Related papers: Layer-adapted meshes for weak boundary layers
Existing metric learning losses can be categorized into two classes: pair-based and proxy-based losses. The former class can leverage fine-grained semantic relations between data points, but slows convergence in general due to its high…
In this note we give a precise statement and a detailed proof for reconstruction problem of weak bialgebra maps. As an application we characterize indecomposability of weak algebras in categorical setting.
An adaptive algorithm for computing eigenmodes and propagation constants of optical fibers is proposed. The algorithm is built using a dual-weighted residual error estimator. The residuals are based on the eigensystem for leaky hybrid modes…
Deep neural networks are learning models having achieved state of the art performance in many fields like prediction, computer vision, language processing and so on. However, it has been shown that certain inputs exist which would not trick…
Deep learning has thrived by training on large-scale datasets. However, in robotics applications sample efficiency is critical. We propose a novel adaptive masked proxies method that constructs the final segmentation layer weights from few…
In this paper, we present an immersed weak Galerkin method for solving second-order elliptic interface problems. The proposed method does not require the meshes to be aligned with the interface. Consequently, uniform Cartesian meshes can be…
We construct positive weak solutions of a class of semilinear elliptic equation which vanish in suitable trace sense on the boundary of a given smooth bounded N-dimensional domain, but which are singular at prescribed isolated points of the…
This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…
We generalize the "facial weak order" of a finite Coxeter group to a partial order on a set of intervals in a complete lattice. We apply our construction to the lattice of torsion classes of a finite-dimensional algebra and consider its…
For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of meso-scale approximations. There are no assumptions of periodicity involved…
In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…
This paper introduces an approach to decoupling singularly perturbed boundary value problems for fourth-order ordinary differential equations that feature a small positive parameter $\epsilon$ multiplying the highest derivative. We…
Glass-like objects such as windows, bottles, and mirrors exist widely in the real world. Sensing these objects has many applications, including robot navigation and grasping. However, this task is very challenging due to the arbitrary…
In this paper, we use various ansatzes with undetermined functions and the technique of moving frame to find solutions with parameter functions modulo the Lie point symmetries for the classical non-steady boundary layer problems. These…
We define a weak compatibility condition for the Newest Vertex Bisection algorithm on simplex grids of any dimension and show that using this condition the iterative algorithm terminates successfully. Additionally we provide an O(n)…
Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…
Meta-learning algorithms are widely used for few-shot learning. For example, image recognition systems that readily adapt to unseen classes after seeing only a few labeled examples. Despite their success, we show that modern meta-learning…
Metamaterials are being used to model various exotic "optical spaces" for such applications as novel lenses and cloaking. While most effort is directed towards engineering of continuously changing dielectric permittivity and magnetic…
Deep learning models have been efficient lately on image parsing tasks. However, deep learning models are not fully capable of exploiting visual and contextual information simultaneously. The proposed three-layer context-based deep…
We introduce a new class of absorbing boundary conditions (ABCs) for the Helmholtz equation. The proposed ABCs are obtained by using $L$ discrete layers and the $Q_N$ Lagrange finite element in conjunction with the $N$-point Gauss-Legendre…