Representation of few-group homogenized cross section by multi-variate polynomial regression

Université Paris-Saclay, CEA, Service d’Etudes des Réacteurs et de Mathématiques Appliquées, 91191 Gif-sur-Yvette, France

^* e-mail: dinh-quocdang.nguyen@cea.fr
^** e-mail: emiliano.masiello@cea.fr

Published online: 15 October 2024

Abstract

In this paper, a representation of few-group homogenized cross section by multi-variate polynomial regression is presented. The method is applied on the few-group assembly homogenized cross sections of the assembly 22UA from the benchmark X2VVER[1], generated by the lattice transport code APOLLO3®[2], and conducted over a Cartesian grid of parametric state-points. The regression model [3, 4] allow to input a significantly larger number of points for training compared to the number of monomials, thus yielding higher accuracy than polynomial interpolation without being affected by the choice of points in the training set. Additionally, it can reduce data preparation time because the size of the training set can be smaller than the number of points in the complete Cartesian grid, while still providing a good approximation. Furthermore, its evaluation algorithm can be adapted for GPU utilization, similar to polynomial interpolation with the Newton method [5].