5 citations · 18 across the 18 of their papers we have counts for
20 papers
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 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 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…
Randomized low-rank Runge-Kutta methods
Hei Yin Lam, Gianluca Ceruti, Daniel Kressner
This work proposes and analyzes a new class of numerical integrators for computing low-rank approximations to solutions of matrix differential equation. We combine an explicit Rung…
Low-rank Tree Tensor Network Operators for Long-Range Pairwise Interactions
Gianluca Ceruti, Daniel Kressner, Dominik Sulz
Compactly representing and efficently applying linear operators are fundamental ingredients in tensor network methods for simulating quantum many-body problems and solving high-dim…
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…
From low-rank retractions to dynamical low-rank approximation and back
Axel Séguin, Gianluca Ceruti, Daniel Kressner
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More rec…
Robust low-rank training via approximate orthonormal constraints
Dayana Savostianova, Emanuele Zangrando, Gianluca Ceruti +1
With the growth of model and data sizes, a broad effort has been made to design pruning techniques that reduce the resource demand of deep learning pipelines, while retaining model…
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…
Numerical simulations of long-range open quantum many-body dynamics with tree tensor networks
Dominik Sulz, Christian Lubich, Gianluca Ceruti +2
Open quantum systems provide a conceptually simple setting for the exploration of collective behavior stemming from the competition between quantum effects, many-body interactions,…
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…
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…
Rank-adaptive time integration of tree tensor networks
Gianluca Ceruti, Christian Lubich, Dominik Sulz
A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves…
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…
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…
An unconventional robust integrator for dynamical low-rank approximation
Gianluca Ceruti, Christian Lubich
We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are t…
Time integration of tree tensor networks
Gianluca Ceruti, Christian Lubich, Hanna Walach
Dynamical low-rank approximation by tree tensor networks is studied for the data-sparse approximation to large time-dependent data tensors and unknown solutions of tensor different…
Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors
Gianluca Ceruti, Christian Lubich
A numerical integrator is presented that computes a symmetric or skew-symmetric low-rank approximation to large symmetric or skew-symmetric time-dependent matrices that are either…