# Geometry-aware Active Learning of Spatiotemporal Dynamic Systems

arXiv: https://arxiv.org/abs/2504.19012 · HTML: https://mlsanity.com/paper/2504.19012/

## 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 (most cited first, 19 of 19)

- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Bi-Directional ConvLSTM U-Net with Densley Connected Convolutions](https://mlsanity.com/paper/1909.00166/) (2019)
- [Mat'ern Gaussian processes on Riemannian manifolds](https://mlsanity.com/paper/2006.10160/) (2020)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [Graph Neural Processes for Spatio-Temporal Extrapolation](https://mlsanity.com/paper/2305.18719/) (2023)
- [Hierarchical Deep Learning with Generative Adversarial Network for Automatic Cardiac Diagnosis from ECG Signals](https://mlsanity.com/paper/2210.11408/) (2022)
- [Active Learning for Gaussian Process Considering Uncertainties with Application to Shape Control of Composite Fuselage](https://mlsanity.com/paper/2004.10931/) (2020)
- [Gaussian Process Manifold Interpolation for Probabilistic Atrial Activation Maps and Uncertain Conduction Velocity](https://mlsanity.com/paper/2004.10586/) (2020)
- [Spatiotemporal Data Mining: A Survey on Challenges and Open Problems](https://mlsanity.com/paper/2103.17128/) (2021)
- [Physics-constrained Deep Learning for Robust Inverse ECG Modeling](https://mlsanity.com/paper/2107.12780/) (2021)
- [Function-on-function kriging, with applications to 3D printing of aortic tissues](https://mlsanity.com/paper/1910.01754/) (2019)
- [Spatiotemporal wildfire modeling through point processes with moderate and extreme marks](https://mlsanity.com/paper/2105.08004/) (2021)
- [Deep Spatio-temporal Sparse Decomposition for Trend Prediction and Anomaly Detection in Cardiac Electrical Conduction](https://mlsanity.com/paper/2109.09317/) (2021)
- [Inverse Models for Estimating the Initial Condition of Spatio-Temporal Advection-Diffusion Processes](https://mlsanity.com/paper/2302.04134/) (2023)

## Built on by (most cited first, 3 of 3)

- [Transformer with Koopman-Enhanced Graph Convolutional Network for Spatiotemporal Dynamics Forecasting](https://mlsanity.com/paper/2507.03855/) (2025)
- [Physics-augmented Multi-task Gaussian Process for Modeling Spatiotemporal Dynamics](https://mlsanity.com/paper/2510.13601/) (2025)
- [P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for Deep Spatiotemporal Super-resolution](https://mlsanity.com/paper/2606.19303/) (2026)

## 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.