Dynamical low-rank approximation has become a valuable tool to perform an on-the-fly
model order reduction for prohibitively large matrix differential equations. A core ingredient …

Time-dependent kinetic models are ubiquitous in computational science and engineering.
The underlying integro-differential equations in these models are high-dimensional …

Dynamical low-rank approximation, as has been demonstrated recently, can be extremely
efficient in solving kinetic equations. However, a major deficiency is that it does not preserve …

Tensor network techniques, known for their low-rank approximation ability that breaks the
curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra …

The dynamical low-rank (DLR) approximation is an efficient technique to approximate the
solution to matrix differential equations. Recently, the DLR method was applied to radiation …

Radiation transport problems are posed in a high-dimensional phase space, limiting the use
of finely resolved numerical simulations. An emerging tool to efficiently reduce …

The stochastic description of chemical reaction networks with the kinetic chemical master
equation (CME) is important for studying biological cells, but it suffers from the curse of …

Computing the dominant eigenvalue is important in nuclear systems as it determines the
stability of the system (ie whether the system is sub or supercritical). Recently, the work of …

This paper introduces a novel computational approach termed the Reduced Augmentation
Implicit Low-rank (RAIL) method by investigating two predominant research directions in low …

In this article, we develop and validate an a priori Reduced-Order Model (ROM) of neutron
transport separated in energy by Proper Generalized Decomposition (PGD) as applied to …