用多任务高斯过程解决工程中少样本高精度建模难题
Multi-task Modeling for Engineering Applications with Sparse Data
- 构建跨任务、跨精度的多任务高斯过程框架
- 在三个工程场景中提升预测精度并降低计算开销
- 适合数据稀疏、实验成本高的工程建模领域
现代工程与科学工作流常需同时预测多个相关任务及不同精度层级，其中高保真数据稀缺且昂贵，而低保真数据更为丰富。本文提出一种面向多源、多精度工程数据的多任务高斯过程（MTGP）框架，应对数据稀疏性与任务间相关性变化的挑战。该框架利用输出维度和精度层级间的跨任务关系，提升预测性能并降低计算成本。在Forrester函数基准、三维椭球空洞建模和摩擦搅拌焊三个典型场景中进行了验证。通过量化并利用任务间关系，所提MTGP框架为具有显著计算与实验成本的领域提供了稳健且可扩展的预测建模方案，支持决策优化与资源高效利用。
原文摘要 · Abstract (English)
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.
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