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

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in AI for Science »
Event URL: https://openreview.net/forum?id=G3TRIsmMhhf »

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.

Author Information

Meire Fortunato (DEEPMIND)
Tobias Pfaff (DeepMind)
Peter Wirnsberger (DeepMind)
Alexander Pritzel (Deepmind)
Peter Battaglia (DeepMind)

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