Physics-informed 3D wind field reconstruction in the urban canopy from LiDAR observations

The spatial sparsity and blind zones of current wind LiDAR measurements limit the safe operation of unmanned aerial vehicles in the urban areas. To address this challenge, we propose a novel Physics-Informed Neural Network (PINN) model to reconstruct wind fields in the urban canopy based on limited LiDAR observations. Our model can reconstruct wind speeds at any arbitrary coordinates. By embedding the continuity equation into the loss function, the model enforces physical constraints and reduces unphysical divergence. Additionally, the model employs Fourier feature mapping to capture high-frequency components in the data, alleviating the spectral bias existing in standard multi-layer perceptrons (MLPs). The proposed model is verified at Haixinsha Island, Guangzhou, effectively fusing observational data from three Doppler LiDARs. Results show that our model achieved a mean absolute error (MAE) of 0.39 m/s for the u component and 0.47 m/s for the v component, outperforming baselines. This approach provides a robust method to generate continuous and physically consistent wind data essential for navigation safety and complex flow analysis.