A user's guide to PINNs in geometric analysis: lessons from the asymptotic Plateau problem
This proceedings contribution elaborates on the findings of arXiv:2605.26234v2: a joint work with Marco Usula, where we introduced a machine learning framework based on physics-informed neural networks (PINNs), aimed at constructing near-minimal discs in hyperbolic space asymptotic to a prescribed knot at infinity. We used this method to provide numerical evidence for a conjecture of Joel Fine relating minimal surfaces in $H^{4}$ to the coefficients of the HOMFLY polynomial. This is a methodological companion to that paper, based on a presentation given at the 2026 edition of the workshop "DANGER: Data, Numbers, and Geometry". Rather than reviewing the results, which are presented extensi...
| Authors | Tancredi Schettini Gherardini |
|---|---|
| Primary category | math.DG |
| Published | 30 July 2026 |
| Last updated at source | 30 July 2026 |
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