Search for rogue waves in Bose-Einstein condensates via a theory-guided neural network

Xiao-Dong Bai and Dongxiao Zhang
Phys. Rev. E 106, 025305 – Published 5 August 2022

Abstract

An important and incompletely answered question is whether machine learning methods can be used to discover the excitation of rogue waves (RWs) in nonlinear systems, especially their dynamic properties and phase transitions. In this work, a theory-guided neural network (TgNN) is constructed to explore the RWs of one-dimensional Bose-Einstein condensates. We find that such method is superior to the ordinary deep neural network due to theory guidance of underlying problems. The former can directly give any excited location, timing, and structure of RWs using only a small amount of dynamic evolution data as the training data, without the tedious step-by-step iterative calculation process. In addition, based on the TgNN approach, a phase transition boundary is also discovered, which clearly distinguishes the first-order RW phase from the non-RW phase. The results not only greatly reduce computational time for exploring RWs, but also provide a promising technique for discovering phase transitions in parameterized nonlinear systems.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 14 February 2022
  • Accepted 25 July 2022

DOI:https://doi.org/10.1103/PhysRevE.106.025305

©2022 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

Xiao-Dong Bai1 and Dongxiao Zhang2,*

  • 1Department of Mathematics and Theories, Peng Cheng Laboratory, Shenzhen 518055, Guangdong, People's Republic of China
  • 2National Center for Applied Mathematics Shenzhen (NCAMS), Southern University of Science and Technology, Shenzhen 518055, Guangdong, People's Republic of China

  • *zhangdx@sustech.edu.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 106, Iss. 2 — August 2022

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×