In system analysis and design optimization, multiple computational models are typically available to represent a given physical system. These models can be broadly classified as high-fidelity models, which provide highly accurate predictions but require significant computational resources, and low-fidelity models, which are computationally efficient but less accurate. Multi-fidelity methods integrate high- and low-fidelity models to balance computational cost and predictive accuracy. This perspective paper provides an in-depth overview of the emerging field of machine learning-based multi-fidelity methods, with a particular emphasis on uncertainty quantification and optimization. For uncertainty quantification, a particular focus is on multi-fidelity graph neural networks, compared with multi-fidelity polynomial chaos expansion. For optimization, our emphasis is on multi-fidelity Bayesian optimization, offering a unified perspective on multi-fidelity priors and proposing an application strategy when the objective function is an integral or a weighted sum. We highlight the current state of the art, identify critical gaps in the literature, and outline key research opportunities in this evolving field.

翻译：在系统分析与设计优化中，通常存在多种计算模型可用于表征给定的物理系统。这些模型可大致分为高保真度模型和低保真度模型：前者能提供高精度预测但需要大量计算资源，后者计算效率高但精度较低。多保真度方法通过整合高、低保真度模型，在计算成本与预测精度之间实现平衡。本视角论文深入综述了基于机器学习的多保真度方法这一新兴领域，特别聚焦于不确定性量化与优化两大方向。在不确定性量化方面，重点探讨多保真度图神经网络，并与多保真度多项式混沌展开方法进行对比。在优化领域，着重分析多保真度贝叶斯优化，提出关于多保真度先验的统一理论框架，并针对目标函数为积分或加权和的情形提出应用策略。本文系统梳理了该领域的前沿进展，指出当前文献中的关键空白，并展望了这一动态发展领域的重要研究方向。