Landslides are major geological hazards that pose serious threats to life and property, particularly in the high-mountain canyon regions of Sichuan, Yunnan, and southeastern Tibet. Displacement prediction plays a critical role in disaster prevention and mitigation. In recent years, machine learning methods based on InSAR data have achieved significant breakthroughs in landslide forecasting. However, models relying solely on a single data-driven approach may fail to fully capture the complex physical mechanisms of landslides, affecting both the reliability and interpretability of predictions. Therefore, developing effective landslide displacement prediction models is essential. The paper introduces a model designed to forecast the landslide displacement using Variational Mode Decomposition (VMD), Bayesian Optimization (BO), and Gated Recurrent Units (GRU). First, wavelet analysis is employed to identify the trend component in the landslide displacement data. Then, the total displacement is separated into its trend and periodic components through the application of the Variational Mode Decomposition (VMD) technique. A wide range of influencing factors is introduced, and Utilizing Grey Relational Analysis, we evaluate the interplay between contributing factors and all components of landslide displacement, both trend and periodic. Prediction models incorporate the trend and periodic terms, alongside the contributing factors, as input variables. The overall displacement is computed by summing the trend and periodic terms series using the Mianshawan landslide as a case study, experimental studies were conducted with landslide data from January 2019 to December 2022 with a Root Mean Squared Error (RMSE) of 0.402, Mean Absolute Error (MAE) of 0.187, Mean Absolute Percentage Error (MAPE) of 2.05%, and a coefficient of determination (R²) of 0.998. These findings indicate that, compared to traditional methods, our model delivers remarkable improvements in performance, offering higher prediction accuracy and greater reliability in the landslide forecasting task for the Mianshawan area.