Kernel-based parameter screening for conditional Bayesian calibration of chained numerical models: application to fuel performance simulation of pressurized water reactors

Numerical models are widely used in engineering to study complex physical systems. They are affected by various uncertainties that impact the accuracy of model outputs. Some epistemic uncertainty comes from input parameters and can be reduced through Bayesian calibration using experimental data. Additionally, global sensitivity analysis (GSA) quantifies how input uncertainties impact the variability of the quantity of interest. In this work, we propose a new GSA method based on the Hilbert-Schmidt Independence Criterion (HSIC) in support of Bayesian calibration in the context of two chained numerical models. The objective is to identify the calibration parameters θ of the downstream model, taking into account all uncertainties associated with the parameters λ of the upstream model. By incorporating the uncertainty of λ into the computation of HSIC indices, our method enables the associated independence tests to identify the most influential parameters θ for Bayesian calibration. The proposed estimators are consistent, with convergence rates comparable to standard Monte Carlo estimators. Finally, we have applied this approach in nuclear fuel simulation in order to find the most influential calibration parameters θ of a fission gas behavior model while accounting for the uncertainty of the thermal conductivity λ of an upstream thermal model.