Related papers: A high-order deterministic dynamical low-rank meth…
The claim that Monte Carlo is the most accurate method is a case of misattributed credit. This claim is based on experience with advanced systems MCNPX, Geant4 and EGS. These systems achieve remarkable performance because they use most…
Large Language Models (LLMs) have transformed both everyday life and scientific research. However, adapting LLMs from general-purpose models to specialized tasks remains challenging, particularly in resource-constrained environments.…
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 solution of a master equation which inherently suffers from…
Long-range interactions play a central role in electron transport. At the same time, they present a challenge for direct computer simulations, since sufficiently large portions of the bath have to be included in the computation to…
We introduce an $hp$-version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
Constrained tensor and matrix factorization models allow to extract interpretable patterns from multiway data. Therefore identifiability properties and efficient algorithms for constrained low-rank approximations are nowadays important…
This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of…
The radiative transfer equation models various physical processes ranging from plasma simulations to radiation therapy. In practice, these phenomena are often subject to uncertainties. Modeling and propagating these uncertainties requires…
In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semilinear stiff matrix differential equations, we propose…
Accurate dose calculation is vitally important for proton therapy. Pencil beam (PB) model-based dose calculation is fast but inaccurate due to the approximation when dealing with inhomogeneities. Monte Carlo (MC) dose calculation is the…
Low rank approximation of a matrix (hereafter LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with an LRA at sublinear cost -- by using much fewer memory cells and…
This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the…
Proton pencil beam scanning (PBS) treatment planning for head and neck (H&N) cancers is a time-consuming and experience-demanding task where a large number of planning objectives are involved. Deep reinforcement learning (DRL) has recently…
In this paper, we propose a novel reduced-rank algorithm for direction of arrival (DOA) estimation based on the minimum variance (MV) power spectral evaluation. It is suitable to DOA estimation with large arrays and can be applied to…
Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…
Low-Rank Adaptation (LoRA) has emerged as an effective technique for reducing memory overhead in fine-tuning large language models. However, it often suffers from sub-optimal performance compared with full fine-tuning since the update is…
We analyze connections between two low rank modeling approaches from the last decade for treating dynamical data. The first one is the coherence problem (or coherent set approach), where groups of states are sought that evolve under the…
Weighted low rank approximation (WLRA) is an important yet computationally challenging primitive with applications ranging from statistical analysis, model compression, and signal processing. To cope with the NP-hardness of this problem,…