Related papers: MeshODENet: A Graph-Informed Neural Ordinary Diffe…

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…

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…

Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often…

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…

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…

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…

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…

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…

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…

Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) to the corresponding…

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…

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.…

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

Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer…

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…

This study aims to predict the spatio-temporal evolution of physical quantities observed in multi-layered display panels subjected to the drop impact of a ball. To model these complex interactions, graph neural networks have emerged as…

Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models…

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,…

Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many…