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arXiv 2510.13601cs.LG
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物理增强的多任务高斯过程用于时空动力学建模

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

Department of Industrial and Systems Engineering, The University of Tennessee(工业与系统工程系,田纳西大学)

Xizhuo Zhang, Bing Yao

AI总结:

本文提出物理增强多任务高斯过程框架,通过几何感知和物理正则化约束,在三维心脏电动力学任务上显著提升时空预测精度。

摘要:

近年来,传感和成像技术的进步使得在复杂几何域上收集高维时空数据成为可能。然而,由于不规则的空间结构、快速的时变动态以及需要联合预测多个相互关联的物理变量,对此类数据的有效建模仍然具有挑战性。本文提出了一种针对时空动态系统量身定制的物理增强多任务高斯过程(P-M-GP)框架。具体而言,我们开发了一种几何感知的多任务高斯过程(M-GP)模型,以有效捕获内在的时空结构和任务间依赖关系。为了进一步增强模型的保真度和鲁棒性,我们通过基于物理的正则化方案纳入控制物理定律,从而约束预测与主导动力学原理保持一致。我们在一个三维心脏电动力学建模任务上验证了所提出的P-M-GP框架。数值实验表明,通过有效整合特定领域的物理约束和几何先验,我们的方法在预测精度上显著优于现有方法。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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