Related papers: A unified framework for mesh refinement in random …

The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…

Image smoothing is a fundamental procedure in applications of both computer vision and graphics. The required smoothing properties can be different or even contradictive among different tasks. Nevertheless, the inherent smoothing nature of…

The de Rham complex arises naturally when studying problems in electromagnetism and fluid mechanics. Stable numerical methods to solve these problems can be obtained by using a discrete de Rham complex that preserves the structure of the…

An approach to utilizing adaptive mesh refinement algorithms for storm surge modeling is proposed. Currently numerical models exist that can resolve the details of coastal regions but are often too costly to be run in an ensemble…

Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…

In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a…

Material properties such as permeability fields in heterogeneous porous media are often represented as discontinuous, piecewise constant data tied to a given spatial discretization. Such representations are inherently mesh-dependent,…

Deep learning techniques have successfully been employed in numerous computer vision tasks including image segmentation. The techniques have also been applied to medical image segmentation, one of the most critical tasks in computer-aided…

A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…

In 3D shape reconstruction based on template mesh deformation, a regularization, such as smoothness energy, is employed to guide the reconstruction into a desirable direction. In this paper, we highlight an often overlooked property in the…

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…

This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Such data are commonly found in spatial applications, such as climatology and criminology, where measurements are restricted to a…

We present a suite of techniques for jointly optimizing triangle meshes and shading models to match the appearance of reference scenes. This capability has a number of uses, including appearance-preserving simplification of extremely…

Much recent progress has been made in reconstructing the 3D shape of an object from an image of it, i.e. single view 3D reconstruction. However, it has been suggested that current methods simply adopt a "nearest-neighbor" strategy, instead…

This paper presents a novel framework to recover detailed human body shapes from a single image. It is a challenging task due to factors such as variations in human shapes, body poses, and viewpoints. Prior methods typically attempt to…

Reasoning about 3D scenes from their 2D image projections is one of the core problems in computer vision. Solutions to this inverse and ill-posed problem typically involve a search for models that best explain observed image data. Notably,…

In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…

Model-free data-driven computational mechanics (DDCM) is a new paradigm for simulations in solid mechanics. The modeling step associated to the definition of a material constitutive law is circumvented through the introduction of an…

Accurate modeling of complex physical problems, such as fluid-structure interaction, requires multiphysics coupling across the interface, which often has intricate geometry and dynamic boundaries. Conventional numerical methods face…