Mesh-based GNN surrogates for time-independent PDEs
Abstract Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of requiring long-range exchange of information acros...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2024-02-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-024-53185-y |
| _version_ | 1827327725819396096 |
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| author | Rini Jasmine Gladstone Helia Rahmani Vishvas Suryakumar Hadi Meidani Marta D’Elia Ahmad Zareei |
| author_facet | Rini Jasmine Gladstone Helia Rahmani Vishvas Suryakumar Hadi Meidani Marta D’Elia Ahmad Zareei |
| author_sort | Rini Jasmine Gladstone |
| collection | DOAJ |
| description | Abstract Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of requiring long-range exchange of information across the computational domain for obtaining accurate predictions. In the context of graph neural networks (GNNs), this calls for deeper networks, which, in turn, may compromise or slow down the training process. In this work, we present two GNN architectures to overcome this challenge—the edge augmented GNN and the multi-GNN. We show that both these networks perform significantly better than baseline methods, such as MeshGraphNets, when applied to time-independent solid mechanics problems. Furthermore, the proposed architectures generalize well to unseen domains, boundary conditions, and materials. Here, the treatment of variable domains is facilitated by a novel coordinate transformation that enables rotation and translation invariance. By broadening the range of problems that neural operators based on graph neural networks can tackle, this paper provides the groundwork for their application to complex scientific and industrial settings. |
| first_indexed | 2024-03-07T15:06:26Z |
| format | Article |
| id | doaj.art-af155f6f76414373a7db8ad6f69c59e7 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-07T15:06:26Z |
| publishDate | 2024-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-af155f6f76414373a7db8ad6f69c59e72024-03-05T18:53:38ZengNature PortfolioScientific Reports2045-23222024-02-0114111410.1038/s41598-024-53185-yMesh-based GNN surrogates for time-independent PDEsRini Jasmine Gladstone0Helia Rahmani1Vishvas Suryakumar2Hadi Meidani3Marta D’Elia4Ahmad Zareei5Civil and Environmental Engineering, University of Illinois Urbana-ChampaignMeta Reality LabsMeta Reality LabsCivil and Environmental Engineering, University of Illinois Urbana-ChampaignPasteur LabsMeta Reality LabsAbstract Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of requiring long-range exchange of information across the computational domain for obtaining accurate predictions. In the context of graph neural networks (GNNs), this calls for deeper networks, which, in turn, may compromise or slow down the training process. In this work, we present two GNN architectures to overcome this challenge—the edge augmented GNN and the multi-GNN. We show that both these networks perform significantly better than baseline methods, such as MeshGraphNets, when applied to time-independent solid mechanics problems. Furthermore, the proposed architectures generalize well to unseen domains, boundary conditions, and materials. Here, the treatment of variable domains is facilitated by a novel coordinate transformation that enables rotation and translation invariance. By broadening the range of problems that neural operators based on graph neural networks can tackle, this paper provides the groundwork for their application to complex scientific and industrial settings.https://doi.org/10.1038/s41598-024-53185-y |
| spellingShingle | Rini Jasmine Gladstone Helia Rahmani Vishvas Suryakumar Hadi Meidani Marta D’Elia Ahmad Zareei Mesh-based GNN surrogates for time-independent PDEs Scientific Reports |
| title | Mesh-based GNN surrogates for time-independent PDEs |
| title_full | Mesh-based GNN surrogates for time-independent PDEs |
| title_fullStr | Mesh-based GNN surrogates for time-independent PDEs |
| title_full_unstemmed | Mesh-based GNN surrogates for time-independent PDEs |
| title_short | Mesh-based GNN surrogates for time-independent PDEs |
| title_sort | mesh based gnn surrogates for time independent pdes |
| url | https://doi.org/10.1038/s41598-024-53185-y |
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