Getting CICY high

Supervised machine learning can be used to predict properties of string geometries with previously unknown features. Using the complete intersection Calabi-Yau (CICY) threefold dataset as a theoretical laboratory for this investigation, we use low $h^{1,1}$ geometries for training and validate on geometries with large $h^{1,1}$. Neural networks and Support Vector Machines successfully predict trends in the number of Kahler parameters of CICY threefolds. The numerical accuracy of machine learning improves upon seeding the training set with a small number of samples at higher $h^{1,1}$.

[1]  Victor V. Batyrev,et al.  Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties , 1993, alg-geom/9310003.

[2]  M. Lynker,et al.  Calabi-Yau manifolds in weighted P4 , 1990 .

[3]  Challenger Mishra,et al.  Highly Symmetric Quintic Quotients , 2017, 1709.01081.

[4]  B. Nelson,et al.  Vacuum Selection from Cosmology on Networks of String Geometries. , 2017, Physical review letters.

[5]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[6]  Nitish Srivastava,et al.  Dropout: a simple way to prevent neural networks from overfitting , 2014, J. Mach. Learn. Res..

[7]  Yang-Hui He,et al.  Machine-learning the string landscape , 2017 .

[8]  D. Krefl,et al.  Machine Learning of Calabi-Yau Volumes : arXiv , 2017, 1706.03346.

[9]  A. Constantin,et al.  Hodge numbers for all CICY quotients , 2016, 1607.01830.

[10]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, STOC '84.

[11]  Challenger Mishra,et al.  Hodge numbers for CICYs with symmetries of order divisible by 4 , 2015, 1511.01103.

[12]  Yang-Hui He,et al.  Monad bundles in heterotic string compactifications , 2008, 0805.2875.

[13]  Fibrations in CICY threefolds , 2017, 1708.07907.

[14]  P. Candelas,et al.  New Calabi‐Yau manifolds with small Hodge numbers , 2008, 0809.4681.

[15]  C. Lütken,et al.  Complete intersection Calabi-Yau manifolds , 1988 .

[16]  Tom Rudelius Learning to inflate. A gradient ascent approach to random inflation , 2018, Journal of Cosmology and Astroparticle Physics.

[17]  A. Constantin,et al.  Completing the web of ℤ3‐quotients of complete intersection Calabi‐Yau manifolds , 2010, 1010.1878.

[18]  Vacuum configurations for superstrings , 1985 .

[19]  Vishnu Jejjala,et al.  Patterns in Calabi–Yau Distributions , 2015, 1512.01579.

[20]  D. Straten,et al.  Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties , 1993, alg-geom/9307010.

[21]  Junyu Liu,et al.  Artificial neural network in cosmic landscape , 2017, 1707.02800.

[22]  A. Constantin,et al.  Counting string theory standard models , 2018, Physics Letters B.

[23]  A. Mutter,et al.  Deep learning in the heterotic orbifold landscape , 2018, Nuclear Physics B.

[24]  B. Nelson,et al.  Estimating Calabi-Yau hypersurface and triangulation counts with equation learners , 2018, Journal of High Energy Physics.

[25]  Tristan Hübsck,et al.  Calabi-Yau manifolds , 1992 .

[26]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[27]  James Gray,et al.  A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list , 2014, 1411.1418.

[28]  Dmitri Krioukov,et al.  Machine learning in the string landscape , 2017, Journal of High Energy Physics.

[29]  J. Rizos,et al.  Genetic algorithms and the search for viable string vacua , 2014, 1404.7359.

[30]  J. Gray,et al.  All complete intersection Calabi-Yau four-folds , 2013, 1303.1832.

[31]  E. Palti,et al.  Heterotic line bundle standard models , 2012, 1202.1757.

[32]  Yang-Hui He,et al.  The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning , 2018, 1812.02893.

[33]  Fabian Ruehle,et al.  Computational complexity of vacua and near-vacua in field and string theory , 2018, Physical Review D.

[34]  The exact MSSM spectrum from string theory , 2005, hep-th/0512177.

[35]  H. Skarke,et al.  All Weight Systems for Calabi–Yau Fourfolds from Reflexive Polyhedra , 2018, Communications in Mathematical Physics.

[36]  M. P. Casado,et al.  Measurement of charged-particle distributions sensitive to the underlying event in s=13$$ \sqrt{s}=13 $$ TeV proton-proton collisions with the ATLAS detector at the LHC , 2017 .

[37]  Seung-Joo Lee,et al.  A new construction of Calabi–Yau manifolds: Generalized CICYs , 2015, 1507.03235.

[38]  Vishnu Jejjala,et al.  Deep learning the hyperbolic volume of a knot , 2019, Physics Letters B.

[39]  Heterotic Compactification, An Algorithmic Approach , 2007, hep-th/0702210.

[40]  F. Riva,et al.  Calabi-Yau Manifolds , 2003 .

[41]  C. Lütken,et al.  All the Hodge numbers for all Calabi-Yau complete intersections , 1989 .

[42]  Vishnu Jejjala,et al.  Machine learning CICY threefolds , 2018, Physics Letters B.

[43]  V. Braun On free quotients of complete intersection Calabi-Yau manifolds , 2010, 1003.3235.

[44]  A. Constantin,et al.  A Comprehensive Scan for Heterotic SU(5) GUT models , 2013, 1307.4787.

[45]  W. Taylor,et al.  Scanning the skeleton of the 4D F-theory landscape , 2017, 1710.11235.

[46]  Lorenz Schlechter,et al.  Machine learning line bundle cohomologies of hypersurfaces in toric varieties , 2018, Physics Letters B.

[47]  Fabian Ruehle Evolving neural networks with genetic algorithms to study the string landscape , 2017, 1706.07024.

[48]  Yi-Nan Wang,et al.  Learning non-Higgsable gauge groups in 4D F-theory , 2018, Journal of High Energy Physics.

[49]  Yang-Hui He,et al.  Deep-Learning the Landscape , 2017, 1706.02714.

[50]  E. Witten,et al.  Calabi‐Yau Manifolds: A Bestiary for Physicists , 1992 .

[51]  M. A. Diaz Corchero,et al.  W and Z boson production in p-Pb collisions at \( \sqrt{s_{\mathrm{NN}}}=5.02 \) TeV , 2016, 1611.03002.

[52]  Challenger Mishra,et al.  Discrete Symmetries of Complete Intersection Calabi–Yau Manifolds , 2017, Communications in Mathematical Physics.

[53]  E. Palti,et al.  Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds , 2011, 1106.4804.

[54]  Tristan Hübsch,et al.  Calabi-Yau manifolds , 1992 .

[55]  Maximilian Kreuzer,et al.  Complete classification of reflexive polyhedra in four dimensions , 2000, hep-th/0002240.

[56]  B. Greene,et al.  A three-generation superstring model: (I). Compactification and discrete symmetries , 1986 .