Geometry-aware active learning of spatiotemporal dynamic systems

Rapid developments in advanced sensing and imaging have significantly enhanced information visibility, opening opportunities for predictive modeling of complex dynamic systems. However, sensing signals acquired from such complex systems are often distributed across 3D geometries and rapidly evolve over time, posing significant challenges in spatiotemporal predictive modeling. This paper proposes a geometry-aware active learning framework for modeling spatiotemporal dynamic systems. In particular, we focus on high-resolution spatial reconstruction, i.e., estimating time-series signals at unmeasured spatial locations by leveraging measurements from observed locations over a shared time interval. To achieve this goal, we propose a geometry-aware spatiotemporal Gaussian Process (G-ST-GP) to effectively integrate the temporal correlations and geometric manifold features for reliable prediction of high-dimensional dynamic behaviors. In addition, we develop an adaptive active learning strategy to strategically identify informative spatial locations for data collection and further maximize the prediction accuracy. This strategy achieves the adaptive tradeoff between the prediction uncertainty in the G-ST-GP model and the space-filling design guided by the geodesic distance across the 3D geometry. We implement the proposed framework to model spatiotemporal electrodynamics in 3D ventricular and atrial geometries. Numerical experiments show that our framework outperforms traditional methods lacking geometric information incorporation or effective data collection mechanisms.