024-00841-7","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍:
The European Physical Journal D (EPJ D) presents new and original research results in:
Atomic Physics;
Molecular Physics and Chemical Physics;
Atomic and Molecular Collisions;
Clusters and Nanostructures;
Plasma Physics;
Laser Cooling and Quantum Gas;
Nonlinear Dynamics;
Optical Physics;
Quantum Optics and Quantum Information;
Ultraintense and Ultrashort Laser Fields.
The range of topics covered in these areas is extensive, from Molecular Interaction and Reactivity to Spectroscopy and Thermodynamics of Clusters, from Atomic Optics to Bose-Einstein Condensation to Femtochemistry.