The dual-motor drive system is a highly coupled, nonlinear, and time-varying system. During practical operation, the parameters of servo motors may drift under varying working conditions, making it difficult for mechanism-based mathematical models to accurately capture the system′s dynamic characteristics and thereby affecting the synchronization control performance.To address these issues, this paper proposes a data-driven modeling approach based on a gated recurrent unit (GRU) optimized by an improved Bayesian optimization algorithm (BO-AdaMG-SGRU). In addition, a dual-motor synchronous control strategy is developed, in which the optimization objective is solved using the rime ice optimization (RIME) algorithm.Based on the multi-input multi-output (MIMO) framework of GRU, a unified data-driven model for the dual-motor system is established, effectively capturing the coupling dynamics between the two motors and improving prediction accuracy and generalization capability. To mitigate the sensitivity of GRU to hyperparameters, an improved Bayesian optimization algorithm combined with the AdaMG optimizer is employed to perform global hyperparameter tuning, thereby overcoming the limitations of manual parameter adjustment and obtaining a robust high-precision prediction model through offline training.In terms of control strategy, an objective function incorporating both synchronization error and tracking error is designed. The RIME algorithm, featuring enhanced global search capability, is applied to optimize the objective function, reducing the risk of convergence to local optima and improving synchronization control accuracy.Simulation and experimental results demonstrate that, compared with the cross-coupled sliding mode control method, the proposed approach reduces torque synchronization error by approximately 52% and torque tracking error by about 45%. These results validate the effectiveness and engineering applicability of the proposed dual-motor model predictive synchronous control strategy in improving control accuracy and operational stability.