Oberseminar "Mathematik des Maschinellen Lernens und Angewandte Analysis" - M.Sc. Christoph Smoch

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.