Offline Maximizing Minimally Invasive Proper Orthogonal Decomposition for Reduced Order Modeling of $S_n$ Radiation Transport
Quincy Huhn, Jean Ragusa, Youngsoo Choi
TL;DR
The paper tackles the computational burden of solving the six-dimensional steady-state $S_n$ neutron transport equation by introducing Offline Maximizing Minimally Invasive POD (OMMI-POD). It builds a POD-based reduced basis and leverages a matrix-free, minimally invasive operator sweep to form reduced systems, with all sweeps performed offline and online solutions obtained by interpolating a library of reduced systems. The approach achieves very low relative errors (around $1.2\times10^{-4}$) and substantial online speedups (approximately 1190×) on a challenging two-group 2-D checkerboard test, demonstrating the practicality of offline ROM construction for radiation transport. This method has potential impact for design optimization and uncertainty quantification tasks where repeated, fast approximations of the transport solution are essential.
Abstract
Deterministic solutions to the Sn transport equation can be computationally expensive to calculate. Reduced Order Models (ROMs) provide an efficient means of approximating the Full Order Model (FOM) solution. We propose a novel approach for constructing ROMs of the Sn radiation transport equation, Offline Maximizing Minimally Invasive (OMMI) Proper Orthogonal Decomposition (POD). POD uses snapshot data to build a reduced basis, which is then used to project the FOM. Minimally Invasive POD leverages the sweep infrastructure within deterministic Sn transport solvers to construct the reduced linear system, even though the FOM linear system is never directly assembled. OMMI-POD extends Minimally Invasive POD by performing transport sweeps offline, thereby maximizing the potential speedup. It achieves this by generating a library of reduced systems from a training set, which is then interpolated in the online stage to provide a rapid approximate solution to the Sn transport equation. The model's performance is evaluated on a multigroup 2-D test problem, demonstrating low error and a 1600-fold speedup over the full order model.