相关论文: A non-uniform corner-cutting subdivision scheme wi…

It is shown in this paper that non-conforming finite elements on the triangle using $P^{1}$-nonconforming polynomials and $P^{2}$ -conforming polynomials can be easily built and used.They appear as an 'enriched' version of the standard…

The aim of this paper is to study a whole class of first order differential inclusions, which fit into the framework of perturbed sweeping process by uniformly prox-regular sets. After obtaining well-posedness results, we propose a…

In this paper, a parameter-uniform fitted mesh finite difference scheme is constructed and analyzed for a class of singularly perturbed interior turning point problems. The solution of this class of turning point problem possess two outflow…

In this article, we propose a new algorithm for supervised learning methods, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, an ideal…

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…

This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…

A new second-order numerical scheme based on an operator splitting is proposed for the Godunov-Peshkov-Romenski model of continuum mechanics. The homogeneous part of the system is solved with a finite volume method based on a WENO…

Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…

Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…

A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic…

Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic…

The ability to extrapolate gene expression dynamics in living single cells requires robust cell segmentation, and one of the challenges is the amorphous or irregularly shaped cell boundaries. To address this issue, we modified the U-Net…

Organ segmentation in CT volumes is an important pre-processing step in many computer assisted intervention and diagnosis methods. In recent years, convolutional neural networks have dominated the state of the art in this task. However,…

Deep neural networks (DNNs) offer significant flexibility and robust performance. This makes them ideal for building not only system models but also advanced neural network controllers (NNCs). However, their high complexity and…

We propose two new strategies based on Machine Learning techniques to handle polyhedral grid refinement, to be possibly employed within an adaptive framework. The first one employs the k-means clustering algorithm to partition the points of…

This paper introduces an efficient algorithm for computing the best approximation of a given matrix onto the intersection of linear equalities, inequalities and the doubly nonnegative cone (the cone of all positive semidefinite matrices…

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

The aim of this study is to develop a novel WENO scheme that improves the performance of the well-known fifth-order WENO methods. The approximation space consists of exponential polynomials with a tension parameter that may be optimized to…

In this paper, a new algorithm for extracting features from sequences of multidimensional observations is presented. The independently developed Dynamic Mode Decomposition and Matrix Pencil methods provide a least-squares model-based…

This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradients. Based on this observation, we propose three numerical…