Related papers: Polytopal mesh agglomeration via geometrical deep …

Agglomeration-based strategies are important both within adaptive refinement algorithms and to construct scalable multilevel algebraic solvers. In order to automatically perform agglomeration of polygonal grids, we propose the use of…

We introduce MAGNET, an open-source Python library designed for mesh agglomeration in both two- and three-dimensions, based on employing Graph Neural Networks (GNN). MAGNET serves as a comprehensive solution for training a variety of GNN…

3D meshes are fundamental data representations for capturing complex geometric shapes in computer vision and graphics applications. While Convolutional Neural Networks (CNNs) have excelled in structured data like images, extending them to…

We present GeGnn, a learning-based method for computing the approximate geodesic distance between two arbitrary points on discrete polyhedra surfaces with constant time complexity after fast precomputation. Previous relevant methods either…

Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as…

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network…

Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in…

This work provides an architecture that incorporates depth and tactile information to create rich and accurate 3D models useful for robotic manipulation tasks. This is accomplished through the use of a 3D convolutional neural network (CNN).…

This paper compares the performance of seven different element agglomeration algorithms on unstructured triangular/tetrahedral meshes when used as part of a geometric multigrid. Five of these algorithms come from the literature on AMGe…

We present a novel approach to perform agglomeration of polygonal and polyhedral grids based on spatial indices. Agglomeration strategies are a key ingredient in polytopal methods for PDEs as they are used to generate (hierarchies of)…

The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer…

In CFD, mesh smoothing methods are commonly utilized to refine the mesh quality to achieve high-precision numerical simulations. Specifically, optimization-based smoothing is used for high-quality mesh smoothing, but it incurs significant…

Graph convolutional networks (GCNs) have been employed as a kind of significant tool on many graph-based applications recently. Inspired by convolutional neural networks (CNNs), GCNs generate the embeddings of nodes by aggregating the…

Computer representations of three-dimensional (3D) geometries are crucial for simulating systems and processes in engineering and science. In medicine, and more specifically, biomechanics and orthopaedics, obtaining and using 3D geometries…

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This…

3D models are widely used in various industries, and mesh data has become an indispensable part of 3D modeling because of its unique advantages. Mesh data can provide an intuitive and practical expression of rich 3D information. However,…

This paper presents new designs of graph convolutional neural networks (GCNs) on 3D meshes for 3D object segmentation and classification. We use the faces of the mesh as basic processing units and represent a 3D mesh as a graph where each…

This paper presents an innovative framework for remote sensing image analysis by fusing deep learning techniques, specifically Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) networks, with Geographic Information…

We propose a quality-based optimization strategy to reduce the total number of degrees of freedom associated to a discrete problem defined over a polygonal tessellation with the Virtual Element Method. The presented Quality Agglomeration…