Neural geometric PDEs on neural implicit surfacesCRC 1720: Early Career Seminar

by Samuel Weidemaier

Tuesday Dec 2, 2025, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

This seminar talk presents work on a neural framework for solving geometric partial differential equations (PDEs) on neural implicit manifolds. The key ingredient is a new method for constructing accurate signed distance functions (SDFs) from unoriented point clouds, replacing the standard Eikonal-based approach with a neural variational heat method. This idea results in a two-step method: first approximating unsigned gradient directions, and then recovering the correct normal orientation. Both steps are shown to be well-posed. Numerical results demonstrate state-of-the-art surface reconstruction with consistent SDF gradients. The talk will also discuss an adaptation of the classical narrow-band method to neural settings, enabling accurate PDE solutions on zero-level sets and opening new directions in neural geometric PDEs.