SummaryStochastic ground motion models can facilitate a versatile description of earthquake acceleration time‐histories by modulating a white‐noise sequence through functions that address spectral and temporal properties of the excitation. This is established by relating the parameters of these functions to earthquake and site characteristics through appropriate predictive relationships. This study focuses on the selection of these predictive relationships to establish direct compatibility to the mean predictions of ground motion prediction equations (GMPEs). A record‐based ground motion model is selected as a stochastic ground motion model, and its match to both elastic and inelastic GMPEs is examined. The novel contribution of the present work is that it develops a computationally efficient approach for providing ground motions that can match any chosen GMPE for any desired set of seismicity characteristics or structural periods. Foundation of the methodology is the development of a metamodel to approximate the median predictions of the ground motion model. This is established by selecting a wide range for the parameters of the model, generating ground motions for each of them, and then calculating the median (over different white‐noise sequences) spectral acceleration for different structural periods. Based on this database, a Kriging metamodel is developed to provide an efficient approximation of the predictions of the ground motion model. This metamodel is subsequently used to efficiently select the predictive relationships that optimize the match to the chosen GMPE. The numerical accuracy of the metamodel predictions is also explicitly incorporated in this optimization. Copyright © 2015 John Wiley & Sons, Ltd.