mlsanityData to 14 Oct 2026

Geometry-aware Active Learning of Spatiotemporal Dynamic Systems

arXiv 2504.19012 ↗First posted 26 Apr 2025stat.ML cs.LGcited by 3

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Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 19 of its 63 references that are in the map. First posted on arXiv 26 Apr 2025.

Builds on

19 of 63 references.

References · 19

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7 more
  1. 2020Gaussian Process Manifold Interpolation for Probabilistic Atrial Activation Maps and Uncertain Conduction Velocitycited by 13
  2. 2021Spatiotemporal Data Mining: A Survey on Challenges and Open Problemscited by 13
  3. 2021Physics-constrained Deep Learning for Robust Inverse ECG Modelingcited by 12
  4. 2019Function-on-function kriging, with applications to 3D printing of aortic tissuescited by 9
  5. 2021Spatiotemporal wildfire modeling through point processes with moderate and extreme markscited by 9
  6. 2021Deep Spatio-temporal Sparse Decomposition for Trend Prediction and Anomaly Detection in Cardiac Electrical Conductioncited by 3
  7. 2023Inverse Models for Estimating the Initial Condition of Spatio-Temporal Advection-Diffusion Processescited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025Transformer with Koopman-Enhanced Graph Convolutional Network for Spatiotemporal Dynamics Forecastingcited by 3
  2. 2025Physics-augmented Multi-task Gaussian Process for Modeling Spatiotemporal Dynamicscited by 1
  3. 2026P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for Deep Spatiotemporal Super-resolutioncited by 0