×

zbMATH — the first resource for mathematics

Machine learning line bundle cohomologies of hypersurfaces in toric varieties. (English) Zbl 1406.14001
Summary: Different techniques from machine learning are applied to the problem of computing line bundle cohomologies of (hypersurfaces in) toric varieties. While a naive approach of training a neural network to reproduce the cohomologies fails in the general case, by inspecting the underlying functional form of the data we propose a second approach. The cohomologies depend in a piecewise polynomial way on the line bundle charges. We use unsupervised learning to separate the different polynomial phases. The result is an analytic formula for the cohomologies. This can be turned into an algorithm for computing analytic expressions for arbitrary (hypersurfaces in) toric varieties.

MSC:
14-04 Software, source code, etc. for problems pertaining to algebraic geometry
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
Software:
cohomCalg; GitHub
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Douglas, M. R., The statistics of string / M theory vacua, JHEP, 05, (2003)
[2] Abel, S.; Rizos, J., Genetic algorithms and the search for viable string vacua, JHEP, 08, (2014)
[3] Allanach, B. C.; Grellscheid, D.; Quevedo, F., Genetic algorithms and experimental discrimination of SUSY models, JHEP, 07, (2004)
[4] He, Y.-H., Deep-learning the landscape
[5] He, Y.-H., Machine-learning the string landscape, Phys. Lett. B, 774, 564-568, (2017)
[6] Krefl, D.; Seong, R.-K., Machine learning of Calabi-Yau volumes, Phys. Rev. D, 96, 6, (2017)
[7] Ruehle, F., Evolving neural networks with genetic algorithms to study the string landscape, JHEP, 08, (2017) · Zbl 1381.83128
[8] Carifio, J.; Halverson, J.; Krioukov, D.; Nelson, B. D., Machine learning in the string landscape, JHEP, 09, (2017) · Zbl 1382.81155
[9] Carifio, J.; Cunningham, W. J.; Halverson, J.; Krioukov, D.; Long, C.; Nelson, B. D., Vacuum selection from cosmology on networks of string geometries, Phys. Rev. Lett., 121, 10, (2018)
[10] Wang, Y.-N.; Zhang, Z., Learning non-Higgsable gauge groups in 4D F-theory, JHEP, 08, (2018)
[11] Bull, K.; He, Y.-H.; Jejjala, V.; Mishra, C., Machine learning CICY threefolds, Phys. Lett. B, 785, 65-72, (2018)
[12] Erbin, H.; Krippendorf, S., GANs for generating EFT models
[13] cohomCalg package, high-performance line bundle cohomology computation based on [16] (2010), https://github.com/BenjaminJurke/cohomCalg.
[14] Constantin, A.; Lukas, A., Formulae for line bundle cohomology on Calabi-Yau threefolds
[15] Witten, E., Phases of \(N = 2\) theories in two-dimensions, Nucl. Phys. B, 403, 159-222, (1993); Witten, E., Phases of \(N = 2\) theories in two-dimensions, AMS/IP Stud. Adv. Math., 143, 1, (1996) · Zbl 0910.14020
[16] Blumenhagen, R.; Jurke, B.; Rahn, T.; Roschy, H., Cohomology of line bundles: a computational algorithm, J. Math. Phys., 51, 10, (2010) · Zbl 1314.55012
[17] Rahn, T.; Roschy, H., Cohomology of line bundles: proof of the algorithm, J. Math. Phys., 51, (2010) · Zbl 1314.55013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.