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

arXiv: https://arxiv.org/abs/2012.09984 · HTML: https://mlsanity.com/paper/2012.09984/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2020.

## Built on by (most cited first, 12 of 12)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations](https://mlsanity.com/paper/2206.09299/) (2022)
- [Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning](https://mlsanity.com/paper/2101.04371/) (2021)
- [Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue waves](https://mlsanity.com/paper/2104.14809/) (2021)
- [Deep learning soliton dynamics and complex potentials recognition for 1D and 2D PT-symmetric saturable nonlinear Schr"odinger equations](https://mlsanity.com/paper/2310.02276/) (2023)
- [Data-driven modeling of Landau damping by physics-informed neural networks](https://mlsanity.com/paper/2211.01021/) (2022)
- [Data-driven discoveries of B"acklund transforms and soliton evolution equations via deep neural network learning schemes](https://mlsanity.com/paper/2111.09489/) (2021)
- [Data assimilation and parameter identification for water waves using the nonlinear Schr"odinger equation and physics-informed neural networks](https://mlsanity.com/paper/2401.03708/) (2024)
- [Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons](https://mlsanity.com/paper/2112.14040/) (2021)
- [Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones](https://mlsanity.com/paper/2309.17240/) (2023)
- [Data-driven 2D stationary quantum droplets and wave propagations in the amended GP equation with two potentials via deep neural networks learning](https://mlsanity.com/paper/2409.02339/) (2024)

## 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.