A modeling method based on adaptive differential evolution-extreme learning machine (ADE-ELM) was proposed to solve the balance equations for turbo-shaft engine models. The model achieved high accuracy and real time properties. The extreme learning machine (ELM) was trained by the data got from the Newton-Raphson (N-R) iteration model. The inputs were the residuals of balance equations before iteration

and the outputs were the adjustments of guess values after iteration. The parameters of the ELM were optimized by adaptive differential evolution (ADE) algorithm to enhance the mapping accuracy of the guess values adjustments. The sigmoid type adaptive scaling factor was adopted by ADE algorithm to improve its optimization ability. Taking the N-R iteration model as a criterion

the simulation results of ADE-ELM model under different flying states show that

the maximum modeling error is about 1/3 that of the single iteration per time step

and the time consumption is about 1/3 that of the single iteration per time step. The modeling method is valid.