  We consider the exact rogue periodic wave (rogue wave on the periodic
background) and periodic wave solutions for the Chen-Lee-Liu equation via the
odd-th order Darboux transformation. Then, the multi-layer physics-informed
neural networks (PINNs) deep learning method is applied to research the
data-driven rogue periodic wave, breather wave, soliton wave and periodic wave
solutions of well-known Chen-Lee-Liu equation. Especially, the data-driven
rogue periodic wave is learned for the first time to solve the partial
differential equation. In addition, using image simulation, the relevant
dynamical behaviors and error analysis for there solutions are presented. The
numerical results indicate that the rogue periodic wave, breather wave, soliton
wave and periodic wave solutions for Chen-Lee-Liu equation can be generated
well by PINNs deep learning method.
