Related papers: An adaptive dynamical low-rank optimizer for solvi…
Computing numerical solutions of the thermal radiative transfer equations on a finely resolved grid can be costly due to high computational and memory requirements. A numerical reduced order method that has recently been applied to a wide…
Radiation transport problems are posed in a high-dimensional phase space, limiting the use of finely resolved numerical simulations. An emerging tool to efficiently reduce computational costs and memory footprint in such settings is…
Low-rank methods have emerged as a promising strategy for reducing the memory footprint and computational cost of discrete-ordinates discretizations of the radiative transfer equation (RTE). However, most existing rank-adaptive approaches…
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 though it is well known that certain spatial and temporal…
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…
Dynamical low-rank approximation (DLRA) is a widely used paradigm for solving large-scale matrix differential equations, as they arise, for example, from the discretization of time-dependent partial differential equations on tensorized…
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…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…
Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…
PDE-constrained optimization problems arise in a broad number of applications such as hyperthermia cancer treatment or blood flow simulation. Discretization of the optimization problem and using a Lagrangian approach result in a large-scale…
Fine-tuning large-scale pre-trained models is inherently a resource-intensive task. While it can enhance the capabilities of the model, it also incurs substantial computational costs, posing challenges to the practical application of…
The numerical solution of kinetic equations is challenging due to the high dimensionality of the underlying phase space. In this paper, we develop a dynamical low-rank method based on the projector-splitting integrator in tensor-train (TT)…
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…
Due to its reduced memory and computational demands, dynamical low-rank approximation (DLRA) has sparked significant interest in multiple research communities. A central challenge in DLRA is the development of time integrators that are…
We introduce a dynamical low-rank method to reduce the computational complexity for solving the multi-scale multi-dimensional linear transport equation. The method is based on a macro-micro decomposition of the equation. The proposed…
In this paper, we develop a low-rank method with high-order temporal accuracy using spectral deferred correction (SDC) to compute linear matrix differential equations. In [1], a low rank numerical method is proposed to correct the modeling…
In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a…
Computing the numerical solution to high-dimensional tensor differential equations can lead to prohibitive computational costs and memory requirements. To reduce the memory and computational footprint, dynamical low-rank approximation…
Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction…