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The physics-informed neural networks (PINNs) can be used to deep learn thenonlinear partial differential equations and other types of physical models. Inthis paper, we use the multi-layer PINN deep learning method to study thedata-driven rogue wave solutions of the defocusing nonlinear Schr\"odinger(NLS) equation with the time-dependent potential by considering several initialconditions such as the rogue wave, Jacobi elliptic cosine function,two-Gaussian function, or three-hyperbolic-secant function, and periodicboundary conditions. Moreover, the multi-layer PINN algorithm can also be usedto learn the parameter in the defocusing NLS equation with the time-dependentpotential under the sense of the rogue wave solution. These results will beuseful to further discuss the rogue wave solutions of the defocusing NLSequation with a potential in the study of deep learning neural networks.

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