Multi-output gaussian processes for the reconstruction of homogenized cross-sections

Abstract

Deterministic nuclear reactor simulators employing the prevalent two-step scheme often generate a substantial amount of intermediate data at the interface of their two subcodes, which can impede the overall performance of the software. The bulk of this data comprises “few-groups homogenized cross-sections” or HXS, which are stored as tabulated multivariate functions and interpolated inside the core simulator. A number of mathematical tools have been studied for this interpolation purpose over the years, but few meet all the challenging requirements of neutronics computation chains: extreme accuracy, low memory footprint, fast predictions… We here present a new framework to tackle this task, based on multi-outputs gaussian processes (MOGP). This machine learning model enables us to interpolate HXS’s with improved accuracy compared to the current multilinear standard, using only a fraction of its training data – meaning that the amount of required precomputation is reduced by a factor of several dozens. It also necessitates an even smaller fraction of its storage requirements, preserves its reconstruction speed, and unlocks new functionalities such as adaptive sampling and facilitated uncertainty quantification. We demonstrate the efficiency of this approach on a rich test case reproducing the VERA benchmark, proving in particular its scalability to datasets of millions of HXS.