Neural Representation of Minimal Surfaces

• URL: http://arxiv.org/abs/2607.23437v1
• Date: Sun, 26 Jul 2026 03:26:42 GMT
• Title: Neural Representation of Minimal Surfaces
• Abstract summary: We propose a neural representation for minimal surfaces.<n>Our method builds on an exact representation, similar to the classical Weierstrass--Enneper parameterization, yielding minimal surfaces up to negligible quadrature error in evaluation.
• Score: 8.141515451812818
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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