Related papers: Generalization capabilities of MeshGraphNets to un…

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…

Nowadays, Computational Fluid Dynamics (CFD) is a fundamental tool for industrial design. However, the computational cost of doing such simulations is expensive and can be detrimental for real-world use cases where many simulations are…

Nonlinear finite element crash simulations are accurate but computationally expensive, limiting their use in iterative design optimisation. Machine-learning surrogate models based on graph neural networks (GNNs) offer a faster alternative.…

Simulating fluid dynamics is crucial for the design and development process, ranging from simple valves to complex turbomachinery. Accurately solving the underlying physical equations is computationally expensive. Therefore, learning-based…

In many cutting-edge applications, high-fidelity computational models prove to be too slow for practical use and are therefore replaced by much faster surrogate models. Recently, deep learning techniques have increasingly been utilized to…

In this paper, we study the generalization capabilities of geometric graph neural networks (GNNs). We consider GNNs over a geometric graph constructed from a finite set of randomly sampled points over an embedded manifold with topological…

This study aims to overcome the limitations of conventional deep-learning approaches based on convolutional neural networks in complex geometries and unstructured meshes by exploring the potential of Graph U-Nets for unsteady flow-field…

Meshing is a critical, but user-intensive process necessary for stable and accurate simulations in computational fluid dynamics (CFD). Mesh generation is often a bottleneck in CFD pipelines. Adaptive meshing techniques allow the mesh to be…

The recent introduction of Graph Neural Networks (GNNs) and their growing popularity in the past few years has enabled the application of deep learning algorithms to non-Euclidean, graph-structured data. GNNs have achieved state-of-the-art…

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…

The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. Data-driven networks like GNN, Neural Operators have…

Graph networks are a new machine learning (ML) paradigm that supports both relational reasoning and combinatorial generalization. Here, we develop universal MatErials Graph Network (MEGNet) models for accurate property prediction in both…

Deep neural networks have enabled researchers to create powerful generalized frameworks, such as transformers, that can be used to solve well-studied problems in various application domains, such as text and image. However, such generalized…

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…

We present MeshGraphNet-Transformer (MGN-T), a novel architecture that combines the global modeling capabilities of Transformers with the geometric inductive bias of MeshGraphNets, while preserving a mesh-based graph representation. MGN-T…

Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and…

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…

3D models are widely used in various industries, and mesh data has become an indispensable part of 3D modeling because of its unique advantages. Mesh data can provide an intuitive and practical expression of rich 3D information. However,…

To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for…