MultiScale MeshGraphNets

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 learn accurate surrogate dynamics of a high-resolution system on a much coarser mesh, both removing the message passing bottleneck and improving performance; and second, we introduce a hierarchical approach (MultiScale MeshGraphNets) which passes messages on two different resolutions (fine and coarse), significantly improving the accuracy of MeshGraphNets while requiring less computational resources.