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

¹ CEA, DES, IRESNE, DER, SESI, Cadarache, 13108 Saint-Paul-Lez-Durance, France
² Université Paris-Saclay, CEA, DES, ISAS, DM2S, SGLS, 91191 Gif-sur-Yvette, France
³ Avignon Université, LMA UPR 2151, 84140 Avignon, France
⁴ CEA, DES, IRESNE, DEC, SESC, Cadarache, 13108 Saint-Paul-Lez-Durance, France

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 24 September 2025
Accepted: 26 February 2026

Abstract

Numerical simulation is widely used in many fields of engineering to study complex physical systems. The numerical models, designed to faithfully represent the underlying physical phenomena, are subject to uncertainties of different natures (either numerical, stochastic or epistemic) that degrade the accuracy of the simulated outputs. Part of epistemic uncertainty arises from limited knowledge regarding some input model parameters θ. This component can be reduced through Bayesian calibration of the model against experimental data. Before calibration itself, sensitivity analysis can be used to better understand how parameter uncertainties impact the model output, and this may help confine calibration to the most impactful parameters. In this work, we show that kernel methods, especially those based on the Hilbert—Schmidt independence criterion (HSIC), are effective tools in support of Bayesian calibration, both for a single model and for two chained models. In the latter case, our main contribution is a screening methodology for the parameters θ of the downstream model, which accounts for the posterior distribution of the upstream model parameters λ. By taking the expectation of the HSIC over λ, we define a new sensitivity measure that is able to incorporate the residual uncertainty due to the upstream model calibration. We show that the resulting sensitivity indices can be estimated from the same data used for conditional Bayesian calibration. We further demonstrate that the corresponding estimators are consistent and achieve convergence rates comparable to those of classical Monte Carlo estimators. Importantly, we construct two test procedures that enable rigorous decisions on which parameters among θ should be selected. Finally, we apply the proposed approach to nuclear fuel simulation to screen the calibration parameters θ of a fission gas behavior model which follows an upstream thermal model whose thermal conductivity λ was calibrated in previous work.