A BAYESIAN NEURAL NETWORK APPROACH TO MULTI-FIDELITY SURROGATE MODELING

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