Nowadays, numerical simulations run in the nuclear field are essential to study the behavior of existing and innovative nuclear power plants. Simulation results are affected by various means of uncertainty (e.g. physical parameters, modeling parameters). Quantifying and propagating these uncertainties to simulation results is a crucial issue for robust forecasting of the output quantities of interest. During an accidental transient, the latter can be the maximum cladding temperature in the reactor core or the pressure in the containment vessel.

This doctoral project focuses on the so-called 'Best Estimate Plus Uncertainty' (BEPU) methodology dedicated to the simulation of accidental scenarios for safety demonstration. This methodology first consists in simulating the scenario of interest using a Best Estimate computing code, i.e., running simulations of the scenario as realistically as possible, then quantifying the uncertainty of input parameters by probability distributions. These uncertainties are then propagated to the outputs quantities of interests, and the configurations (of the inputs) that are critical to reactor core safety can be identified. As the simulations are generally time-expensive, the previous steps often rely on the construction of a surrogate model, also called metamodel, emulating each output of interest. Built from a limited number of code simulations, this metamodel (such as the Gaussian process metamodel) then allows more intensive exploration of the space of uncertain parameters. This BEPU methodology was developed for regular transient, but never for transients with threshold effects.

In this context, this doctoral work will aim at implementing advanced Machine Learning techniques to perform metamodeling and uncertainty propagation steps for simulations subject to some threshold effects due to physical bifurcations of the accidental scenario being simulated. Those techniques will be applied to the simulation of a reactivity-initiated accident where some bifurcations have been identified but which the impact on the uncertainty was not fully characterized. This work will contribute to the simulation-based safety demonstration of such nuclear accidents tainted by thresholds.