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Message-passing has proved to be an effective way to design graph neural networks, as it is able to leverage both permutation equivariance and an inductive bias towards learning local structures in order to achieve good generalization.…

Mesh-based 3D static analysis methods have recently emerged as efficient alternatives to traditional computational numerical solvers, significantly reducing computational costs and runtime for various physics-based analyses. However, these…

Graph neural networks (GNNs) have shown promise in learning unstructured mesh-based simulations of physical systems, including fluid dynamics. In tandem, geometric deep learning principles have informed the development of equivariant…

Recently, graph-based models designed for downstream tasks have significantly advanced research on graph neural networks (GNNs). GNN baselines based on neural message-passing mechanisms such as GCN and GAT perform worse as the network…

Graph Transformers (GTs) facilitate the comprehension of graph-structured data by calculating the self-attention of node pairs without considering node position information. To address this limitation, we introduce an innovative and…

Graph neural networks have been used for a variety of learning tasks, such as link prediction, node classification, and node clustering. Among them, link prediction is a relatively under-studied graph learning task, with current…

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical…

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

Accurate prediction of molecular properties is essential in drug discovery and related fields. However, existing graph neural networks (GNNs) often struggle to simultaneously capture both local and global molecular structures. In this work,…

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…

We present a new class of equivariant neural networks, hereby dubbed Lattice-Equivariant Neural Networks (LENNs), designed to satisfy local symmetries of a lattice structure. Our approach develops within a recently introduced framework…

Accurate prediction of physical properties is critical for discovering and designing novel materials. Machine learning technologies have attracted significant attention in the materials science community for their potential for large-scale…

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…

Graph Neural Networks (graph NNs) are a promising deep learning approach for analyzing graph-structured data. However, it is known that they do not improve (or sometimes worsen) their predictive performance as we pile up many layers and add…

The key to device-edge co-inference paradigm is to partition models into computation-friendly and computation-intensive parts across the device and the edge, respectively. However, for Graph Neural Networks (GNNs), we find that simply…

Interpreting graph neural networks (GNNs) is difficult because message passing mixes signals and internal channels rarely align with human concepts. We study superposition, the sharing of directions by multiple features, directly in the…

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 Neural Networks (GNNs) are powerful deep learning models to generate node embeddings on graphs. When applying deep GNNs on large graphs, it is still challenging to perform training in an efficient and scalable way. We propose a novel…

Graph neural networks (GNNs) have shown considerable promise in computational chemistry. However, the limited availability of molecular data raises concerns regarding GNNs' ability to effectively capture the fundamental principles of…

Segmentation of ultra-high resolution images is increasingly demanded, yet poses significant challenges for algorithm efficiency, in particular considering the (GPU) memory limits. Current approaches either downsample an ultra-high…