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.

💡 Research Summary

This paper introduces a novel framework for reconstructing four‑dimensional (space‑time) atmospheric wind fields by exploiting measurements from a coordinated swarm of unmanned aircraft systems (UAS) without the need for dedicated wind sensors. The authors first generate a synthetic turbulent environment using a von Kármán spectral model, which captures realistic low‑altitude turbulence statistics, vertical shear, directional veer, and low‑frequency gust modulation. The turbulent field is superimposed on a mean wind profile defined by a power‑law vertical shear and a linear veer term, yielding a total wind vector that obeys Taylor’s frozen‑field hypothesis. This synthetic wind field is realized on a 210 m × 210 m × 1010 m domain discretized into a 64 × 64 × 128 grid, allowing the production of thousands of wind realizations for training and testing.

Each UAS is modeled as a rigid‑body 6‑DOF system (position, velocity, attitude, angular velocity) with a mass of 2.59 kg. Translational dynamics include thrust, aerodynamic drag, and gravity, while a PID‑based controller tracks pre‑defined three‑dimensional trajectories. The high‑fidelity multirotor dynamics simulator couples the synthetic wind field to the UAS, generating realistic responses to turbulent disturbances. Importantly, only the onboard inertial measurements (accelerations, velocities, angular rates, and control inputs) are recorded; no anemometer or pitot tube data are used.

A bidirectional long short‑term memory network (Bi‑LSTM) is trained to map these inertial time series to local wind components in the North‑East‑Down (NED) frame. Because the Bi‑LSTM processes both past and future context, it can recover the horizontal wind components with root‑mean‑square errors (RMSE) of 0.064 m/s (north) and 0.062 m/s (east) under low‑wind conditions, increasing to 0.122 m/s / 0.129 m/s for moderate winds and 0.273 m/s / 0.271 m/s for high winds. The vertical component is more challenging, yielding RMSE values ranging from 0.029 m/s (low wind) to 0.091 m/s (high wind), reflecting limited observability of vertical accelerations in multirotor dynamics.

The locally estimated wind fields are then assimilated into a physics‑informed neural network (PINN). The PINN treats the wind components as continuous functions of space and time and enforces the incompressible continuity equation and the Navier‑Stokes momentum equations as soft constraints by penalizing their residuals during training. Automatic differentiation enables exact computation of these residuals. By blending sparse Bi‑LSTM estimates with the governing equations, the PINN reconstructs a smooth, physically consistent wind field throughout the entire domain, preserving mean flow direction, vertical shear, and large‑scale temporal evolution while smoothing unresolved turbulent fluctuations.

Extensive experiments evaluate different swarm sizes (3, 5, and 7 UAS). Under moderate wind conditions, the reconstructed mean wind field achieves overall RMSEs of 0.154 m/s (3‑UAS), 0.118 m/s (5‑UAS), and 0.132 m/s (7‑UAS). The five‑UAS configuration yields the lowest error, suggesting an optimal balance between spatial coverage and redundancy; larger swarms do not guarantee monotonic improvement due to increased data correlation and computational overhead. The framework successfully recovers dominant wind structures up to 1000 m altitude, demonstrating scalability to higher altitudes and longer temporal windows.

Key contributions of the work include: (1) a sensor‑light approach that extracts wind information solely from UAS inertial dynamics, eliminating the need for bulky wind sensors; (2) a hybrid data‑driven / physics‑informed pipeline that leverages a Bi‑LSTM for local wind estimation and a PINN for global reconstruction; (3) a comprehensive synthetic turbulence generation pipeline that balances physical realism with computational tractability. Limitations are acknowledged: the current study relies on simulated data, omits sensor noise, communication latency, and complex aerodynamic effects such as blade‑tip vortices; the PINN training is computationally intensive and may require hyper‑parameter tuning for different atmospheric regimes.

Future work should focus on (i) validating the methodology with real‑world flight experiments, incorporating realistic sensor noise models and real‑time data streaming; (ii) extending the PINN to handle adaptive mesh refinement or domain decomposition for larger operational volumes; (iii) exploring lightweight PINN architectures or physics‑guided model reduction to enable on‑board or edge‑computing deployment; and (iv) integrating additional data sources (e.g., lidar, radiosonde) to further constrain the reconstruction in highly heterogeneous environments.

In summary, the paper demonstrates that coordinated UAS swarms, combined with advanced deep learning and physics‑informed techniques, can accurately reconstruct four‑dimensional atmospheric wind fields without fixed infrastructure or dedicated wind sensors. This capability opens new avenues for high‑resolution, low‑cost atmospheric monitoring relevant to weather forecasting, hazard mitigation, and wind‑energy site assessment.