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<title>Machine Learning Simulation: Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction</title>
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<meta name="citation_title" content="Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction" />
<meta name="citation_author" content="Filipe de Avila Belbute-Peres" />
<meta name="citation_author" content="Thomas D. Economon" />
<meta name="citation_author" content="J. Zico Kolter" />
<meta name="citation_abstract" content="Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the PDE solutions, yet the simulation results predicted from these approaches typically do not generalize well to truly novel scenarios. In this work, we develop a hybrid (graph) neural network that combines a traditional graph convolutional network with an embedded differentiable fluid dynamics simulator inside the network itself. By combining an actual CFD simulator (run on a much coarser resolution representation of the problem) with the graph network, we show that we can both generalize well to new situations and benefit from the substantial speedup of neural network CFD predictions, while also substantially outperforming the coarse CFD simulation alone." />
<meta name="citation_keywords" content="Graph Neural Networks" />
<meta name="citation_keywords" content="GNNs" />
<meta name="citation_keywords" content="Graph Convolutional Networks" />
<meta name="citation_keywords" content="GCNs" />
<meta name="citation_keywords" content="message passing" />
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<meta name="citation_keywords" content="CFD simulation" />
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<meta name="citation_keywords" content="adjoint-based differentiation" />
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Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction
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16/8/2020
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class="text-secondary text-decoration-none filterByKeywordLink">message passing</a>,
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class="text-secondary text-decoration-none filterByKeywordLink">hybrid simulator</a>,
<a href="papers.html?keyword=computational efficiency" target="_blank"
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<a href="papers.html?keyword=CFD simulation" target="_blank"
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<span>Venue: </span>
<a href="papers.html?venue=ICML" target="_blank" class="text-secondary text-decoration-none">ICML 2020</a>
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<span id="invisible-paper-id" style="display: none;">5</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{DBLP:conf/icml/Belbute-PeresEK20,
author = {Filipe de Avila Belbute{-}Peres and
Thomas D. Economon and
J. Zico Kolter},
title = {Combining Differentiable {PDE} Solvers and Graph Neural Networks for
Fluid Flow Prediction},
booktitle = {Proceedings of the 37th International Conference on Machine Learning,
{ICML} 2020, 13-18 July 2020, Virtual Event},
series = {Proceedings of Machine Learning Research},
volume = {119},
pages = {2402--2411},
publisher = {{PMLR}},
year = {2020},
url = {http://proceedings.mlr.press/v119/de-avila-belbute-peres20a.html},
timestamp = {Tue, 15 Dec 2020 17:40:18 +0100},
biburl = {https://dblp.org/rec/conf/icml/Belbute-PeresEK20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
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<p style="font-weight: bolder; font-size: 25px; text-align: center;">Abstract</p>
Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the PDE solutions, yet the simulation results predicted from these approaches typically do not generalize well to truly novel scenarios. In this work, we develop a hybrid (graph) neural network that combines a traditional graph convolutional network with an embedded differentiable fluid dynamics simulator inside the network itself. By combining an actual CFD simulator (run on a much coarser resolution representation of the problem) with the graph network, we show that we can both generalize well to new situations and benefit from the substantial speedup of neural network CFD predictions, while also substantially outperforming the coarse CFD simulation alone.
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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=Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction&sort=relevance">Semantic Scholar</a>. For full citation graphs, visit <a href="https://www.connectedpapers.com/search?q=Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction">ConnectedPapers</a>.</p>
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