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Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning

arXiv 2012.09984 ↗First posted 18 Dec 2020nlin.PS cs.LG quant-phcited by 12

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Abstract (arXiv)

The physics-informed neural networks (PINNs) can be used to deep learn the nonlinear partial differential equations and other types of physical models. In this paper, we use the multi-layer PINN deep learning method to study the data-driven rogue wave solutions of the defocusing nonlinear Schr"odinger (NLS) equation with the time-dependent potential by considering several initial conditions such as the rogue wave, Jacobi elliptic cosine function, two-Gaussian function, or three-hyperbolic-secant function, and periodic boundary conditions. Moreover, the multi-layer PINN algorithm can also be used to learn the parameter in the defocusing NLS equation with the time-dependent potential under the sense of the rogue wave solution. These results will be useful to further discuss the rogue wave solutions of the defocusing NLS equation with a potential in the study of deep learning neural networks.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Dec 2020.

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Citing papers per year: 2021: 4; 2022: 3; 2023: 2; 2024: 3.

12 papers.

  1. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  2. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  3. 2022Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equationscited by 11
  4. 2021Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learningcited by 6
  5. 2021Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue wavescited by 4
  6. 2023Deep learning soliton dynamics and complex potentials recognition for 1D and 2D PT-symmetric saturable nonlinear Schr"odinger equationscited by 3
  7. 2022Data-driven modeling of Landau damping by physics-informed neural networkscited by 2
  8. 2021Data-driven discoveries of B"acklund transforms and soliton evolution equations via deep neural network learning schemescited by 1
  9. 2024Data assimilation and parameter identification for water waves using the nonlinear Schr"odinger equation and physics-informed neural networkscited by 1
  10. 2021Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitonscited by 0
  11. 2023Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zonescited by 0
  12. 2024Data-driven 2D stationary quantum droplets and wave propagations in the amended GP equation with two potentials via deep neural networks learningcited by 0