Towards detailed and interpretable hybrid modeling of continental-scale bird migration

TL;DR

This work extends hybrid physics–machine learning modeling of continental-scale bird migration by introducing FluxRGNN+, which decouples the computational grid from the radar network to enable high-resolution forecasts on arbitrary tessellations and adds velocity supervision to improve interpretability of take-off and landing. Built on a finite-volume, mass-conserving continuity framework, FluxRGNN+ replaces implicit flux terms with a velocity parameterization learned by neural nets and constrains predictions via a velocity-based loss when velocity measurements are available. In experiments with the NEXRAD radar network and environmental predictors, FluxRGNN+ achieves predictive performance on par with the original FluxRGNN while delivering finer spatial detail and better extrapolation to unobserved locations; increasing velocity supervision improves movement realism with a modest trade-off in density accuracy. The approach offers a practical pathway to detailed, ecologically interpretable forecasting in data-sparse continental-scale systems and may integrate effectively with data assimilation and citizen-science inputs to advance migration ecology and conservation planning.

Abstract

Hybrid modeling aims to augment traditional theory-driven models with machine learning components that learn unknown parameters, sub-models or correction terms from data. In this work, we build on FluxRGNN, a recently developed hybrid model of continental-scale bird migration, which combines a movement model inspired by fluid dynamics with recurrent neural networks that capture the complex decision-making processes of birds. While FluxRGNN has been shown to successfully predict key migration patterns, its spatial resolution is constrained by the typically sparse observations obtained from weather radars. Additionally, its trainable components lack explicit incentives to adequately predict take-off and landing events. Both aspects limit our ability to interpret model results ecologically. To address this, we propose two major modifications that allow for more detailed predictions on any desired tessellation while providing control over the interpretability of model components. In experiments on the U.S. weather radar network, the enhanced model effectively leverages the underlying movement model, resulting in strong extrapolation capabilities to unobserved locations.

Figures (9)

• Figure 1: Map of the NEXRAD weather radar network, with black circles indicating measurement areas $A_m$, and the hexagonal tessellation on which movements are modeled. During encoding, $f_{\mathcal{R}\to\mathcal{C}}$ maps sparse radar measurements to cell space (bottom left), in which the forecast is generated based on within-cell source/sink terms $s_i$ and cell-to-cell fluxes $F_{j\to i}$ (bottom center). Finally, $f_{\mathcal{C}\to\mathcal{R}}$ maps cell-level predictions back to measurement space (bottom right).
• Figure 2: Spatial cross-validation of bird density predictions. Box plots show the variability of evaluation metrics across 10 cross-validation folds, where different subsets of radars were held out during training. Note that the subsets of training radars for different folds overlap, which naturally leads to less variability in evaluation metrics than for the distinct subsets of test radars.
• Figure 3: Evaluation of flight speeds and directions predicted by FluxRGNN+ trained with varying $\lambda$. Left: Results of the spatial cross-validation for training and test radars respectively. Right: Histograms of predicted and measured quantities for held out test radars across all 10 cross-validation folds.
• Figure 4: An example forecast of three consecutive high intensity migration nights (numbers 1-3) in September 2021 generated by FluxRGNN+ trained with $\lambda=0.1$ on years 2013-2020. The three time series on the left correspond to the radars marked in the maps on the right. To distinguish between take-off and landing, we separate hours with positive and negative source/sink term and aggregate them respectively. Red arrows on the maps indicate average velocities in areas with substantial migration.
• Figure 5: Evaluation of bird density predictions, separated by forecasting horizons. All metrics are reported as mean $\pm$ std across 5 different random seeds.