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<title>Machine Learning Simulation: MultiScale MeshGraphNets</title>
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<meta name="citation_title" content="MultiScale MeshGraphNets" />
<meta name="citation_author" content="Meire Fortunato" />
<meta name="citation_author" content="Tobias Pfaff" />
<meta name="citation_author" content="Peter Wirnsberger" />
<meta name="citation_author" content="Alexander Pritzel" />
<meta name="citation_author" content="Peter Battaglia" />
<meta name="citation_abstract" content="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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<meta name="citation_keywords" content="Graph Neural Networks" />
<meta name="citation_keywords" content="GNNs" />
<meta name="citation_keywords" content="message passing" />
<meta name="citation_keywords" content="encoder-processor-decoder" />
<meta name="citation_keywords" content="computational efficiency" />
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<meta name="citation_keywords" content="CFD simulation" />
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MultiScale MeshGraphNets
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<a href="papers.html?author=Meire Fortunato" target="_blank"
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<a href="papers.html?author=Tobias Pfaff" target="_blank"
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class="text-muted filterByAuthorLink">Tobias Pfaff</a>,
<a href="papers.html?author=Peter Wirnsberger" target="_blank"
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class="text-muted filterByAuthorLink">Peter Wirnsberger</a>,
<a href="papers.html?author=Alexander Pritzel" target="_blank"
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class="text-muted filterByAuthorLink">Alexander Pritzel</a>,
<a href="papers.html?author=Peter Battaglia" target="_blank"
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15/6/2022
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<span>Keywords:</span>
<a href="papers.html?keyword=Multiscale MeshGraphNets" target="_blank"
data-tippy-content="See all papers with keyword 'Multiscale MeshGraphNets'"
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<a href="papers.html?keyword=Graph Neural Networks" target="_blank"
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class="text-secondary text-decoration-none filterByKeywordLink">Graph Neural Networks</a>,
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class="text-secondary text-decoration-none filterByKeywordLink">GNNs</a>,
<a href="papers.html?keyword=message passing" target="_blank"
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class="text-secondary text-decoration-none filterByKeywordLink">message passing</a>,
<a href="papers.html?keyword=encoder-processor-decoder" target="_blank"
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class="text-secondary text-decoration-none filterByKeywordLink">encoder-processor-decoder</a>,
<a href="papers.html?keyword=computational efficiency" target="_blank"
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class="text-secondary text-decoration-none filterByKeywordLink">computational efficiency</a>,
<a href="papers.html?keyword=neural network simulators" target="_blank"
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<a href="papers.html?keyword=computational fluid dynamics" target="_blank"
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class="text-secondary text-decoration-none filterByKeywordLink">computational fluid dynamics</a>,
<a href="papers.html?keyword=CFD simulation" target="_blank"
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class="text-secondary text-decoration-none filterByKeywordLink">CFD simulation</a>,
<a href="papers.html?keyword=COMSOL" target="_blank"
data-tippy-content="See all papers with keyword 'COMSOL'"
class="text-secondary text-decoration-none filterByKeywordLink">COMSOL</a>,
<a href="papers.html?keyword=CylinderFlow" target="_blank"
data-tippy-content="See all papers with keyword 'CylinderFlow'"
class="text-secondary text-decoration-none filterByKeywordLink">CylinderFlow</a>
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<span>Venue: </span>
<a href="papers.html?venue=ICML-AI4Science" target="_blank" class="text-secondary text-decoration-none">ICML-AI4Science 2022</a>
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Paper
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Citation
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<span id="invisible-paper-id" style="display: none;">3</span>
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<span style="font-size: large; font-weight: bold;">Bibtex:</span>
<span style="white-space: pre-line; position: relative; left: 20px;">
@inproceedings{fortunato2022multiscale,
title={MultiScale MeshGraphNets},
author={Fortunato, Meire and Pfaff, Tobias and Wirnsberger, Peter and Pritzel, Alexander and Battaglia, Peter},
booktitle={ICML 2022 2nd AI for Science Workshop},
year={2022}
}
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<p style="font-weight: bolder; font-size: 25px; text-align: center;">Abstract</p>
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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<p><span style="font-size: 10px;">*</span> Showing citation graph for papers within our database. Data retrieved from <a href="https://www.semanticscholar.org/search?q=MultiScale MeshGraphNets&sort=relevance">Semantic Scholar</a>. For full citation graphs, visit <a href="https://www.connectedpapers.com/search?q=MultiScale MeshGraphNets">ConnectedPapers</a>.</p>
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