相关论文: Surface Networks

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical…

In engineering design, surrogate models are widely employed to replace computationally expensive simulations by leveraging design variables and geometric parameters from computer-aided design (CAD) models. However, these models often lose…

This paper introduces a generative model for 3D surfaces based on a representation of shapes with mean curvature and metric, which are invariant under rigid transformation. Hence, compared with existing 3D machine learning frameworks, our…

This paper presents a novel method, named geodesic deformable networks (GDN), that for the first time enables the learning of geodesic flows of deformation fields derived from images. In particular, the capability of our proposed GDN being…

We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…

The understanding of geographical reality is a process of data representation and pattern discovery. Former studies mainly adopted continuous-field models to represent spatial variables and to investigate the underlying spatial…

This study addresses the challenge of real-time metaverse applications by proposing an in-network placement and task-offloading solution for delay-constrained computing tasks in next-generation networks. The metaverse, envisioned as a…

Graph Neural Networks (GNNs) are a popular technique for modelling graph-structured data and computing node-level representations via aggregation of information from the neighborhood of each node. However, this aggregation implies an…

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…

Recent research on graph neural networks (GNNs) has explored mechanisms for capturing local uncertainty and exploiting graph hierarchies to mitigate data sparsity and leverage structural properties. However, the synergistic integration of…

Social and information networks are gaining huge popularity recently due to their various applications. Knowledge representation through graphs in the form of nodes and edges should preserve as many characteristics of the original data as…

In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $\Delta{}G$ of the graph and try to improve generalization. Based on quantum…

Recently, graph convolutional network (GCN) has been widely used for semi-supervised classification and deep feature representation on graph-structured data. However, existing GCN generally fails to consider the local invariance constraint…

We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

A graph neural network (GCN) is employed in the deep energy method (DEM) model to solve the momentum balance equation in 3D for the deformation of linear elastic and hyperelastic materials due to its ability to handle irregular domains over…

Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of…

Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into…

In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static surface case, with the aid of level set function, the…