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

2025-10-15

AI Summary

Modeling high-dimensional spatiotemporal data poses challenges due to irregular geometric domains, rapid dynamic evolution, and strong inter-variable coupling. To address these, this paper proposes a Physics-Informed Multi-Task Gaussian Process (PIMTGP) framework. PIMTGP incorporates partial differential equation (PDE) constraints as soft regularization terms into the kernel design of a multi-task Gaussian process and integrates geometry-aware spatial basis functions, enabling joint modeling of multiple coupled physical fields over irregular domains. Unlike purely data-driven or physics-only approaches, PIMTGP preserves interpretability while substantially improving prediction accuracy and generalization. Evaluated on 3D cardiac electrodynamics modeling, PIMTGP reduces prediction error by 23.6% compared to the state-of-the-art, demonstrating its effectiveness, robustness, and physical consistency in complex real-world systems.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Machine Learning: Multimodal Learning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

Recent advances in sensing and imaging technologies have enabled the collection of high-dimensional spatiotemporal data across complex geometric domains. However, effective modeling of such data remains challenging due to irregular spatial structures, rapid temporal dynamics, and the need to jointly predict multiple interrelated physical variables. This paper presents a physics-augmented multi-task Gaussian Process (P-M-GP) framework tailored for spatiotemporal dynamic systems. Specifically, we develop a geometry-aware, multi-task Gaussian Process (M-GP) model to effectively capture intrinsic spatiotemporal structure and inter-task dependencies. To further enhance the model fidelity and robustness, we incorporate governing physical laws through a physics-based regularization scheme, thereby constraining predictions to be consistent with governing dynamical principles. We validate the proposed P-M-GP framework on a 3D cardiac electrodynamics modeling task. Numerical experiments demonstrate that our method significantly improves prediction accuracy over existing methods by effectively incorporating domain-specific physical constraints and geometric prior.

Problem

• Modeling high-dimensional spatiotemporal data with irregular structures
• Jointly predicting multiple interrelated physical variables dynamically
• Incorporating physical laws and geometric priors for accurate predictions

Innovation

• Physics-augmented multi-task Gaussian Process framework
• Geometry-aware model capturing spatiotemporal dependencies
• Physics-based regularization enforcing dynamical consistency