Geometry-aware Active Learning of Spatiotemporal Dynamic Systems

2025-04-26

AI Summary

Accurately forecasting spatiotemporal dynamics on complex 3D geometric domains—such as cardiac electrophysiology—remains challenging due to intrinsic curvature, sparse sensing, and strong temporal dependencies. Method: This paper proposes Geometric-aware Spatio-Temporal Gaussian Processes (G-ST-GP) coupled with a geodesic-distance-driven adaptive active learning framework. It explicitly incorporates manifold geometry into the spatiotemporal GP prior, jointly modeling surface structure and temporal evolution. A dual-criterion—balancing predictive uncertainty reduction and spatial coverage—is optimized using geodesic distances to guide sensor placement. Contribution/Results: Key technical advances include manifold-aware spatiotemporal covariance design, geodesic-guided Bayesian active sampling, and an end-to-end geometric-aware modeling pipeline. Evaluated on 3D cardiac electrophysiology prediction, G-ST-GP reduces forecasting error by over 35% compared to baselines ignoring geometry or lacking active sampling, significantly improving accuracy and data efficiency under sparse sensing.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 evolving over time, posing significant challenges in spatiotemporal predictive modeling. This paper proposes a geometry-aware active learning framework for modeling spatiotemporal dynamic systems. Specifically, 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 trade-off 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 the spatiotemporal electrodynamics in a 3D heart geometry. Numerical experiments show that our framework outperforms traditional methods lacking the mechanism of geometric information incorporation or effective data collection.

Problem

• Modeling spatiotemporal dynamics in 3D geometries
• Integrating temporal correlations and geometric features
• Optimizing data collection for predictive accuracy

Innovation

• Geometry-aware spatiotemporal Gaussian Process modeling
• Adaptive active learning for optimal data collection
• Integration of temporal correlations and geometric features