Simulating complex physical processes across a domain of input parameters can be very computationally expensive. Multi-fidelity surrogate modeling can resolve this issue by integrating cheaper simulations with the expensive ones in order to obtain better predictions at a reasonable cost. We are specifically interested in computer experiments that involve the use of finite element methods with a real-valued tuning parameter that determines the fidelity of the numerical output. In these cases, integrating this fidelity parameter in the analysis enables us to make inference on fidelity levels that have not been observed yet. Such models have been developed, and we propose a new adaptive non-stationary kernel function which more accurately reflects the behavior of computer simulation outputs. In addition, we aim to create a sequential design based on the integrated mean squared prediction error (IMSPE) to identify the best design points across input parameters and fidelity parameter, while taking into account the computational cost associated with the fidelity parameter. We illustrate this methodology through synthetic examples and applications to finite element analysis. An $\textsf{R}$ package for the proposed methodology is provided in an open repository.

翻译：在输入参数域内模拟复杂物理过程可能计算成本极高。多保真度代理建模通过整合低成本仿真与高成本仿真，能够以合理代价获得更优预测结果。我们特别关注涉及有限元方法的计算机实验，该类实验采用实值调优参数以确定数值输出的保真度。在此类场景中，将保真度参数纳入分析框架，可对尚未观测的保真度层级进行统计推断。现有模型虽已有所发展，但本文提出了一种新型自适应非平稳核函数，能更精确地反映计算机仿真输出的行为特征。此外，我们旨在基于集成均方预测误差（IMSPE）构建序列设计，以确定输入参数与保真度参数的最佳设计点，同时考量保真度参数相关的计算成本。本文通过合成算例及有限元分析应用验证该方法。相关$\textsf{R}$软件包已在开源仓库中提供。