Physics Informed Reconstruction of Four-Dimensional Atmospheric Wind Fields Using Multi-UAS Swarm Observations in a Synthetic Turbulent Environment

Accurate reconstruction of atmospheric wind fields is essential for applications such as weather forecasting, hazard prediction, and wind energy assessment, yet conventional instruments leave spatio-temporal gaps within the lower atmospheric boundary layer. Unmanned aircraft systems (UAS) provide flexible in situ measurements, but individual platforms sample wind only along their flight trajectories, limiting full wind-field recovery. This study presents a framework for reconstructing four-dimensional atmospheric wind fields using measurements obtained from a coordinated UAS swarm. A synthetic turbulence environment and high-fidelity multirotor simulation are used to generate training and evaluation data. Local wind components are estimated from UAS dynamics using a bidirectional long short-term memory network (Bi-LSTM) and assimilated into a physics-informed neural network (PINN) to reconstruct a continuous wind field in space and time. For local wind estimation, the bidirectional LSTM achieves root-mean-square errors (RMSE) of 0.064 and 0.062 m/s for the north and east components in low-wind conditions, increasing to 0.122 to 0.129 m/s under moderate winds and 0.271 to 0.273 m/s in high-wind conditions, while the vertical component exhibits higher error, with RMSE values of 0.029 to 0.091 m/s. The physics-informed reconstruction recovers the dominant spatial and temporal structure of the wind field up to 1000 m altitude while preserving mean flow direction and vertical shear. Under moderate wind conditions, the reconstructed mean wind field achieves an overall RMSE between 0.118 and 0.154 m/s across evaluated UAS configurations, with the lowest error obtained using a five-UAS swarm. These results demonstrate that coordinated UAS measurements enable accurate and scalable four-dimensional wind-field reconstruction without dedicated wind sensors or fixed infrastructure.