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.

Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this structure to develop a computationally efficient approach to state estimation and learning in graph-structured state-space models with (partially) unknown dynamics and limited historical data. Building on recent methods that combine ideas from deep learning with principled inference in Gaussian Markov random fields (GMRF), we reformulate graph-structured state-space models as Deep GMRFs defined by simple spatial and temporal graph layers. This results in a flexible spatiotemporal prior that can be learned efficiently from a single time sequence via variational inference. Under linear Gaussian assumptions, we retain a closed-form posterior, which can be sampled efficiently using the conjugate gradient method, scaling favorably compared to classical Kalman filter based approaches.