Use cases of Tucker decomposition method for reconstruction of neutron macroscopic cross-sections

The neutron cross-sections are inputs for nuclear reactor core simulations, they depend on various physical parameters. Because of industrial constraint (e.g. calculation time), the cross-sections can not be calculated on the fly due to the huge number of them. Hence, a reconstruction (or interpolation) process is used in order to evaluate the cross-sections at every point required, from (as few as possible) pre-calculated points. With most classical methods (for example: multilinear interpolation which is used in the core code COCAGNE of EDF (Électricité De France)), high accuracy for the reconstruction often requires a lot of pre-calculated points. We propose to use the Tucker decomposition, a low-rank tensor approximation method, to deal with this problem. The Tucker decomposition allows us to capture the most important information (one parameter at a time) to reconstruct the cross-sections. This information is stored as basis functions (called tensor directional basis functions) and the coefficients of the decomposition instead of pre-calculated points. Full reconstruction is done at the core code level using these decompositions. In this paper, a simplified multivariate analysis technique (based on statistical analysis) is also proposed in order to demonstrate that we can improve the quality of the acquired information as well as the accuracy of our approach. Using the Tucker decomposition, we will show in proposed use cases that we can reduce significantly the number of pre-calculated points and the storage size (compared to the multilinear interpolations) while achieving high accuracy for the reconstruction, even on a larger domain of parameters.