用物理规律增强多任务高斯过程，提升复杂时空动态建模精度
Physics-augmented Multi-task Gaussian Process for Modeling Spatiotemporal Dynamics
- 基于几何感知的多任务高斯过程捕捉时空结构与变量关联
- 引入物理约束正则化，使预测符合动力学原理，误差降低32%
- 适合需融合物理知识的生物医学、气象等时空建模场景
传感与成像技术的发展使得在复杂几何域上获取高维时空数据成为可能。然而，由于空间结构不规则、时间动态迅速以及需联合预测多个相关物理变量，有效建模仍具挑战。本文提出一种面向时空动态系统的物理增强多任务高斯过程（P-M-GP）框架。我们构建了具备几何感知能力的多任务高斯过程（M-GP）模型，以有效捕捉内在时空结构与任务间依赖关系。为进一步提升模型保真度与鲁棒性，通过基于物理规律的正则化方案引入控制方程约束，确保预测结果与动力学原理一致。我们在三维心脏电生理建模任务上验证了所提P-M-GP框架的有效性。数值实验表明，相比现有方法，该方法在预测精度上显著提升，通过融入领域特定的物理约束和几何先验实现更优性能。
原文摘要 · Abstract (English)
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.
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