MultiScale MeshGraphNets
Meire Fortunato, Tobias Pfaff, Peter Wirnsberger, Alexander Pritzel,, Peter Battaglia

TL;DR
This paper introduces MultiScale MeshGraphNets, a hierarchical graph neural network approach that enhances high-resolution physical system simulations by using multi-resolution message passing, reducing computational costs and improving accuracy.
Contribution
It proposes a hierarchical multi-resolution framework for MeshGraphNets, enabling scalable and accurate high-resolution simulations with less computational effort.
Findings
Accurate surrogate dynamics learned on coarser meshes.
Hierarchical message passing improves accuracy and efficiency.
Reduces message passing bottleneck in high-resolution settings.
Abstract
In recent years, there has been a growing interest in using machine learning to overcome the high cost of numerical simulation, with some learned models achieving impressive speed-ups over classical solvers whilst maintaining accuracy. However, these methods are usually tested at low-resolution settings, and it remains to be seen whether they can scale to the costly high-resolution simulations that we ultimately want to tackle. In this work, we propose two complementary approaches to improve the framework from MeshGraphNets, which demonstrated accurate predictions in a broad range of physical systems. MeshGraphNets relies on a message passing graph neural network to propagate information, and this structure becomes a limiting factor for high-resolution simulations, as equally distant points in space become further apart in graph space. First, we demonstrate that it is possible to…
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Taxonomy
TopicsModel Reduction and Neural Networks · Parallel Computing and Optimization Techniques · Tensor decomposition and applications
MethodsGraph Neural Network
