Spatiotemporal graph neural process for reconstruction, extrapolation, and classification of cardiac trajectories

We present a probabilistic framework for modeling structured spatiotemporal dynamics from sparse observations, focusing on cardiac motion. Our approach integrates neural ordinary differential equations (NODEs), graph neural networks (GNNs), and neural processes into a unified model that captures uncertainty, temporal continuity, and anatomical structure. We represent dynamic systems as spatiotemporal multiplex graphs and model their latent trajectories using a GNN-parameterized vector field. Given the sparse context observations at node and edge levels, the model infers a distribution over latent initial states and control variables, enabling both interpolation and extrapolation of trajectories. We validate the method on three synthetic dynamical systems (coupled pendulum, Lorenz attractor, and Kuramoto oscillators) and two real-world cardiac imaging datasets - ACDC (N=150) and UK Biobank (N=526) - demonstrating accurate reconstruction, extrapolation, and disease classification capabilities. The model accurately reconstructs trajectories and extrapolates future cardiac cycles from a single observed cycle. It achieves state-of-the-art results on the ACDC classification task (up to 99% accuracy), and detects atrial fibrillation in UK Biobank subjects with competitive performance (up to 67% accuracy). This work introduces a flexible approach for analyzing cardiac motion and offers a foundation for graph-based learning in structured biomedical spatiotemporal time-series data.