  A new group of reduced-order models (ROMs) for nonlinear thermal radiative
transfer (TRT) problems is presented. They are formulated by means of the
nonlinear projective approach and data compression techniques. The nonlinear
projection is applied to the Boltzmann transport equation (BTE) to derive a
hierarchy of low-order moment equations. The Eddington (quasidiffusion) tensor
that provides exact closure for the system of moment equations is approximated
via one of several data-based methods of model-order reduction. These methods
are the (i) proper orthogonal decomposition, (ii) dynamic mode decomposition
(DMD), (iii) an equilibrium-subtracted DMD variant. Numerical results are
presented to demonstrate the performance of these ROMs for the simulation of
evolving radiation and heat waves. Results show these models to be accurate
even with very low-rank representations of the Eddington tensor. As the rank of
the approximation is increased, the errors of solutions generated by the ROMs
gradually decreases.
