相关论文: Energy stable and conservative dynamical low-rank …
Existing low-rank adaptation (LoRA) methods face challenges on sparse large language models (LLMs) due to the inability to maintain sparsity. Recent works introduced methods that maintain sparsity by augmenting LoRA techniques with…
The widespread adoption of photovoltaic (PV), electric vehicles (EVs), and stationary energy storage systems (ESS) in households increases system complexity while simultaneously offering new opportunities for energy regulation. However,…
Continual machine unlearning aims to remove the influence of data that should no longer be retained, while preserving the usefulness of the model on everything else. This setting becomes especially difficult when deletion requests arrive…
With the ever-growing size of pretrained models (PMs), fine-tuning them has become more expensive and resource-hungry. As a remedy, low-rank adapters (LoRA) keep the main pretrained weights of the model frozen and just introduce some…
The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the under-resolved regime, mass conservation as well as energy stability…
In this work, we propose a Crank-Nicolson-type scheme with variable steps for the time fractional Allen-Cahn equation. The proposed scheme is shown to be unconditionally stable (in a variational energy sense), and is maximum bound…
The structure-preserving doubling algorithm (SDA) is a fairly efficient method for solving problems closely related to Hamiltonian (or Hamiltonian-like) matrices, such as computing the required solutions to algebraic Riccati equations.…
Predicting how the microstructure governs the mechanical response of heterogeneous materials is essential for optimizing design and performance. Yet this task remains difficult due to the complex, high dimensional nature of microstructural…
Heating, ventilation, and air conditioning (HVAC) systems are well proved to be capable to provide operating reserve for power systems. As a type of large-capacity and energy-efficient HVAC system (up to 100 MW), district cooling system…
We devise a space-time tensor method for the low-rank approximation of linear parabolic evolution equations. The proposed method is a stable Galerkin method, uniformly in the discretization parameters, based on a Minimal Residual…
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…
We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature,…
The integration of distributed energy resources (DER) has escalated the challenge of voltage magnitude regulation in distribution networks. Traditional model-based approaches, which rely on complex sequential mathematical formulations,…
We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple…
In this paper, a novel non-intrusive probabilistic power flow (PPF) analysis method based on the low-rank approximation (LRA) is proposed, which can accurately and efficiently estimate the probabilistic characteristics (e.g., mean,…
We present an energy conserving space discretisation based on a Poisson bracket that can be used to derive the dry compressible Euler as well as thermal shallow water equations. It is formulated using the compatible finite element method,…
We present a twofold contribution to the numerical simulation of Lindblad equations. First, an adaptive numerical approach to approximate Lindblad equations using low-rank dynamics is described: a deterministic low-rank approximation of the…
We introduce two novel interpolatory dynamical low-rank (DLR) approximation methods for the efficient time integration of the Boltzmann-BGK equation. Both methods overcome limitations of classic DLR schemes based on orthogonal projections…
Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In…
In this paper, we present a linearly implicit energy-preserving scheme for the Camassa-Holm equation by using the multiple scalar auxiliary variables approach, which is first developed to construct efficient and robust energy stable schemes…