A robust second-order low-rank BUG integrator based on the midpoint rule
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 …
model order reduction for prohibitively large matrix differential equations. A core ingredient …
A review of low-rank methods for time-dependent kinetic simulations
Time-dependent kinetic models are ubiquitous in computational science and engineering.
The underlying integro-differential equations in these models are high-dimensional …
The underlying integro-differential equations in these models are high-dimensional …
A hierarchical dynamical low-rank algorithm for the stochastic description of large reaction networks
L Einkemmer, J Mangott, M Prugger - arXiv preprint arXiv:2407.11792, 2024 - arxiv.org
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 …
equation (CME) is important for studying biological cells, but it suffers from the curse of …
Reduced Augmentation Implicit Low-rank (RAIL) integrators for advection-diffusion and Fokker-Planck models
This paper introduces a novel computational approach termed the Reduced Augmentation
Implicit Low-rank (RAIL) method by investigating two predominant research directions in low …
Implicit Low-rank (RAIL) method by investigating two predominant research directions in low …
Automatic partitioning for the low-rank integration of stochastic Boolean reaction networks
L Einkemmer, J Mangott, M Prugger - arXiv preprint arXiv:2501.04157, 2025 - arxiv.org
Boolean reaction networks are an important tool in biochemistry for studying mechanisms in
the biological cell. However, the stochastic formulation of such networks requires the …
the biological cell. However, the stochastic formulation of such networks requires the …
Second-order robust parallel integrators for dynamical low-rank approximation
J Kusch - arXiv preprint arXiv:2403.02834, 2024 - arxiv.org
Due to its reduced memory and computational demands, dynamical low-rank approximation
(DLRA) has sparked significant interest in multiple research communities. A central …
(DLRA) has sparked significant interest in multiple research communities. A central …
A stable multiplicative dynamical low-rank discretization for the linear Boltzmann-BGK equation
L Baumann, L Einkemmer, C Klingenberg… - arXiv preprint arXiv …, 2024 - arxiv.org
The numerical method of dynamical low-rank approximation (DLRA) has recently been
applied to various kinetic equations showing a significant reduction of the computational …
applied to various kinetic equations showing a significant reduction of the computational …
Bounds and Low-Rank Approximation for Controlled Markov Processes
F Holtorf - 2024 - dspace.mit.edu
Stochastic processes have captivated scientific interest by balancing conceptual simplicity
with the ability to model complex, poorly understood, or even entirely unknown phenomena …
with the ability to model complex, poorly understood, or even entirely unknown phenomena …