This paper deals with surrogate modeling of a computer code output in a hierarchical multi-fidelity context, i.e., when the output can be evaluated at different levels of accuracy and computational cost. Using observations of the output at low- and high-fidelity levels, we propose a method that combines Gaussian process (GP) regression and the Bayesian neural network (BNN), called the GPBNN method. The low-fidelity output is treated as a single-fidelity code using classical GP regression. The high-fidelity output is approximated by a BNN that incorporates, in addition to the highfidelity observations, well-chosen realizations of the low-fidelity output emulator. The predictive uncertainty of the final surrogate model is then quantified by a complete characterization of the uncertainties of the different models and their interaction. The GPBNN is compared to most of the multi-fidelity regression methods allowing one to quantify the prediction uncertainty.

中文翻译：

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多保真代理建模的贝叶斯神经网络方法

本文讨论了分层多保真环境中计算机代码输出的代理建模，即当输出可以在不同级别的精度和计算成本下进行评估时。通过对低保真度和高保真度输出的观察，我们提出了一种结合高斯过程 (GP) 回归和贝叶斯神经网络 (BNN) 的方法，称为 GPBNN 方法。使用经典 GP 回归将低保真度输出视为单保真度代码。高保真输出由 BNN 近似，除了高保真观察之外，BNN 还包含精心选择的低保真输出模拟器的实现。然后通过不同模型的不确定性及其相互作用的完整表征来量化最终替代模型的预测不确定性。