arXiv Machine Learning 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.

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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.

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