5 papers
A low-rank, high-order implicit-explicit integrator for three-dimensional convection-diffusion equations
Joseph Nakao, Gianluca Ceruti, Lukas Einkemmer
This paper presents a rank-adaptive implicit-explicit integrator for the tensor approximation of three-dimensional convection-diffusion equations. In particular, the recently devel…
A Galerkin Alternating Projection Method for Kinetic Equations in the Diffusive Limit
Gianluca Ceruti, Nicolas Crouseilles, Lukas Einkemmer
The numerical approximation of high-dimensional evolution equations poses significant computational challenges, particularly in kinetic theory and radiative transfer. In this work,…
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…