This paper presents a multi-fidelity Gaussian process surrogate modeling that generalizes the recursive formulation of the auto-regressive model when the high-fidelity and low-fidelity data sets are noisy and not necessarily nested. The estimation of high-fidelity parameters by the EM (expectation-maximization) algorithm is shown to be still possible in this context and a closed-form update formula is derived when the scaling factor is a parametric linear predictor function. This yields a decoupled optimization strategy for the parameter selection that is more efficient and scalable than the direct maximum likelihood maximization. The proposed approach is compared to other multi-fidelity models, and benchmarks for different application cases of increasing complexity are provided.

翻译：本文提出了一种多保真度高斯过程代理建模方法，当高保真度与低保真度数据集存在噪声且不一定嵌套时，该方法推广了自回归模型的递归形式。研究表明，在此背景下仍可通过EM（期望最大化）算法估计高保真度参数，并在缩放因子为参数化线性预测函数时推导出闭式更新公式。这产生了一种解耦的参数选择优化策略，其比直接最大似然最大化更高效且可扩展。所提方法与其他多保真度模型进行了比较，并提供了复杂度递增的不同应用案例基准测试。