Efficient probabilistic inference for expensive-to-evaluate black-box models for full-scale nuclear reactor thermal hydraulics

Uncertainty quantification (UQ) is essential for ensuring the safety and reliability of advanced nuclear reactors, yet inverse UQ (IUQ) has been largely confined to simplified models or component-level studies due to the computational burden of high-fidelity simulations and the black-box nature of proprietary or commercial nuclear thermal-hydraulic simulation models. This work introduces an IUQ framework that integrates an expensive-to-evaluate black-box simulator (Flownex SE) with efficient gradient-free Bayesian sampling schemes for application to a full-transient, system-level IUQ of the Natural Circulation Experiment. The key physical parameters incorporated in the UQ analysis include the heater power bias, hydraulic resistance, heat transfer coefficient, and powder gap thermal conductivity, which are calibrated against available experimental data, resulting in a significant reduction of uncertainty in simulation model predictions of the output responses (up to 62% reduction in the predictive uncertainty compared to a model based on the predictive prior distribution). A comparative assessment of Markov chain Monte Carlo (MCMC) strategies demonstrates that the ensemble slice sampling scheme provides superior computational efficiency relative to the affine-invariant ensemble sampler, while Bayesian optimization-based informed initialization further accelerates convergence. The calibrated parameters not only correct systematic model biases but also yield significantly tighter and more accurate posterior predictive intervals for both quantities used in calibration and additional responses and operating conditions not included in the inference, including an independent steady-state case. Overall, this study demonstrates the feasibility of performing full-transient, system-level IUQ with a complex black-box simulator and provides a practical pathway for advanced nuclear safety analysis.