The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition(POD)and discrete empirical interpolation method(DEIM).Instead of using the classical DEIM to directly approximate the nonlinear term of a system,our approach extracts the main part of the nonlinear term with a linear approximation before approximating the residual with the DEIM.We construct the linear term by Taylor series expansion and dynamic mode decomposition(DMD),respectively,so as to obtain a more accurate reconstruction of the nonlinear term.In addition,a novel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid of error data.The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy.Finally,numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.