Related papers: Analysis-Aware Defeaturing of Dirichlet Features
We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…
Point clouds and polygonal meshes are widely used when modeling real-world scenarios. Here, point clouds arise, for instance, from acquisition processes applied in various surroundings, such as reverse engineering, rapid prototyping, or…
Feature reduction is an important concept which is used for reducing dimensions to decrease the computation complexity and time of classification. Since now many approaches have been proposed for solving this problem, but almost all of them…
We derive a computable a posteriori error estimator for the $\alpha$-harmonic extension problem, which localizes the fractional powers of elliptic operators supplemented with Dirichlet boundary conditions. Our a posteriori error estimator…
We propose a new and simpler residual based a posteriori error estimator for finite element approximation of the elliptic obstacle problem. The results in the article are two fold. Firstly, we address the influence of the inhomogeneous…
A convincing feature of least-squares finite element methods is the built-in a posteriori error estimator for any conforming discretization. In order to generalize this property to discontinuous finite element ansatz functions, this paper…
A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide…
We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a…
Shape descriptors, i.e., per-vertex features of 3D meshes or point clouds, are fundamental to shape analysis. Historically, various handcrafted geometry-aware descriptors and feature refinement techniques have been proposed. Recently,…
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…
For classification problems, feature extraction is a crucial process which aims to find a suitable data representation that increases the performance of the machine learning algorithm. According to the curse of dimensionality theorem, the…
Identifying defect patterns in a wafer map during manufacturing is crucial to find the root cause of the underlying issue and provides valuable insights on improving yield in the foundry. Currently used methods use deep neural networks to…
Approximate computing is being considered as a promising design paradigm to overcome the energy and performance challenges in computationally demanding applications. If the case where the accuracy can be configured, the quality level versus…
De-Rating or Vulnerability Factors are a major feature of failure analysis efforts mandated by today's Functional Safety requirements. Determining the Functional De-Rating of sequential logic cells typically requires computationally…
Feature selection is a crucial step in building machine learning models. This process is often achieved with accuracy as an objective, and can be cumbersome and computationally expensive for large-scale datasets. Several additional model…
Auxiliary features such as geometric buffers (G-buffers) and path descriptors (P-buffers) have been shown to significantly improve Monte Carlo (MC) denoising. However, recent approaches implicitly learn to exploit auxiliary features for…
The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…
This paper is concerned with adaptive mesh refinement strategies for the spatial discretization of parabolic problems with dynamic boundary conditions. This includes the characterization of inf-sup stable discretization schemes for a…
The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to…
Predictable Feature Analysis (PFA) (Richthofer, Wiskott, ICMLA 2015) is an algorithm that performs dimensionality reduction on high dimensional input signal. It extracts those subsignals that are most predictable according to a certain…