# Neural Representation of Minimal Surfaces

arXiv: https://arxiv.org/abs/2607.23437 · HTML: https://mlsanity.com/paper/2607.23437/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 50 references that are in the map.
- First posted on arXiv 26 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [DeepCurrents: Learning Implicit Representations of Shapes with Boundaries](https://mlsanity.com/paper/2111.09383/) (2021)
- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [Physics-informed neural network solves minimal surfaces in curved spacetime](https://mlsanity.com/paper/2509.10866/) (2025)
- [Geometric implicit neural representations for signed distance functions](https://mlsanity.com/paper/2511.07206/) (2025)

## Abstract (arXiv)

We propose a neural representation for minimal surfaces. Unlike prior approaches based on discretization or Physics-Informed Neural Networks (PINNs), where meshes or neural fields are optimized to approximate the governing equations, our method builds on an exact representation, similar to the classical Weierstrass--Enneper parameterization, yielding minimal surfaces up to negligible quadrature error in evaluation. We formulate a training objective for the Plateau problem that optimizes over this representation.