Real-time and accurate dynamic wake information is essential for wind resource assessment and the optimization of wind farm operations. To further understand the wake characteristics of wind turbines, we propose a hierarchical learning approach integrated with a deep neural network-based prediction method. The integrated framework combines physical and mathematical models, enabling 3D spatiotemporal wind field predictions with minimal measured data requirements. Evaluation and validation results demonstrate that the proposed method achieves accurate ultra-short-term wake predictions across the entire domain with minimal prediction errors. Compared with conventional methods, the proposed hierarchical learning framework markedly lowers the training-data requirements of physics-informed neural networks for large-scale flow-field prediction while maintaining high accuracy. In addition, it demonstrates superior performance in both local and global wake forecasts, offering practical insights for efficient turbine operation and wake analysis.
Sun et al. (2026) studied this question.