Data-driven reduced-order models for the radiative transfer equation

Abstract

We present a data-driven reduced-order modeling (ROM) framework for the zeroth angular moment of the solution to the radiative transfer equation (RTE) rather than the full phase-space solution. Our construction is based on the Peierls integral formulation of the angularly averaged density. For media with isotropic scattering, the density satisfies a closed second-kind Fredholm equation with a globally attenuated, weakly singular kernel. We project this equation directly. For media with anisotropic scattering, we utilize the average-fluctuation decomposition to derive a closed system for a projection-based ROM. Numerical simulations are presented to illustrate the effectiveness of the ROMs we implemented.