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Amortized Finite Element Analysis for Fast PDE-Constrained Optimization

Author(s): Xue, Tianju; Beatson, Alex; Adriaenssens, Sigrid; Adams, Ryan

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dc.contributor.authorXue, Tianju-
dc.contributor.authorBeatson, Alex-
dc.contributor.authorAdriaenssens, Sigrid-
dc.contributor.authorAdams, Ryan-
dc.date.accessioned2021-10-08T19:51:03Z-
dc.date.available2021-10-08T19:51:03Z-
dc.date.issued2020en_US
dc.identifier.citationXue, Tianju, Alex Beatson, Sigrid Adriaenssens, and Ryan Adams. "Amortized finite element analysis for fast PDE-constrained optimization." In Proceedings of the 37th International Conference on Machine Learning (2020): pp. 10638-10647.en_US
dc.identifier.urihttp://proceedings.mlr.press/v119/xue20a/xue20a.pdf-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1nr9b-
dc.description.abstractOptimizing the parameters of partial differential equations (PDEs), i.e., PDE-constrained optimization (PDE-CO), allows us to model natural systems from observations or perform rational design of structures with complicated mechanical, thermal, or electromagnetic properties. However, PDE-CO is often computationally prohibitive due to the need to solve the PDE—typically via finite element analysis (FEA)—at each step of the optimization procedure. In this paper we propose amortized finite element analysis (AmorFEA), in which a neural network learns to produce accurate PDE solutions, while preserving many of the advantages of traditional finite element methods. This network is trained to directly minimize the potential energy from which the PDE and finite element method are derived, avoiding the need to generate costly supervised training data by solving PDEs with traditional FEA. As FEA is a variational procedure, AmorFEA is a direct analogue to popular amortized inference approaches in latent variable models, with the finite element basis acting as the variational family. AmorFEA can perform PDE-CO without the need to repeatedly solve the associated PDE, accelerating optimization when compared to a traditional workflow using FEA and the adjoint method.en_US
dc.format.extent10638 - 10647en_US
dc.language.isoen_USen_US
dc.relation.ispartofProceedings of the 37th International Conference on Machine Learningen_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleAmortized Finite Element Analysis for Fast PDE-Constrained Optimizationen_US
dc.typeConference Articleen_US
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/conference-proceedingen_US

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