arXiv Machine Learning June 11, 2026 By Tancredi Schettini Gherardini, Marco Usula

Minimal surfaces, Knots, and Neural Networks

Read the original on arXiv Machine Learning →

arXiv:2605. 26234v2 Announce Type: replace-cross Abstract: A recent conjecture by Joel Fine posits a relationship between the coefficients of the HOMFLY polynomial of a knot $K$ in the 3-sphere $S^3$, and the signed count of minimal surfaces in hyperbolic 4-space $\mathrm{H}^4$ meeting the sphere at infinity at $K$, with prescribed genus and self-intersection number.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

arXiv AI

Aug 3

A user's guide to PINNs in geometric analysis: lessons from the asymptotic Plateau problem

arXiv:2607. 28733v1 Announce Type: cross Abstract: This proceedings contribution elaborates on the findings of arXiv:2605.

By Tancredi Schettini Gherardini

arXiv Machine Learning

Jul 28

Neural Representation of Minimal Surfaces

arXiv:2607. 23437v1 Announce Type: cross Abstract: We propose a neural representation for minimal surfaces.

By Jiayin Sun, Albert Chern

arXiv Machine Learning

Jun 18

A Neural Network Framework for Geodesic-Like Curve Computation on Parametric Surfaces

arXiv:2606. 18759v1 Announce Type: cross Abstract: The concept of geodesic-like curves was introduced by Chen in 2010 as a method for estimating shortest paths (geodesics) on parametric surfaces, with its convergence established theoretically.

By Sheng-Gwo Chen, Chen-Chang Peng

arXiv Machine Learning

Aug 11

Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles

arXiv:2608. 08322v1 Announce Type: cross Abstract: Physics-informed neural networks applied to the level-set formulation of interface advection commonly augment the residual and initial-condition losses with an eikonal regulariser, penalising the deviation of $\|\nabla\phi\|$ from unity.

By Muhammad Akbar Khan

benchmarks

arXiv AI

Jun 10

Moonshine: An Autonomous Mathematical Research Agent Centered on Conjecture Generation

arXiv:2606. 10806v1 Announce Type: new Abstract: Moonshine is an autonomous agent whose central objective is to generate mathematical conjectures.

By Xiaoyang Chen, Xiang Jiang

llms agents

arXiv Machine Learning

Jul 1

Low-dimensional topology of deep neural networks

arXiv:2606. 31856v1 Announce Type: new Abstract: We study layered models, including feedforward networks, ResNets, and transformers, by limiting each layer to a width of $d = 3$, i.

By Junyu Ren, Lek-Heng Lim

llms

Related stories

A user's guide to PINNs in geometric analysis: lessons from the asymptotic Plateau problem

Neural Representation of Minimal Surfaces

A Neural Network Framework for Geodesic-Like Curve Computation on Parametric Surfaces

Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles

Moonshine: An Autonomous Mathematical Research Agent Centered on Conjecture Generation

Low-dimensional topology of deep neural networks