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Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning
Physics Letters A ( IF 2.6 ) Pub Date : 2021-05-06 , DOI: 10.1016/j.physleta.2021.127408
Li Wang , Zhenya Yan

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 Schrödinger (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.



中文翻译:

使用PINN深度学习的散焦非线性Schrödinger方程中具有数据驱动的无赖波和参数发现

物理信息神经网络(PINN)可用于深度学习非线性偏微分方程和其他类型的物理模型。本文采用多层PINN深度学习方法,通过考虑流氓波,雅可比等几个初始条件,研究具有时变势的离焦非线性Schrödinger(NLS)方程的数据驱动流浪解椭圆余弦函数,二高斯函数或三双曲正割函数以及周期边界条件。此外,在流浪波解的意义下,多层PINN算法还可以用于学习散焦NLS方程中具有时变电位的参数。

更新日期:2021-05-12
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