相关论文: A categorical embedding discontinuity-capturing sh…

Solving high dimensional partial differential equations (PDEs) has historically posed a considerable challenge when utilizing conventional numerical methods, such as those involving domain meshes. Recent advancements in the field have seen…

While deep learning algorithms demonstrate a great potential in scientific computing, its application to multi-scale problems remains to be a big challenge. This is manifested by the "frequency principle" that neural networks tend to learn…

Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick…

Graph neural networks (GNNs) are widely used for modelling graph-structured data in numerous applications. However, with their inherently finite aggregation layers, existing GNN models may not be able to effectively capture long-range…

While nowadays deep neural networks achieve impressive performances on semantic segmentation tasks, they are usually trained by optimizing pixel-wise losses such as cross-entropy. As a result, the predictions outputted by such networks…

In this paper, we propose an end-to-end graph learning framework, namely Deep Iterative and Adaptive Learning for Graph Neural Networks (DIAL-GNN), for jointly learning the graph structure and graph embeddings simultaneously. We first cast…

We introduce a novel self-supervised learning framework that automatically learns representations from input computer-aided design (CAD) models for downstream tasks, including part classification, modeling segmentation, and machining…

Existing network embedding approaches tackle the problem of learning low-dimensional node representations. However, networks can also be seen in the light of edges interlinking pairs of nodes. The broad goal of this paper is to introduce…

This paper proposes a deep neural network structure that exploits edge information in addressing representative low-level vision tasks such as layer separation and image filtering. Unlike most other deep learning strategies applied in this…

We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an…

In this paper we develop finite difference schemes for elliptic problems with piecewise continuous coefficients that have (possibly huge) jumps across fixed internal interfaces. In contrast with such problems involving one smooth…

Graph Neural Networks often struggle with long-range information propagation and in the presence of heterophilous neighborhoods. We address both challenges with a unified framework that incorporates a clustering inductive bias into the…

Remote sensing image segmentation faces persistent challenges in distinguishing morphologically similar categories and adapting to diverse scene variations. While existing methods rely on implicit representation learning paradigms, they…

Inspired by the recent neuroscience studies on the left-right asymmetry of the human brain in processing low and high spatial frequency information, this paper introduces a dual skipping network which carries out coarse-to-fine object…

Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. In this paper, we introduce a method that simultaneously learns an embedding space along…

In this paper, we develop and analyze a trilinear immersed finite element method for solving three-dimensional elliptic interface problems. The proposed method can be utilized on interface-unfitted meshes such as Cartesian grids consisting…

In domains where computational resources and labeled data are limited, such as in robotics, deep networks with millions of weights might not be the optimal solution. In this paper, we introduce a connectivity scheme for pyramidal…

We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…

Semantic segmentation has been a hot topic across diverse research fields. Along with the success of deep convolutional neural networks, semantic segmentation has made great achievements and improvements, in terms of both urban scene…

Despite Graph neural networks' significant performance gain over many classic techniques in various graph-related downstream tasks, their successes are restricted in shallow models due to over-smoothness and the difficulties of…