Related papers: Impact Study of Numerical Discretization Accuracy …
In this paper we analyze several strategies for the estimation of the roughness parameter of the $\mathcal G_I^0$ distribution. It has been shown that this distribution is able to characterize a large number of targets in monopolarized SAR…
Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain…
In this paper we address the problem of discretization in the context of learning Bayesian networks (BNs) from data containing both continuous and discrete variables. We describe a new technique for <EM>multivariate</EM> discretization,…
Determining the dimensions of nanostructures is critical to ensuring the maximum performance of many geometry-sensitive nanoscale functional devices. However, accurate metrology at the nanoscale is difficult using optics-based methods due…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
We study a higher-order surface finite element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which are equivalent in the continuous setting. The impact of the…
The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to…
In this article we apply reduced order techniques for the approximation of parametric eigenvalue problems. The effect of the choice of sampling points is investigated. Here we use the standard proper orthogonal decomposition technique to…
Highly confined vectorial electromagnetic field distributions represent an excellent tool for detailed studies in nano-optics and high resolution microscopy, such as nonlinear microscopy, advanced fluorescence imaging or nanoplasmonics.…
The goal of the present paper is to understand the impact of numerical schemes for the reconstruction of data at cell faces in finite-volume methods, and to assess their interaction with the quadrature rule used to compute the average over…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…
We propose a new modeling approach for scatter estimation and descattering in polyenergetic X-ray computed tomography (CT) based on fitting models to local neighborhoods of a training set. X-ray CT is widely used in medical and industrial…
We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discretisation method is proposed based on a finite element…
Microstructure reconstruction has been an essential part of computational material engineering to reveal the relationship between microstructures and material properties. However, finding a general solution for microstructure…
Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space,…
Convolutional autoencoders have emerged as popular methods for unsupervised defect segmentation on image data. Most commonly, this task is performed by thresholding a pixel-wise reconstruction error based on an $\ell^p$ distance. This…
The problem of the logarithmic discretization of an arbitrary positive function (such as the density of states) is studied in general terms. Logarithmic discretization has arbitrary high resolution around some chosen point (such as Fermi…
Low-variance gradient estimation is crucial for learning directed graphical models parameterized by neural networks, where the reparameterization trick is widely used for those with continuous variables. While this technique gives…
In this work, we develop a novel technique for reconstructing images from projection-based nano- and microtomography. Our contribution focuses on enhancing reconstruction quality, particularly for specimen composed of homogeneous material…