A High-Order / Low-Order (HOLO) Algorithm with Low-Rank Evolution for Time-Dependent Transport Calculations

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

“…Plugging the auxiliary equations (55) in Eq. ( 54) we obtain the corner-balance equations in terms of the corner normalized intensities…”

“…The PGD has been used to seperate variables in the BTE solution in several geometries [51,52,53]. A low-rank manifold projection technique has been used in constructing ROMs for time-dependent problems [54,55,56,57]. Surrogate models for the BTE have been created using the DMD [58] and various neural network architectures [59,60,61].…”

“…A new approach based on data-driven reduced-order models (ROMs) has been gaining popularity in recent years which make use of data-based methodologies to dimensionality reduction. Data-driven models have been developed for (i) linear particle transport problems [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] (ii) nonlinear RT problems [49,50,51,52,53,54,55,56,57,58,59,60], and (iii) various problems in nuclear reactor-physics [61,62,63,64,65,66,67,68,69,70,71]. The fundamental idea behind these ROMs is to leverage databases of solutions to their problems of interest (known a-priori) to develop some reduction in the dimensionality for their involved equations.…”