Related papers: Concurrent multiscale analysis without meshing: Mi…
We consider in this paper a challenging problem of simulating fluid flows, in complex multiscale media possessing multi-continuum background. As an effort to handle this obstacle, model reduction is employed. In \cite{rh2}, homogenization…
We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain computational efficiency. By using a conveniently constructed…
Stochastic modeling has become a popular approach to quantify uncertainty in flows through heterogeneous porous media. The uncertainty in heterogeneous structure properties is often parameterized by a high-dimensional random variable. This…
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 paper, we study the development of efficient multiscale methods for flows in heterogeneous media. Our approach uses the Generalized Multiscale Finite Element (GMsFEM) framework. The main idea of GMsFEM is to approximate the solution…
Modern 'smart' materials have complex heterogeneous microscale structure, often with unknown macroscale closure but one we need to realise for large scale engineering and science. The multiscale Equation-Free Patch Scheme empowers us to…
We present MIX'EM, a novel solution for unsupervised image classification. MIX'EM generates representations that by themselves are sufficient to drive a general-purpose clustering algorithm to deliver high-quality classification. This is…
In this work, we extend the meshfree generalized multiscale exponential integration framework introduced in Nikiforov et al. (2025) to the simulation of three-dimensional advection--diffusion problems in heterogeneous and high-contrast…
Deep learning-based image fusion approaches have obtained wide attention in recent years, achieving promising performance in terms of visual perception. However, the fusion module in the current deep learning-based methods suffers from two…
Materials exhibit geometric structures across mesoscopic to microscopic scales, influencing macroscale properties such as appearance, mechanical strength, and thermal behavior. Capturing and modeling these multiscale structures is…
Whole slide image (WSI) analysis has emerged as an increasingly essential technique in computational pathology. Recent advances in the pathology foundation models (FMs) have demonstrated significant advantages in deriving meaningful…
The Multiscale Finite Element Method (MsFEM) is developed in the vein of Crouzeix-Raviart element for solving viscous incompressible flows in genuine heterogeneous media. Such flows are relevant in many branches of engineering, often at…
Image analysis using more than one modality (i.e. multi-modal) has been increasingly applied in the field of biomedical imaging. One of the challenges in performing the multimodal analysis is that there exist multiple schemes for fusing the…
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite…
In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced-order methods are demanded. Combining these…
Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions…
This paper presents a multiscale modeling framework (MMF) to model moist atmospheric limited-area weather. The MMF resolves large-scale convection using a coarse grid while simultaneously resolving local features through numerous fine local…
This work presents a multi-level modeling and design framework for weft knitted fabrics, beginning with a volumetric finite element analysis capturing their mechanical behavior from fundamental principles. Incorporating yarn-level data, it…
In multiscale modelling, multiple models are used simultaneously to describe scale-dependent phenomena in a system of interest. Here we introduce a machine learning (ML)-based multiscale modelling framework for modelling hierarchical…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…