Related papers: MgNet: A Unified Framework of Multigrid and Convol…
By investigating iterative methods for a constrained linear model, we propose a new class of fully connected V-cycle MgNet for long-term time series forecasting, which is one of the most difficult tasks in forecasting. MgNet is a CNN model…
Convolutional neural networks (CNNs) are one of the most popular models of Artificial Neural Networks (ANN)s in Computer Vision (CV). A variety of CNN-based structures were developed by researchers to solve problems like image…
In computer vision, convolutional networks (CNNs) often adopts pooling to enlarge receptive field which has the advantage of low computational complexity. However, pooling can cause information loss and thus is detrimental to further…
Object segmentation and structure localization are important steps in automated image analysis pipelines for microscopy images. We present a convolution neural network (CNN) based deep learning architecture for segmentation of objects in…
Deep Convolutional Neural Networks (CNNs) are capable of learning unprecedentedly effective features from images. Some researchers have struggled to enhance the parameters' efficiency using grouped convolution. However, the relation between…
Convolutional Neural Networks (CNNs) have advanced significantly in visual representation learning and recognition. However, they face notable challenges in performance and computational efficiency when dealing with real-world, multi-scale…
This study used a multigrid-based convolutional neural network architecture known as MgNet in operator learning to solve numerical partial differential equations (PDEs). Given the property of smoothing iterations in multigrid methods where…
Graph Convolutional Networks (GCNs) have shown to be effective in handling unordered data like point clouds and meshes. In this work we propose novel approaches for graph convolution, pooling and unpooling, inspired from finite differences…
This paper studies numerical solutions for parameterized partial differential equations (P-PDEs) with deep learning (DL). P-PDEs arise in many important application areas and the computational cost using traditional numerical schemes can be…
Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters,…
We propose a constrained linear data-feature-mapping model as an interpretable mathematical model for image classification using a convolutional neural network (CNN). From this viewpoint, we establish detailed connections between the…
This paper presents a deep learning approach for the classification of Engineering (CAD) models using Convolutional Neural Networks (CNNs). Owing to the availability of large annotated datasets and also enough computational power in the…
Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending convolution operations…
This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…
Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…
A unified deep neural network, denoted the multi-scale CNN (MS-CNN), is proposed for fast multi-scale object detection. The MS-CNN consists of a proposal sub-network and a detection sub-network. In the proposal sub-network, detection is…
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…
The benefit of localized features within the regular domain has given rise to the use of Convolutional Neural Networks (CNNs) in machine learning, with great proficiency in the image classification. The use of CNNs becomes problematic…
To better retain the deep features of an image and solve the sparsity problem of the end-to-end segmentation model, we propose a new deep convolutional network model for medical image pixel segmentation, called MC-Net. The core of this…
Geometric deep learning has attracted significant attention in recent years, in part due to the availability of exotic data types for which traditional neural network architectures are not well suited. Our goal in this paper is to…