Physics-augmented Multi-task Gaussian Process for Modeling Spatiotemporal Dynamics

Area of Science:

• Computational science
• Biophysics
• Machine learning

Background:

• High-dimensional spatiotemporal data from complex geometries present modeling challenges.
• Irregular manifolds, multi-output dynamics, and limited data hinder predictive accuracy.
• Reliable uncertainty quantification is crucial for decision-making in complex systems.

Purpose of the Study:

• To develop a physics-augmented, geometry-aware, multi-task Gaussian Process (P-G-MGP) framework.
• To address challenges in spatiotemporal modeling of complex systems.
• To enable robust uncertainty quantification for scientific predictions.

Main Methods:

• Developed a geometry-aware multi-task Gaussian Process (G-MGP) for spatiotemporal structure and inter-task dependencies.
• Incorporated physical laws via physics-based regularization for model fidelity.
• Provided closed-form posterior variance estimates for uncertainty quantification.

Main Results:

• The P-G-MGP framework demonstrated superior predictive performance on 3D cardiac electrophysiological modeling.
• Effectively integrated geometric priors, multi-task learning, and physical constraints.
• Achieved calibrated uncertainty quantification for improved decision-making.

Conclusions:

• The P-G-MGP framework offers a robust approach for spatiotemporal modeling in complex scientific domains.
• Physics augmentation and geometry awareness enhance predictive capabilities.
• Calibrated uncertainty quantification is a key benefit for downstream applications.