Related papers: Graph Neural Networks for Airfoil Design

Deep learning-based approaches have been developed to solve challenging problems in wireless communications, leading to promising results. Early attempts adopted neural network architectures inherited from applications such as computer…

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,…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Graph neural networks (GNNs), which learn the representation of a node by aggregating its neighbors, have become an effective computational tool in downstream applications. Over-smoothing is one of the key issues which limit the performance…

Graph Neural Networks (GNNs) address two key challenges in applying deep learning to graph-structured data: they handle varying size input graphs and ensure invariance under graph isomorphism. While GNNs have demonstrated broad…

Graph Drawing techniques have been developed in the last few years with the purpose of producing aesthetically pleasing node-link layouts. Recently, the employment of differentiable loss functions has paved the road to the massive usage of…

Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as…

Accurate modelling and quantification of predictive uncertainty is crucial in deep learning since it allows a model to make safer decisions when the data is ambiguous and facilitates the users' understanding of the model's confidence in its…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

This work addresses the accurate and efficient simulation of physical phenomena governed by parametric Partial Differential Equations (PDEs) characterized by varying boundary conditions, where parametric instances modify not only the…

Graph Neural Networks (GNNs) have emerged as a prominent research topic in the field of machine learning. Existing GNN models are commonly categorized into two types: spectral GNNs, which are designed based on polynomial graph filters, and…

Deep-learning-based surrogate models provide an efficient complement to numerical simulations for subsurface flow problems such as CO$_2$ geological storage. Accurately capturing the impact of faults on CO$_2$ plume migration remains a…

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

Graphs serve as fundamental descriptors for systems composed of interacting elements, capturing a wide array of data types, from molecular interactions to social networks and knowledge graphs. In this paper, we present an exhaustive review…

In the recent years, the domain of fast flow field prediction has been vastly dominated by pixel-based convolutional neural networks. Yet, the recent advent of graph convolutional neural networks (GCNNs) have attracted a considerable…

Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings between infinite-dimensional function spaces using conventional neural architectures, have…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

For numerical design, the development of efficient and accurate surrogate models is paramount. They allow us to approximate complex physical phenomena, thereby reducing the computational burden of direct numerical simulations. We propose…

The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a…

Many scientific and engineering processes produce spatially unstructured data. However, most data-driven models require a feature matrix that enforces both a set number and order of features for each sample. They thus cannot be easily…