Related papers: The enhanced derived-vector-space approach to doma…

The balancing domain decomposition methods (BDDC) are originally introduced for symmetric positive definite systems and have been extended to the nonsymmetric positive definite system from the linear finite element discretization of…

In this paper, we introduce Segmentation-Driven Deformation Multi-View Stereo (SD-MVS), a method that can effectively tackle challenges in 3D reconstruction of textureless areas. We are the first to adopt the Segment Anything Model (SAM) to…

This work proposes a method for solving linear stochastic optimal control (SOC) problems using sum of squares and semidefinite programming. Previous work had used polynomial optimization to approximate the value function, requiring a high…

A strategy to construct physics-based local surrogate models for parametric Stokes flows and coupled Stokes-Darcy systems is presented. The methodology relies on the proper generalized decomposition (PGD) method to reduce the dimensionality…

Existing image deraining methods typically rely on single-input, single-output, and single-scale architectures, which overlook the joint multi-scale information between external and internal features. Furthermore, single-domain…

The support vector machine (SVM) is a widely used method for classification. Although many efforts have been devoted to develop efficient solvers, it remains challenging to apply SVM to large-scale problems. A nice property of SVM is that…

To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the…

Real-world video super-resolution (VSR) presents significant challenges due to complex and unpredictable degradations. Although some recent methods utilize image diffusion models for VSR and have shown improved detail generation…

This paper presents two novel ensemble domain decomposition methods for fast-solving the Stokes-Darcy coupled models with random hydraulic conductivity and body force. To address such random systems, we employ the Monte Carlo (MC) method to…

In recent work, Li et al.\ (Comm.\ Math.\ Sci., 7:81-107, 2009) developed a diffuse-domain method (DDM) for solving partial differential equations in complex, dynamic geometries with Dirichlet, Neumann, and Robin boundary conditions. The…

Originally designed for applications in computer graphics, visual computing (VC) methods synthesize information about physical and virtual worlds, using prescribed algorithms optimized for spatial computing. VC is used to analyze geometry,…

Mesh reconstruction of the cardiac anatomy from medical images is useful for shape and motion measurements and biophysics simulations to facilitate the assessment of cardiac function and health. However, 3D medical images are often acquired…

Medical image super-resolution (SR) is an active research area that has many potential applications, including reducing scan time, bettering visual understanding, increasing robustness in downstream tasks, etc. However, applying…

Hybrid algorithms, which combine black-box machine learning methods with experience from traditional numerical methods and domain expertise from diverse application areas, are progressively gaining importance in scientific machine learning…

This paper proposes a new approach to achieve direct visual servoing (DVS) based on discrete orthogonal moments (DOMs). DVS is performed in such a way that the extraction of geometric primitives, matching, and tracking steps in the…

Current state-of-the-art self-supervised approaches, are effective when trained on individual domains but show limited generalization on unseen domains. We observe that these models poorly generalize even when trained on a mixture of…

This paper deals with the parallel simulation of delamination problems at the meso-scale by means of multi-scale methods, the aim being the Virtual Delamination Testing of Composite parts. In the non-linear context, Domain Decomposition…

Two-level domain decomposition (DD) methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level…

State of the art domain decomposition algorithms for large-scale boundary value problems (with $M\gg 1$ degrees of freedom) suffer from bounded strong scalability because they involve the synchronisation and communication of workers…

Diffusion models (DMs) have exhibited remarkable efficacy in various image restoration tasks. However, existing approaches typically operate within the high-dimensional pixel space, resulting in high computational overhead. While methods…