6 papers
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.…
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…
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…
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…
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…
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…