Smart cities rely on accurate predictive models to enhance sustainability, optimize resource utilization, and improve the overall quality of urban life. Forecasting key parameters such as air quality, water quality, and waste generation is crucial for efficient urban planning and environmental management. This study proposes a novel deep learning-based prediction model that integrates Capsule Networks and Gated Recurrent Units (GRUs) for multidimensional forecasting in smart cities. The architecture begins with a one-dimensional convolutional layer (Conv1D) to process raw input data, followed by a Capsule layer for efficient spatial feature extraction. These spatial features are subsequently fed into stacked GRU layers to model temporal dependencies and improve predictive accuracy. To further enhance the model’s performance, the Osprey Optimization Algorithm (OOA) is employed for hyperparameter tuning. The proposed hybrid model demonstrates superior forecasting capabilities when evaluated using standard metrics. It achieves a Mean Squared Error (MSE) of 43.8751, Root Mean Square Error (RMSE) of 4.4083, R² Score of 0.6845, and Mean Absolute Error (MAE) of 2.1619. These results highlight the effectiveness of combining Capsule Networks and GRUs, along with OOA optimization, for robust and accurate predictive modeling in smart city applications. This model serves as a scalable and efficient tool for urban administrators and policy-makers to enable data-driven decisions and proactive management of city resources.
P et al. (2026) studied this question.