Multi-fidelity surrogate models combining dimensionality reduction and an intermediate surrogate in the reduced space allow a cost-effective emulation of simulators with functional outputs. The surrogate is an input-output mapping learned from a limited number of simulator evaluations. This computational efficiency makes surrogates commonly used for many-query tasks. Diverse methods for building them have been proposed in the literature, but they have only been partially compared. This paper introduces a unified framework encompassing the different surrogate families, followed by a methodological comparison and the exposition of practical considerations. More than a dozen of existing multi-fidelity surrogates have been implemented under the unified framework and evaluated on a set of benchmark problems. Based on the results, guidelines and recommendations are proposed regarding multi-fidelity surrogates with functional outputs. Our study shows that most multi-fidelity surrogates outperform their tested single-fidelity counterparts under the considered settings. But no particular surrogate is performing better on every test case. Therefore, the selection of a surrogate should consider the specific properties of the emulated functions, in particular the correlation between the low- and high-fidelity simulators, the size of the training set, the local nonlinear variations in the residual fields, and the size of the training datasets.

翻译：结合降维技术与降维空间中间代理模型的多保真度代理模型，能够以经济高效的方式实现对功能输出仿真器的建模。该代理模型是通过有限次仿真器评估学习得到的输入-输出映射关系。这种计算效率优势使得代理模型被广泛应用于多查询任务。文献中已提出多种构建方法，但这些方法仅得到部分比较。本文提出一个涵盖不同代理模型族的统一框架，随后开展方法学比较并阐述实际应用要点。我们在统一框架下实现了十余种现有多保真度代理模型，并在基准问题集上进行了评估。基于实验结果，我们提出了针对功能输出多保真度代理模型的选择指南与建议。研究表明，在给定设置下，大多数多保真度代理模型性能优于测试的单保真度对比模型，但不存在任何特定代理模型在所有测试案例中均表现最优。因此，代理模型的选择需综合考虑被建模函数的特定性质，特别是低保真度与高保真度仿真器间的相关性、训练集规模、残差场的局部非线性变化以及训练数据集的大小。