Related papers: Two continuous extensions of the Neural Approximat…

In this paper, we propose a robust low-order stabilization-free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress-hybrid principle. We refer to this approach as the Stress-Hybrid Virtual…

The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element…

We study a family of $H^m$-conforming piecewise polynomials based on artificial neural network, named as the finite neuron method (FNM), for numerical solution of $2m$-th order partial differential equations in $\mathbb{R}^d$ for any $m,d…

The spectrum of the Laplace-Beltrami (LB) operator is central in geometric deep learning tasks, capturing intrinsic properties of the shape of the object under consideration. The best established method for its estimation, from a…

For the solution of 2D exterior Dirichlet Poisson problems we propose the coupling of a Curved Virtual Element Method (CVEM) with a Boundary Element Method (BEM), by using decoupled approximation orders. We provide optimal convergence error…

The focus of this study is the construction and numerical validation of parallel block preconditioners for low order virtual element discretizations of the three-dimensional Maxwell equations. The virtual element method (VEM) is a recent…

Embedding is a useful technique to project a high-dimensional feature into a low-dimensional space, and it has many successful applications including link prediction, node classification and natural language processing. Current approaches…

We analyse the p- and hp-versions of the virtual element method (VEM) for the the Stokes problem on a polygonal domain. The key tool in the analysis is the existence of a bijection between Poisson-like and Stokes-like VE spaces for the…

Current Deep Learning methods for environment segmentation and velocity estimation rely on Convolutional Recurrent Neural Networks to exploit spatio-temporal relationships within obtained sensor data. These approaches derive scene dynamics…

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

Legged robots have the potential to expand the reach of autonomy beyond paved roads. In this work, we consider the difficult problem of locomotion on challenging terrains using a single forward-facing depth camera. Due to the partial…

We develop a neuroevolution-potential (NEP) framework for generating neural network based machine-learning potentials. They are trained using an evolutionary strategy for performing large-scale molecular dynamics (MD) simulations. A…

In this work, we analyse a simplified frictional contact problem and its variational formulation that has a form of the elliptic variational inequality of the second kind. For this problem, we consider a numerical approximation based on…

This paper summarizes the development of mVEM, a MATLAB software package containing efficient and easy-following codes for various virtual element methods (VEMs) published in the literature. We explain in detail the numerical implementation…

Vision and Language Navigation (VLN) requires an agent to navigate to a target location by following natural language instructions. Most of existing works represent a navigation candidate by the feature of the corresponding single view…

In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is systematically studied. The local spaces are built from selected eigenvectors…

The third medium contact has been proven to be an effective approach for simulating contact problems involving large deformations. Unlike traditional contact algorithms, the third medium contact introduces a third medium between two…

We present a Virtual Element Method (VEM) for a nonlocal reaction-diffusion system of the cardiac electric field. To this system, we analyze an $H^1(\Omega)$-conforming discretization by means of VEM which can make use of general polygonal…

Semi-supervised learning has received a lot of recent attention as it alleviates the need for large amounts of labelled data which can often be expensive, requires expert knowledge and be time consuming to collect. Recent developments in…

The data bottleneck has emerged as a fundamental challenge in learning based image restoration methods. Researchers have attempted to generate synthesized training data using paired or unpaired samples to address this challenge. This study…