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The research of the derivative nonlinear Schrodinger equation (DNLS) hasattracted more and more extensive attention in theoretical analysis andphysical application. The improved physicsinformed neural network (IPINN)approach with neuron-wise locally adaptive activation function is presented toderive the data-driven localized wave solutions, which contain rationalsolution, soliton solution, rogue wave, periodic wave and rogue periodic wavefor the DNLS with initial and boundary conditions in complex space. Especially,the data-driven periodic wave and rogue periodic wave of the DNLS areinvestigated by employing the IPINN method for the first time. Furthermore, therelevant dynamical behaviors, error analysis and vivid plots have beenexhibited in detail. The numerical results indicate the IPINN method can wellsimulate the localized wave solutions of the DNLS under a small data set.

The data-driven localized wave solutions of the derivative nonlinear Schrodinger equation by using improved PINN approach