Physics-informed inference of aerial animal movements from weather radar data

TL;DR

Physics-informed inference combines a convolutional encoder with a locally linear Gaussian state-space model and Kalman smoothing to reconstruct high-dimensional aerial animal movement fields from partial weather radar data. The approach uses a physics-informed loss based on the continuity equation to enforce mass conservation, enabling unsupervised training without ground-truth fields. Experiments on synthetic radar data show improved reconstruction quality and data efficiency over baselines, along with meaningful uncertainty estimates. The work offers a data-efficient pathway to infer detailed density and velocity fields for ecological applications, while acknowledging real-world challenges such as non-biological echoes and 3D radar data formats.

Abstract

Studying animal movements is essential for effective wildlife conservation and conflict mitigation. For aerial movements, operational weather radars have become an indispensable data source in this respect. However, partial measurements, incomplete spatial coverage, and poor understanding of animal behaviours make it difficult to reconstruct complete spatio-temporal movement patterns from available radar data. We tackle this inverse problem by learning a mapping from high-dimensional radar measurements to low-dimensional latent representations using a convolutional encoder. Under the assumption that the latent system dynamics are well approximated by a locally linear Gaussian transition model, we perform efficient posterior estimation using the classical Kalman smoother. A convolutional decoder maps the inferred latent system states back to the physical space in which the known radar observation model can be applied, enabling fully unsupervised training. To encourage physical consistency, we additionally introduce a physics-informed loss term that leverages known mass conservation constraints. Our experiments on synthetic radar data show promising results in terms of reconstruction quality and data-efficiency.

Figures (7)

• Figure 1: Schematic overview of our method. Partial and noisy observations from Doppler weather radars are mapped to lower-dimensional latent observations $\mathbf{w}_t$, which are used to perform efficient inference in the LGSSM using the Kalman smoother. Finally, posterior estimates for latent states $\mathbf{z}_t$ are mapped back to physical space in which the reconstruction loss and a physics-informed loss are computed.
• Figure 2: Qualitative comparison of three different reconstruction methods. We show reconstructions of a single velocity field (t=8) from the test set. For all methods, the radar range was set to $d_n=2$.
• Figure 3: RMSE for velocities (left) and log-densities (right) reconstructed by our method, using a varying number of training sequences. Shaded regions correspond to one standard deviation around the mean using 3 different seeds.
• Figure 4: Reconstruction error (RMSE) and uncertainty as a function of time, using our method with radar range $d_n=2$ and 1000 training sequences. Uncertainties are computed as the standard deviation over reconstructions based on 10 samples from the latent posterior $\mathcal{N}(\mathbf{z}_t^+,\mathbf{\Sigma}_t^+)$. Shaded regions correspond to one standard deviation around the mean computed for 50 test sequences.
• Figure 5: Samples from a time series of synthetic velocity (top row) and density (bottom row) fields.