an:07064352
Zbl 1414.83080
Altman, Ross; Carifio, Jonathan; Halverson, James; Nelson, Brent D.
Estimating Calabi-Yau hypersurface and triangulation counts with equation learners
EN
J. High Energy Phys. 2019, No. 3, Paper No. 186, 29 p. (2019).
00433789
2019
j
83E30 14J32 81T30
superstring vacua; compactification and string models
Summary: 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.