Low-Rank Multigroup Neutron Transport by Galerkin or Balanced Proper Orthogonal Decomposition

This article presents Proper Orthogonal Decomposition (POD) as an alternative to conventional cross section condensation. Although not always framed as such, these two techniques are analogous, except that POD approximates the solution as low-rank rather than rank-one separable in energy within each coarse energy group. Starting with a fine-group neutron transport model of a 2D Watts bar benchmark problem (or an interior and peripheral colorset thereof), we reduce cross sections by Galerkin POD, Balanced POD (BPOD), or conventional condensation. Comparing the accuracies of the resulting reduced-order models (ROMs), we find that a three-group BPOD ROM can often achieve more accurate estimates of the k-eigenvalue and pinwise fission distribution than a conventional coarse-group model with an equal or greater number of degrees of freedom. Remarkably, this is despite that the conventional model assigns a particularized spectrum to each of the problem’s 57 760 spatial regions (e.g., each individual pin or unit-cell of water), whereas the POD ROMs apply the same energy bases throughout. Moreover, this holds even when constructing the BPOD ROM from only the two colorset solutions, as opposed to the full quarter-core solution used for the conventional model (and against which model accuracy is evaluated). That is, BPOD enhances accuracy even while obviating the cumbersome mapping between assembly-level reference solutions and core-wide target problems required in conventional lattice physics workflows—and with it, the usual concerns about the spectral effects of core leakage or assembly interfaces.