Data-driven parameterization schemes have gained much attention in the field of atmospheric science nowadays. We design an ideal case using the Barotropic Vorticity Equation (BVE) model with periodic shear forcing and a deep learning (DL) model. The trained BVE model can greatly improve its initial forecast lead time with the data-driven parameterization scheme. However, the challenge is the significant amount of time required to employ the model, which is a hurdle for practical applications. Thus, this research aims at enhancing the model’s efficiency while minimizing any negative impact on its performance. Here we propose three methods, compressing the amount of model parameters (CNNhk), compressing the amount of training data (SGM), and combining both of them (CFS). Through these three methods and utilizing the solver-in-the-loop (SOL) method, we successfully reduce the model’s runtime while preserving its initial performance. By improving the effectiveness of our model, we believe it can contribute to the development of more efficient data-driven parameterization schemes and inspire further explorations.