Neural Representation of Minimal Surfaces
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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.
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.
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References · 7
- 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,689
- 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,041
- 2021Neural Surface Mapscited by 34
- 2021DeepCurrents: Learning Implicit Representations of Shapes with Boundariescited by 12
- 2024Geometry-Informed Neural Networkscited by 12
- 2025Physics-informed neural network solves minimal surfaces in curved spacetimecited by 6
- 2025Geometric implicit neural representations for signed distance functionscited by 4
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