The properties of the auroral electrojets are studied by modeling the relationships between the solar-wind parameters and the AU and AL indices with a trained echo state network (ESN), a kind of recurrent neural network. To identify the properties of auroral electrojets, we obtain various synthetic AU and AL data by using various artificial inputs with the trained ESN. The synthetic data show that the AU and AL indices are significantly affected by the solar-wind speed in addition to B_z of the interplanetary magnetic field (IMF). A contributions from IMF B_y is are also suggested. In addition, the synthetic data indicate nonlinear effects from the solar-wind density, which is strong when the solar-wind speed is high and when IMF B_z is near zero.