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Accurate flow simulations, especially at higher Reynolds numbers, are a complex challenge in computational science that often pushes classical methods to their limits. To address this, we have developed a hybrid deep neural network/finite element method. It utilizes classical finite element approximation techniques to efficiently represent large flow fields and deep neural networks to learn updates on finer meshes. Here, we evaluate the approach by comparisons across different FEM libraries. Extensive benchmarks underscore the scalability, efficiency, generalizability, and accuracy of DNN-MG.

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Benchmark of Hybrid Finite Element/Deep Neural Network Methods

  • 会议论文

  • 发表日期：

    2025年

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  • Nils Margenberg,
  • Mathias Anselmann,
  • Markus Bause,
  • Robert Jendersie,
  • Christian Lessig,
  • Thomas Richter

摘要

Accurate flow simulations, especially at higher Reynolds numbers, are a complex challenge in computational science that often pushes classical methods to their limits. To address this, we have developed a hybrid deep neural network/finite element method. It utilizes classical finite element approximation techniques to efficiently represent large flow fields and deep neural networks to learn updates on finer meshes. Here, we evaluate the approach by comparisons across different FEM libraries. Extensive benchmarks underscore the scalability, efficiency, generalizability, and accuracy of DNN-MG.