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arXiv · 2607.23437

Neural Representation of Minimal Surfaces

Jiayin Sun·Albert Chern
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Abstract

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.

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Jiayin Sun, Albert Chern. 2026-07-26. Neural Representation of Minimal Surfaces. https://arxiv.org/abs/2607.23437

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