  The research of the derivative nonlinear Schrodinger equation (DNLS) has
attracted more and more extensive attention in theoretical analysis and
physical application. The improved physicsinformed neural network (IPINN)
approach with neuron-wise locally adaptive activation function is presented to
derive the data-driven localized wave solutions, which contain rational
solution, soliton solution, rogue wave, periodic wave and rogue periodic wave
for the DNLS with initial and boundary conditions in complex space. Especially,
the data-driven periodic wave and rogue periodic wave of the DNLS are
investigated by employing the IPINN method for the first time. Furthermore, the
relevant dynamical behaviors, error analysis and vivid plots have been
exhibited in detail. The numerical results indicate the IPINN method can well
simulate the localized wave solutions of the DNLS under a small data set.
