Abstract
This work deals with the representation of homogenized few-groups cross sections libraries by machine learning. A Reproducing Kernel Hilbert Space (RKHS) is used for different Pool Active Learning strategies to obtain an optimal support. Specifically a spline kernel is used and results are compared to multi-linear interpolation as used in industry, discussing the reduction of the library size and of the overall performance. A standard PWR fuel assembly provides the use case (OECD-NEA Burn-up Credit Criticality Benchmark [1]).
Highlights
Few-group cross sections are obtained through an homogenization process from transport calculations, that compute the neutronic flux with a detailed discretization in energy and space
Two approximation scenarios are considered: with and without a shared support for the cross sections, as presented in pseudo code in Algorithms 1 and 2, respectively. In both cases the model starts with an initial support S0 ∈ SP chosen randomly and loss function values are computed within the loop to find new optimal points x† ∈ XP
If absolute errors are considered, even if weighted by the importance (IXS), we find that the only cross section participating in the Active Learning (AL) is 135Xea2 since its absolute values are significantly bigger than the others
Summary
Few-group cross sections are obtained through an homogenization process from transport calculations, that compute the neutronic flux with a detailed discretization in energy and space. For every lattice calculation point, the cross section set Y = {σ(x) → R, x ∈ X } of size |Y| = i × r × g is obtained for every reaction type r, group g and isotope i. These are generally smooth functions with possible strong variations in localized regions. Discrete samples XS = {xi ∈ X } define the support S = {σ(xi), xi ∈ XS}, which is the available information to build the model. Ordinary reactor studies for fuel cycle optimization, transient simulations and core design need to resolve the multi-physics coupling with other computer codes where cross sections models have to deal with ever-growing volumes of data
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