This paper deals with surrogate modelling 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 Bayesian neural network (BNN), in a method called GPBNN. 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 high-fidelity observations, well-chosen realisations of the low-fidelity output emulator. The predictive uncertainty of the final surrogate model is then quantified by a complete characterisation of the uncertainties of the different models and their interaction. GPBNN is compared with most of the multi-fidelity regression methods allowing to quantify the prediction uncertainty.

翻译：本文研究在层次化多保真度背景下计算机代码输出的代理建模问题，即输出可在不同精度级别和计算成本下进行评估。利用低保真度和低保真度级别的输出观测，我们提出了一种结合高斯过程回归与贝叶斯神经网络的方法，称为GPBNN。其中，低保真度输出通过经典高斯过程回归作为单保真度代码处理；而低保真度输出则由一个贝叶斯神经网络近似，该网络在嵌入低保真度观测的同时，还引入经精心选取的低保真度输出仿真器的实现。最终代理模型的预测不确定性通过对不同模型及其交互不确定性的完整表征进行量化。GPBNN与多数可量化预测不确定性的多保真度回归方法进行了比较。