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We present a framework for the Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) tailored for nonlinear finite element analysis. Building upon the structured foundation of HiDeNN, C-HiDeNN introduces a convolution operator…

Isogeometric Analysis (IgA) is a spline based approach to the numerical solution of partial differential equations. There are two major issues that IgA was designed to address. The first issue is the exact representation of domains stemming…

Isogeometric analysis (IGA) is a numerical method that connects computer-aided design (CAD) with finite element analysis (FEA). In CAD the computational domain is usually represented by B-spline or NURBS patches. Given a NURBS…

In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite…

One of the important aspects of IsoGeometric Analysis (IGA) is the strong link between Computer Aided Design and analysis. Two of IGA'a major challenge are the assembly of patches (Constructive Solid Geometry geometries made of Boolean…

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The…

Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the…

Deep learning models have achieved huge success in numerous fields, such as computer vision and natural language processing. However, unlike such fields, it is hard to apply traditional deep learning models on the graph data due to the…

Heterogeneous graph neural networks (HeteGNNs) have demonstrated strong abilities to learn node representations by effectively extracting complex structural and semantic information in heterogeneous graphs. Most of the prevailing HeteGNNs…

Graph neural networks (GNNs) have been widely used in deep learning on graphs. They can learn effective node representations that achieve superior performances in graph analysis tasks such as node classification and node clustering.…

Convolutional neural network (CNN) is a class of artificial neural networks widely used in computer vision tasks. Most CNNs achieve excellent performance by stacking certain types of basic units. In addition to increasing the depth and…

Graph retrieval based on subgraph isomorphism has several real-world applications such as scene graph retrieval, molecular fingerprint detection and circuit design. Roy et al. [35] proposed IsoNet, a late interaction model for subgraph…

Isogeometric analysis (IgA) uses the same class of basis functions for both, representing the geometry of the computational domain and approximating the solution. In practical applications, geometrical patches are used in order to get…

Graph Convolutional Network (GCN) has achieved extraordinary success in learning effective task-specific representations of nodes in graphs. However, regarding Heterogeneous Information Network (HIN), existing HIN-oriented GCN methods still…

We present an approximately $C^1$-smooth multi-patch spline construction which can be used in isogeometric analysis (IGA). A key property of IGA is that it is simple to achieve high order smoothness within a single patch. To represent more…

Many real-world interactions are group-based rather than pairwise such as papers with multiple co-authors and users jointly engaging with items. Hypergraph neural networks have shown great promise at modeling higher-order relations, but…

Neurons exhibit complex geometry in their branched networks of neurites which is essential to the function of individual neuron but also brings challenges to transport a wide variety of essential materials throughout their neurite networks…

Graph Neural Networks (GNNs) often assume strong homophily for graph classification, seldom considering heterophily, which means connected nodes tend to have different class labels and dissimilar features. In real-world scenarios, graphs…

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks…

Recently, convolutional neural network (CNN) has demonstrated significant success for image restoration (IR) tasks (e.g., image super-resolution, image deblurring, rain streak removal, and dehazing). However, existing CNN based models are…