Related papers: MultiScale MeshGraphNets

Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike…

Mesh-based graph neural networks (GNNs) have become effective surrogates for PDE simulations, yet their deep message passing incurs high cost and over-smoothing on large, long-range meshes; hierarchical GNNs shorten propagation paths but…

Graph Neural Networks (GNNs) have gained significant traction for simulating complex physical systems, with models like MeshGraphNet demonstrating strong performance on unstructured simulation meshes. However, these models face several…

Hypergraph representations are both more efficient and better suited to describe data characterized by relations between two or more objects. In this work, we present a new graph neural network based on message passing capable of processing…

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…

Graph neural networks (GNNs) based on message passing between neighboring nodes are known to be insufficient for capturing long-range interactions in graphs. In this project we study hierarchical message passing models that leverage a…

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…

Data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. Among them, graph neural networks (GNNs) that operate on mesh-based data are desirable because they possess inductive biases that promote…

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…

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…

Graphs are the most ubiquitous data structures for representing relational datasets and performing inferences in them. They model, however, only pairwise relations between nodes and are not designed for encoding the higher-order relations.…

Message-Passing Neural Networks (MPNNs) are extensively employed in graph learning tasks but suffer from limitations such as the restricted scope of information exchange, by being confined to neighboring nodes during each round of message…

With many frameworks based on message passing neural networks proposed to predict molecular and bulk properties, machine learning methods have tremendously shifted the paradigms of computational sciences underpinning physics, material…

Most of the current hypergraph learning methodologies and benchmarking datasets in the hypergraph realm are obtained by lifting procedures from their graph analogs, leading to overshadowing specific characteristics of hypergraphs. This…

Simulating object deformations is a critical challenge across many scientific domains, including robotics, manufacturing, and structural mechanics. Learned Graph Network Simulators (GNSs) offer a promising alternative to traditional…

Graph neural networks have been a powerful tool for mesh-based physical simulation. To efficiently model large-scale systems, existing methods mainly employ hierarchical graph structures to capture multi-scale node relations. However, these…

In engineering design, surrogate models are widely employed to replace computationally expensive simulations by leveraging design variables and geometric parameters from computer-aided design (CAD) models. However, these models often lose…

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…

Graph Neural Networks (GNNs) have become a prominent approach to machine learning with graphs and have been increasingly applied in a multitude of domains. Nevertheless, since most existing GNN models are based on flat message-passing…

Multigrid modeling algorithms are a technique used to accelerate relaxation models running on a hierarchy of similar graphlike structures. We introduce and demonstrate a new method for training neural networks which uses multilevel methods.…