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We introduce Universal Solution Manifold Network (USM-Net), a novel surrogate model, based on Artificial Neural Networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. Our…

The quest for efficient and robust deep learning models for molecular systems representation is increasingly critical in scientific exploration. The advent of message passing neural networks has marked a transformative era in graph-based…

Graph Neural Networks (GNNs) have been widely used for modeling graph-structured data. With the development of numerous GNN variants, recent years have witnessed groundbreaking results in improving the scalability of GNNs to work on static…

Graph neural networks (GNNs) provide powerful insights for brain neuroimaging technology from the view of graphical networks. However, most existing GNN-based models assume that the neuroimaging-produced brain connectome network is a…

Graph neural networks (GNNs) have been increasingly deployed in various applications that involve learning on non-Euclidean data. However, recent studies show that GNNs are vulnerable to graph adversarial attacks. Although there are several…

Graph representation learning has been widely studied and demonstrated effectiveness in various graph tasks. Most existing works embed graph data in the Euclidean space, while recent works extend the embedding models to hyperbolic or…

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its…

This paper focuses on the statistical analysis of shapes of data objects called shape graphs, a set of nodes connected by articulated curves with arbitrary shapes. A critical need here is a constrained registration of points (nodes to…

Deep learning-based approaches, particularly graph neural networks (GNNs), have gained prominence in simulating flexible deformations and contacts of solids, due to their ability to handle unstructured physical fields and nonlinear…

In machine learning for fluid mechanics, fully-connected neural network (FNN) only uses the local features for modelling, while the convolutional neural network (CNN) cannot be applied to data on structured/unstructured mesh. In order to…

The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method…

Metal forging is used to manufacture dies. We require the best set of input parameters for the process to be efficient. Currently, we predict the best parameters using the finite element method by generating simulations for the different…

Graph Convolutional Networks (GCNs) have received increasing attention in the machine learning community for effectively leveraging both the content features of nodes and the linkage patterns across graphs in various applications. As…

Accurate simulation of granular flow dynamics is crucial for assessing various geotechnical risks, including landslides and debris flows. Granular flows involve a dynamic rearrangement of particles exhibiting complex transitions from…

Graph Neural Networks (GNNs) have recently been explored as surrogate models for numerical simulations. While their applications in computational fluid dynamics have been investigated, little attention has been given to structural problems,…

Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, however, existing GNNs suffer from two significant limitations: a lack of interpretability in their results due to…

Accurate prediction of structural displacements under external loading is fundamental to structural health monitoring and seismic safety assessment. Although the finite element method (FEM) remains the prevailing approach because of its…

Current simulation of metal forging processes use advanced finite element methods. Such methods consist of solving mathematical equations, which takes a significant amount of time for the simulation to complete. Computational time can be…

Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. However, GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is…

Large-eddy simulations (LES) require closures for filtered production rates because the resolved fields do not contain all correlations that govern chemical source terms. We develop a graph neural network (GNN) that predicts filtered…