论文标题
数据驱动的流氓波和参数发现在使用PINN深度学习的NLS方程中使用NLS方程
Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning
论文作者
论文摘要
物理知识的神经网络（PINN）可用于深入学习非线性偏微分方程和其他类型的物理模型。在本文中，我们使用多层PINN深度学习方法来研究通过考虑多种初始条件，例如Rogue Wave，Jacobi Elliptic eeltiptic cosine cosine函数，两高斯函数，两高西斯，两高西斯，或三高粘液式官能，并定期界限，通过考虑了几个初始条件，研究了数据驱动的无线性schrödinger（NLS）方程的流氓波解（NLS）方程。此外，在Rogue Wave解决方案的意义下，多层PINN算法还可以用来通过具有时间依赖性的NLS方程的参数来学习NLS方程的参数。这些结果将有助于进一步讨论散落的NLS方程的流氓波解决方案，并在深度学习神经网络的研究中具有潜力。
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.
