Related papers: Layer-adapted meshes for weak boundary layers

Neural networks are vulnerable to adversarial attacks -- small visually imperceptible crafted noise which when added to the input drastically changes the output. The most effective method of defending against these adversarial attacks is to…

The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…

Weakly supervised object detection (WSOD) using only image-level annotations has attracted a growing attention over the past few years. Whereas such task is typically addressed with a domain-specific solution focused on natural images, we…

Adaptive, locally refined and locally adjusted meshes are preferred over uniform meshes for capturing singular or localised solutions. Roughly speaking, for a given degree of freedom a solution associated with adaptive, locally refined and…

We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…

This paper proposes a way to improve the performance of existing algorithms for text classification in domains with strong language semantics. We propose a domain adaptation layer learns weights to combine a generic and a domain specific…

Weak gravitational lensing of distant galaxies by foreground structures has proven to be a powerful tool to study the mass distribution in the universe. Nowadays, attention has shifted from clusters of galaxies to the statistical properties…

This paper addresses the problem of evaluating the quality of finite element meshes for the purpose of structural mechanic simulations. It proposes the application of a machine learning model trained on data collected from expert…

Highly expressive models such as deep neural networks (DNNs) have been widely applied to various applications. However, recent studies show that DNNs are vulnerable to adversarial examples, which are carefully crafted inputs aiming to…

We establish a generic weak uniqueness result and partial regularity of the free boundary and of minimizers for the composite membrane problem.

In this paper, we propose a defence strategy to improve adversarial robustness by incorporating hidden layer representation. The key of this defence strategy aims to compress or filter input information including adversarial perturbation.…

Deep neural networks have dramatically advanced the state of the art for many areas of machine learning. Recently they have been shown to have a remarkable ability to generate highly complex visual artifacts such as images and text rather…

In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in $H^1$-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular…

Convolutional neural networks (CNNs) have demonstrated their capability to solve different kind of problems in a very huge number of applications. However, CNNs are limited for their computational and storage requirements. These limitations…

Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer master problem and a continuous…

While deep neural networks have succeeded in several visual applications, such as object recognition, detection, and localization, by reaching very high classification accuracies, it is important to note that many real-world applications…

The single Anti-Reflecting (AR) layer is a classical problem in optics. When all materials are pure dielectrics, the solution is the so-called lambda/4 layer. Here we examine the case of absorbing layers between non absorbing media. We find…

Recent methods for boundary or edge detection built on Deep Convolutional Neural Networks (CNNs) typically suffer from the issue of predicted edges being thick and need post-processing to obtain crisp boundaries. Highly imbalanced…

This paper proposes an importance weighted adversarial nets-based method for unsupervised domain adaptation, specific for partial domain adaptation where the target domain has less number of classes compared to the source domain. Previous…

Scene recognition, particularly for aerial and underwater images, often suffers from various types of degradation, such as blurring or overexposure. Previous works that focus on convolutional neural networks have been shown to be able to…