Related papers: A graph convolutional autoencoder approach to mode…

Graph Convolutional Networks (GCNs) have shown significant improvements in semi-supervised learning on graph-structured data. Concurrently, unsupervised learning of graph embeddings has benefited from the information contained in random…

We introduce a novel encoder-decoder architecture to embed functional processes into latent vector spaces. This embedding can then be decoded to sample the encoded functions over any arbitrary domain. This autoencoder generalizes the…

Reduced Order Models (ROMs) have been regarded as an efficient alternative to conventional high-fidelity Computational Fluid Dynamics (CFD) for accelerating the design and optimization processes in engineering applications. Many industrial…

We define a novel type of ensemble Graph Convolutional Network (GCN) model. Using optimized linear projection operators to map between spatial scales of graph, this ensemble model learns to aggregate information from each scale for its…

Node representation learning on attributed graphs -- whose nodes are associated with rich attributes (e.g., texts and protein sequences) -- plays a crucial role in many important downstream tasks. To encode the attributes and graph…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

Node embeddings have become an ubiquitous technique for representing graph data in a low dimensional space. Graph autoencoders, as one of the widely adapted deep models, have been proposed to learn graph embeddings in an unsupervised way by…

With the rise of IoT-based botnet attacks, researchers have explored various learning models for detection, including traditional machine learning, deep learning, and hybrid approaches. A key advancement involves deploying attention…

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 new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…

Owing to the remarkable capability of extracting effective graph embeddings, graph convolutional network (GCN) and its variants have been successfully applied to a broad range of tasks, such as node classification, link prediction, and…

The generation of voluminous scientific data poses significant challenges for efficient storage, transfer, and analysis. Recently, error-bounded lossy compression methods emerged due to their ability to achieve high compression ratios while…

Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using…

Low dimensional and computationally less expensive Reduced-Order Models (ROMs) have been widely used to capture the dominant behaviors of high-dimensional systems. A ROM can be obtained, using the well-known Proper Orthogonal Decomposition…

A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e.g., exclusively through proper orthogonal decomposition (POD) - when applied to nonlinear…

The availability of affordable and portable depth sensors has made scanning objects and people simpler than ever. However, dealing with occlusions and missing parts is still a significant challenge. The problem of reconstructing a (possibly…

In this paper, we present GCN-Denoiser, a novel feature-preserving mesh denoising method based on graph convolutional networks (GCNs). Unlike previous learning-based mesh denoising methods that exploit hand-crafted or voxel-based…

Graph Convolution Networks (GCNs) are widely considered state-of-the-art for collaborative filtering. Although several GCN-based methods have been proposed and achieved state-of-the-art performance in various tasks, they can be…

A space-time-parameters structure of parametric parabolic PDEs motivates the application of tensor methods to define reduced order models (ROMs). Within a tensor-based ROM framework, the matrix SVD - a traditional dimension reduction…