Taking into account input uncertainties in the Bayesian calibration of time-consuming simulators

Abstract

The consideration of experimental uncertainties is a key element in the quantification of uncertainties and pre-
diction by simulation. While particular attention is paid to experimental uncertainties on simulation outputs, little
work is done on uncertainties on simulation inputs, arguing that they are negligible or small enough to be aggregated
with uncertainties on outputs via Taylor development. However, these uncertainties on inputs are not always low and,
depending on the structure of the code, linearization around them is not always possible. The objective of this work is
therefore twofold. First, it introduces a general Bayesian framework for integrating input uncertainties into the cali-
bration of code parameters. It then proposes several approaches to effectively solve this inference problem, depending
on the regularity of the code and the type of inputs considered. The advantages and disadvantages of the different
methods are finally illustrated on an analytical example, as well as on a ballistic problem.