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

Deterministic solutions to the $S_n$ transport equation are often computationally intensive. Reduced Order Models (ROMs) offer an efficient approach to approximate the Full Order Model (FOM) solution. We propose a novel approach for constructing ROMs for the $S_n$ transport equation, named Offline Maximizing Minimally Invasive (OMMI) Proper Orthogonal Decomposition (POD). POD uses snapshot data to construct a reduced basis that is used to project the FOM. OMMI-POD expands upon the Minimally Invasive POD approach, which utilizes the transport sweep that exists inside deterministic $S_n$ transport solvers to allow for the construction of the reduced linear system, even though the FOM linear system is never directly assembled. OMMI-POD modifies Minimally Invasive POD by performing the transport sweeps offline, thereby maximizing potential speedup. It achieves this by generating a library of reduced systems based on a training set, which is then interpolated in the online stage to provide a quick approximate solution to the $S_n$ transport equation. The model’s performance is evaluated on a 2-D test problem, demonstrating low error and a 150-fold speedup compared to the full order model.