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

arXiv: https://arxiv.org/abs/1901.07903 · HTML: https://mlsanity.com/paper/1901.07903/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2019.

## Built on by (most cited first, 2 of 2)

- [The Minimax Rate of HSIC Estimation for Translation-Invariant Kernels](https://mlsanity.com/paper/2403.07735/) (2024)
- [A Learning-Based Optimal Uncertainty Quantification Method and Its Application to Ballistic Impact Problems](https://mlsanity.com/paper/2212.14709/) (2022)

## Abstract (arXiv)

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.