  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.
