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

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 multi-layer PINN learning method study data-driven rogue wave solutions defocusing Schr\"odinger (NLS) equation with time-dependent potential by considering several initial conditions such as wave, Jacobi elliptic cosine function, two-Gaussian or three-hyperbolic-secant periodic boundary conditions. Moreover, algorithm also parameter in NLS under sense solution. These results will useful further discuss a networks.