Related papers: Multilevel spectral coarsening for graph Laplacian…
We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Data-driven approaches for inverse problems aim for learning model and regularization parameters from observed data samples, and…
In this paper, we present Laplacian multiscale flow matching (LapFlow), a novel framework that enhances flow matching by leveraging multi-scale representations for image generative modeling. Our approach decomposes images into Laplacian…
Inpainting based image compression approaches, especially linear and non-linear diffusion models, are an active research topic for lossy image compression. The major challenge in these compression models is to find a small set of…
A high-performance gas kinetic solver using multi-level parallelization is developed to enable pore-scale simulations of rarefied flows in porous media. The Boltzmann model equation is solved by the discrete velocity method with an…
We study a two-stage mixed-integer linear program (MILP) with more than 1 million binary variables in the second stage. We develop a two-level approach by constructing a semi-coarse model (coarsened with respect to variables) and a coarse…
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…
We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of…
In this paper, we present an upscaling method for problems in perforated domains with non-homogeneous boundary conditions on perforations. Our methodology is based on the recently developed Non-local multicontinuum method (NLMC). The main…
Many Machine Learning algorithms are formulated as regularized optimization problems, but their performance hinges on a regularization parameter that needs to be calibrated to each application at hand. In this paper, we propose a general…
Derivation of macroscopic models for advection-diffusion processes in the presence of dominant heterogeneous (e.g., surface) reactions using homogenisation theory or volume averaging is often deemed unfeasible due to the strong coupling…
Deterministic interpolation and quadrature methods are often unsuitable to address Bayesian inverse problems depending on computationally expensive forward mathematical models. While interpolation may give precise posterior approximations,…
In this paper, we propose a new class of operator factorization methods to discretize the integral fractional Laplacian $(-\Delta)^\frac{\alpha}{2}$ for $\alpha \in (0, 2)$. The main advantage of our method is to easily increase numerical…
In this paper, we consider a class of models for multiphase fluids, in the framework of mixture theory. The considered system, in its more general form, contains both the gradient of a hydrostatic pressure, generated by an incompressibility…
Many large-scale optimization problems arising in science and engineering are naturally defined at multiple levels of discretization or model fidelity. Multilevel methods exploit this hierarchy to accelerate convergence by combining coarse-…
Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…
In this work, we propose a smart idea to couple importance sampling and Multilevel Monte Carlo (MLMC). We advocate a per level approach with as many importance sampling parameters as the number of levels, which enables us to compute the…
A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…
Inverse problems occur in a variety of parameter identification tasks in engineering. Such problems are challenging in practice, as they require repeated evaluation of computationally expensive forward models. We introduce a unifying…