25 citations · 95 across the 27 of their papers we have counts for
30 papers
A review of low-rank methods for time-dependent kinetic simulations
Lukas Einkemmer, Katharina Kormann, Jonas Kusch +2
Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised…
A parallel Basis Update and Galerkin Integrator for Tree Tensor Networks
Gianluca Ceruti, Jonas Kusch, Christian Lubich +1
Computing the numerical solution to high-dimensional tensor differential equations can lead to prohibitive computational costs and memory requirements. To reduce the memory and com…
A stable multiplicative dynamical low-rank discretization for the linear Boltzmann-BGK equation
Lena Baumann, Lukas Einkemmer, Christian Klingenberg +1
The numerical method of dynamical low-rank approximation (DLRA) has recently been applied to various kinetic equations showing a significant reduction of the computational effort.…
GeoLoRA: Geometric integration for parameter efficient fine-tuning
Steffen Schotthöfer, Emanuele Zangrando, Gianluca Ceruti +2
Low-Rank Adaptation (LoRA) has become a widely used method for parameter-efficient fine-tuning of large-scale, pre-trained neural networks. However, LoRA and its extensions face se…
A multi-fidelity adaptive dynamical low-rank based optimization algorithm for fission criticality problems
C. Scalone, L. Einkemmer, J. Kusch +1
Computing the dominant eigenvalue is important in nuclear systems as it determines the stability of the system (i.e. whether the system is sub or supercritical). Recently, the work…
Second-order robust parallel integrators for dynamical low-rank approximation
Jonas Kusch
Due to its reduced memory and computational demands, dynamical low-rank approximation (DLRA) has sparked significant interest in multiple research communities. A central challenge…
Asymptotic-preserving and energy stable dynamical low-rank approximation for thermal radiative transfer equations
Chinmay Patwardhan, Martin Frank, Jonas Kusch
The thermal radiative transfer equations model temperature evolution through a background medium as a result of radiation. When a large number of particles are absorbed in a short…
A robust second-order low-rank BUG integrator based on the midpoint rule
Gianluca Ceruti, Lukas Einkemmer, Jonas Kusch +1
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…
Construction of high-order conservative basis-update and Galerkin dynamical low-rank integrators
Lukas Einkemmer, Jonas Kusch, Steffen Schotthöfer
Numerical simulations of kinetic problems can become prohibitively expensive due to their large memory requirements and computational costs. A method that has proven to successfull…
Energy stable and conservative dynamical low-rank approximation for the Su-Olson problem
Lena Baumann, Lukas Einkemmer, Christian Klingenberg +1
Computational methods for thermal radiative transfer problems exhibit high computational costs and a prohibitive memory footprint when the spatial and directional domains are finel…
Geometry-aware training of factorized layers in tensor Tucker format
Emanuele Zangrando, Steffen Schotthöfer, Gianluca Ceruti +2
Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during training and inference phases. Given…
A parallel rank-adaptive integrator for dynamical low-rank approximation
Gianluca Ceruti, Jonas Kusch, Christian Lubich
This work introduces a parallel and rank-adaptive matrix integrator for dynamical low-rank approximation. The method is related to the previously proposed rank-adaptive basis updat…
Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: A study using POD-Galerkin and dynamical low rank approximation
Julian Koellermeier, Philipp Krah, Jonas Kusch
Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system.…
Asymptotic--preserving and energy stable dynamical low-rank approximation
Lukas Einkemmer, Jingwei Hu, Jonas Kusch
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 computat…
KiT-RT: An extendable framework for radiative transfer and therapy
Jonas Kusch, Steffen Schotthöfer, Pia Stammer +2
In this paper we present KiT-RT (Kinetic Transport Solver for Radiation Therapy), an open-source C++ based framework for solving kinetic equations in radiation therapy applications…
Low-rank lottery tickets: finding efficient low-rank neural networks via matrix differential equations
Steffen Schotthöfer, Emanuele Zangrando, Jonas Kusch +2
Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in applica…
A low-rank power iteration scheme for neutron transport criticality problems
Jonas Kusch, Benjamin Whewell, Ryan McClarren +1
Computing effective eigenvalues for neutron transport often requires a fine numerical resolution. The main challenge of such computations is the high memory effort of classical sol…
A flux reconstruction stochastic Galerkin scheme for hyperbolic conservation laws
Tianbai Xiao, Jonas Kusch, Julian Koellermeier +1
The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the…
A robust collision source method for rank adaptive dynamical low-rank approximation in radiation therapy
Jonas Kusch, Pia Stammer
Deterministic models for radiation transport describe the density of radiation particles moving through a background material. In radiation therapy applications, the phase space of…
On the stability of robust dynamical low-rank approximations for hyperbolic problems
Jonas Kusch, Lukas Einkemmer, Gianluca Ceruti
The dynamical low-rank approximation (DLRA) is used to treat high-dimensional problems that arise in such diverse fields as kinetic transport and uncertainty quantification. Even t…
A Realizable Filtered Intrusive Polynomial Moment Method
Graham Alldredge, Martin Frank, Jonas Kusch +1
Intrusive uncertainty quantification methods for hyperbolic problems exhibit spurious oscillations at shocks, which leads to a significant reduction of the overall approximation qu…
Dynamical low-rank approximation for Burgers' equation with uncertainty
Jonas Kusch, Gianluca Ceruti, Lukas Einkemmer +1
Quantifying uncertainties in hyperbolic equations is a source of several challenges. First, the solution forms shocks leading to oscillatory behaviour in the numerical approximatio…
A rank-adaptive robust integrator for dynamical low-rank approximation
Gianluca Ceruti, Jonas Kusch, Christian Lubich
A rank-adaptive integrator for the dynamical low-rank approximation of matrix and tensor differential equations is presented. The fixed-rank integrator recently proposed by two of…
Oscillation Mitigation of Hyperbolicity-Preserving Intrusive Uncertainty Quantification Methods for Systems of Conservation Laws
Jonas Kusch, Louisa Schlachter
In this article we study intrusive uncertainty quantification schemes for systems of conservation laws with uncertainty. Standard intrusive methods lead to oscillatory solutions wh…