Offline Maximizing Minimally Invasive Proper Orthogonal Decomposition for Reduced Order Modeling of $S_n$ Radiation Transport

TL;DR

This paper introduces a novel offline minimally invasive POD method for reduced order modeling of the Sn radiation transport equation, achieving significant speedup with low error by offline basis construction and interpolation.

Contribution

It extends Minimally Invasive POD by performing offline transport sweeps and interpolation, enabling rapid approximate solutions for Sn transport problems.

Findings

Achieves 1600-fold speedup over full order models.

Demonstrates low error in a 2-D multigroup test problem.

Validates effectiveness of offline basis generation and interpolation.

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.