Non-iterative generation of optimized meshes for finite element simulations with deep learning

Abstract The finite element method is one of the most widely used computational methods in engineering and science. It provides approximate solutions to boundary value problems. The quality of these solutions critically depends on the underlying discretization, the so-called mesh. To optimize the mesh, adaptive refinement methods have been proposed over the last years that can improve mesh quality over a series of iteration steps. Herein, we propose a novel deep learning architecture that can cut short the process of mesh optimization. This architecture exploits fundamental invariance and equivariance properties to keep the amount of training data modest. It can generate high-quality meshes for a given boundary value problem and a desired target approximation error in a direct, non-iterative way. We demonstrate the performance of our method by the application to standard two-dimensional linear-elastic elasticity problems. There, our method generates meshes that reduce the solution error by 22.6%(median) compared to uniform meshes with the same computational demand.

Subjects

Mesh generation

Machine learning

Finite element

Adaptive mesh refinement

DDC Class

006.3: Artificial Intelligence

620.11: Engineering Materials

Publication version

publishedVersion

Lizenz

https://creativecommons.org/licenses/by/4.0/

Name

44379_2025_Article_13.pdf

Size

2.28 MB

Format

Adobe PDF

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Non-iterative generation of optimized meshes for finite element simulations with deep learning