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Estimating Calabi-Yau Hypersurface and Triangulation Counts with Equation Learners

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arxiv 1811.06490 v1 pith:XIK2SJ2B submitted 2018-11-15 hep-th

Ross Altman , Jonathan Carifio , James Halverson , Brent D. Nelson This is my paper
classification hep-th
keywords estimatenumbertriangulationscalabi-yauequationaccuratelyallowingarchitecture
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abstract

We provide the first estimate of the number of fine, regular, star triangulations of the four-dimensional reflexive polytopes, as classified by Kreuzer and Skarke (KS). This provides an upper bound on the number of Calabi-Yau threefold hypersurfaces in toric varieties. The estimate is performed with deep learning, specifically the novel equation learner (EQL) architecture. We demonstrate that EQL networks accurately predict numbers of triangulations far beyond the $h^{1,1}$ training region, allowing for reliable extrapolation. We estimate that number of triangulations in the KS dataset is $10^{10,505}$, dominated by the polytope with the highest $h^{1,1}$ value.

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