Modern engineering and scientific workflows often require simultaneous predictions across related tasks and fidelity levels, where high-fidelity data is scarce and expensive, while low-fidelity data is more abundant. This paper introduces an Multi-Task Gaussian Processes (MTGP) framework tailored for engineering systems characterized by multi-source, multi-fidelity data, addressing challenges of data sparsity and varying task correlations. The proposed framework leverages inter-task relationships across outputs and fidelity levels to improve predictive performance and reduce computational costs. The framework is validated across three representative scenarios: Forrester function benchmark, 3D ellipsoidal void modeling, and friction-stir welding. By quantifying and leveraging inter-task relationships, the proposed MTGP framework offers a robust and scalable solution for predictive modeling in domains with significant computational and experimental costs, supporting informed decision-making and efficient resource utilization.

翻译：现代工程与科学工作流程通常需要同时对相关任务和保真度层级进行预测，其中高保真度数据稀缺且获取成本高昂，而低保真度数据则相对丰富。本文提出一种专为具有多源、多保真度数据特征的工程系统设计的多任务高斯过程（MTGP）框架，以应对数据稀疏性和任务相关性差异的挑战。该框架通过利用跨输出维度与保真度层级的任务间关联性，以提升预测性能并降低计算成本。该框架在三个代表性场景中得到验证：Forrester函数基准测试、三维椭球孔隙建模以及搅拌摩擦焊接。通过量化并利用任务间关联关系，所提出的MTGP框架为计算与实验成本高昂的领域提供了鲁棒且可扩展的预测建模解决方案，有助于支持科学决策与高效资源利用。