Related papers: Domain-Decomposed Graph Neural Network Surrogate M…

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

Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However, existing methodologies struggle to combine geometric…

Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while…

We propose a trainable-by-parts surrogate model for solving forward and inverse parameterized nonlinear partial differential equations. Like several other surrogate and operator learning models, the proposed approach employs an encoder to…

Crash simulations play an essential role in improving vehicle safety, design optimization, and injury risk estimation. Unfortunately, numerical solutions of such problems using state-of-the-art high-fidelity models require significant…

Semi-supervised learning (SSL) over graph-structured data emerges in many network science applications. To efficiently manage learning over graphs, variants of graph neural networks (GNNs) have been developed recently. By succinctly…

Even pruned by the state-of-the-art network compression methods, Graph Neural Networks (GNNs) training upon non-Euclidean graph data often encounters relatively higher time costs, due to its irregular and nasty density properties, compared…

Graph neural networks (GNN) suffer from severe inefficiency. It is mainly caused by the exponential growth of node dependency with the increase of layers. It extremely limits the application of stochastic optimization algorithms so that the…

Graphs are a ubiquitous data structure to model processes and relations in a wide range of domains. Examples include control-flow graphs in programs and semantic scene graphs in images. Identifying subgraph patterns in graphs is an…

During the design cycle of safety critical vehicle components such as B-pillars, crashworthiness performance is a key metric for passenger protection assessment in vehicle accidents. Traditional finite element simulations for…

Graph structured data, specifically text-attributed graphs (TAG), effectively represent relationships among varied entities. Such graphs are essential for semi-supervised node classification tasks. Graph Neural Networks (GNNs) have emerged…

Unsupervised graph representation learning aims to learn low-dimensional node embeddings without supervision while preserving graph topological structures and node attributive features. Previous graph neural networks (GNN) require a large…

Parametric surrogate models for partial differential equations (PDEs) are a necessary component for many applications in the computational sciences, and convolutional neural networks (CNNs) have proved as an excellent tool to generate these…

Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Yet the optimal construction of these methods requires tedious analysis and is often available only in…

The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected…

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-based spatio-temporal neural networks are effective to model the spatial dependency among discrete points sampled irregularly from unstructured grids, thanks to the great expressiveness of graph neural networks. However, these models…

Graph Neural Networks (GNNs) have achieved remarkable success in various real-world applications. However, GNNs may be trained on undesirable graph data, which can degrade their performance and reliability. To enable trained GNNs to…

In smart mobility, large networks of geographically distributed sensors produce vast amounts of high-frequency spatio-temporal data that must be processed in real time to avoid major disruptions. Traditional centralized approaches are…

We propose a novel method to explain trained deep neural networks (DNNs), by distilling them into surrogate models using unsupervised clustering. Our method can be applied flexibly to any subset of layers of a DNN architecture and can…