A hybrid minimizing movement and neural network approach to Willmore flow
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914322575261696 |
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| author | Rumpf, Martin Sassen, Josua Smoch, Christoph |
| author_facet | Rumpf, Martin Sassen, Josua Smoch, Christoph |
| contents | We present a hybrid method combining a minimizing movement scheme with neural operators for the simulation of phase field-based Willmore flow. The minimizing movement component is based on a standard optimization problem on a regular grid whereas the functional to be minimized involves a neural approximation of mean curvature flow proposed by Bretin et al. Numerical experiments confirm stability for large time step sizes, consistency and significantly reduced computational cost compared to a traditional finite element method. Moreover, applications demonstrate its effectiveness in surface fairing and reconstructing of damaged shapes. Thus, the approach offers a robust and efficient tool for geometry processing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A hybrid minimizing movement and neural network approach to Willmore flow Rumpf, Martin Sassen, Josua Smoch, Christoph Numerical Analysis We present a hybrid method combining a minimizing movement scheme with neural operators for the simulation of phase field-based Willmore flow. The minimizing movement component is based on a standard optimization problem on a regular grid whereas the functional to be minimized involves a neural approximation of mean curvature flow proposed by Bretin et al. Numerical experiments confirm stability for large time step sizes, consistency and significantly reduced computational cost compared to a traditional finite element method. Moreover, applications demonstrate its effectiveness in surface fairing and reconstructing of damaged shapes. Thus, the approach offers a robust and efficient tool for geometry processing. |
| title | A hybrid minimizing movement and neural network approach to Willmore flow |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2502.14656 |