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MultiScale MeshGraphNets

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arxiv 2210.00612 v1 pith:ON2PA7K5 submitted 2022-10-02 cs.LG cs.CE

Meire Fortunato , Tobias Pfaff , Peter Wirnsberger , Alexander Pritzel , Peter Battaglia This is my paper · ORCID
classification cs.LGcs.CE
keywords meshgraphnetshigh-resolutionaccuracyaccurategraphimprovingmessagemultiscale
verification ladder T0 review T1 audit T2 compute T3 formal

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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.

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