  The solving of the derivative nonlinear Schrodinger equation (DNLS) has
attracted considerable attention in theoretical analysis and physical
applications. Based on the physics-informed neural network (PINN) which has
been put forward to uncover dynamical behaviors of nonlinear partial different
equation from spatiotemporal data directly, an improved PINN method with
neuron-wise locally adaptive activation function is presented to derive
localized wave solutions of the DNLS in complex space. In order to compare the
performance of above two methods, we reveal the dynamical behaviors and error
analysis for localized wave solutions which include one-rational soliton
solution, genuine rational soliton solutions and rogue wave solution of the
DNLS by employing two methods, also exhibit vivid diagrams and detailed
analysis. The numerical results demonstrate the improved method has faster
convergence and better simulation effect. On the bases of the improved method,
the effects for different numbers of initial points sampled, residual
collocation points sampled, network layers, neurons per hidden layer on the
second order genuine rational soliton solution dynamics of the DNLS are
considered, and the relevant analysis when the locally adaptive activation
function chooses different initial values of scalable parameters are also
exhibited in the simulation of the two-order rogue wave solution.
