# Optimal Uncertainty Quantification of a risk measurement from a thermal-hydraulic code using Canonical Moments

## TL;DR

This paper introduces a method to robustly quantify risk in nuclear safety computer simulations by optimizing the maximum quantile over distributions constrained by moments, using canonical moments for efficient computation.

## Contribution

It develops a novel approach employing canonical moments to optimize risk quantification under moment constraints, enhancing robustness in uncertainty analysis.

## Key findings

- Effective optimization of risk measures under moment constraints.
- Use of canonical moments simplifies complex constrained problems.
- Improved robustness in nuclear safety risk assessment.

## Abstract

We study an industrial computer code related to nuclear safety. A major topic of interest is to assess the uncertainties tainting the results of a computer simulation. In this work we gain robustness on the quantification of a risk measurement by accounting for all sources of uncertainties tainting the inputs of a computer code. To that extent, we evaluate the maximum quantile over a class of distributions defined only by constraints on their moments. Two options are available when dealing with such complex optimization problems: one can either optimize under constraints; or preferably, one should reformulate the objective function. We identify a well suited parameterization to compute the optimal quantile based on the theory of canonical moments. It allows an effective, free of constraints, optimization.