Multi-scale wake modeling based on physics-informed neural networks and transfer learning

Wind turbine wakes exhibit highly nonlinear and multi-scale flow coupling, presenting formidable challenges for high-fidelity modeling. To address these limitations, this study proposes a multi-scale wind turbine wake prediction framework, termed TL_PINN, which integrates Physics-Informed Neural Network (PINN) with transfer learning. Firstly, a physics-informed multi-scale convolutional neural network is constructed to extract both local vortices and shear layers during wake evolution. Secondly, a power-law scaling operator is applied to adjust the network's loss function, mitigating gradient pathologies caused by disparities in loss term magnitudes during multi-scale PINN training, thereby enhancing the robustness of wake modeling. Furthermore, transfer learning strategies are introduced to facilitate collaborative modeling across heterogeneous wake data sources, reducing the model dependence on high-fidelity data and improving computational efficiency. Finally, the TL_PINN framework is validated in three scenarios—single turbine, turbine array, and utility-scale wind farm. The proposed model achieves coefficients of determination (R2) of ≥0.99, 0.97, and 0.98, and corresponding root mean square errors (RMSE) of 0.1090, 0.2095, and 0.2887, respectively, demonstrating high modeling accuracy and adaptability. By integrating multi-source data with physical priors, the proposed framework provides a scalable and extensible approach for wind farm layout optimization and wake control.