Distinguishing Elliptic Fibrations with AI

Abstract

We use the latest techniques in machine-learning to study whether from the landscape of Calabi-Yau manifolds one can distinguish elliptically fibred ones. Using the dataset of complete intersections in products of projective spaces (CICY3 and CICY4, totalling about a million manifolds) as a concrete playground, we find that a relatively simple neural network with forward-feeding multi-layers can very efficiently distinguish the elliptic fibrations, much more so than using the traditional methods of manipulating the defining equations. We cross-check with control cases to ensure that the AI is not randomly guessing and is indeed identifying an inherent structure. Our result should prove useful in F-theory and string model building as well as in pure algebraic geometry.

arXiv comment6 pages, 1 table, 4 figures; v2: four-fold learning vastly improved in section III.C, four-fold statistics fixed in table I, comments added on dataset enhancement

References in corpus (23)

• Evidence for F-Theory
• An SU(5) Heterotic Standard Model
• A Heterotic Standard Model
• A Stringy Test of the Scalar Weak Gravity Conjecture
• Machine Learning of Calabi-Yau Volumes
• Deep Learning and AdS/CFT
• New Calabi-Yau Manifolds with Small Hodge Numbers
• Machine Learning CICY Threefolds
• Machine Learning Line Bundle Cohomologies of Hypersurfaces in Toric Varieties
• A New Construction of Calabi-Yau Manifolds: Generalized CICYs
• An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts
• Deep learning in the heterotic orbifold landscape
• Computational Complexity of Vacua and Near-Vacua in Field and String Theory
• Vacuum Selection from Cosmology on Networks of String Geometries
• The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
• Completing the Web of $Z_3$ - Quotients of Complete Intersection Calabi-Yau Manifolds
• Calabi-Yau Threefolds With Small Hodge Numbers
• On Instanton Superpotentials, Calabi-Yau Geometry, and Fibrations
• Hodge Numbers for CICYs with Symmetries of Order Divisible by 4
• Machine learning for bounce calculation
• Deep-Learning the Landscape
• Emergent Strings, Duality and Weak Coupling Limits for Two-Form Fields

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• Accessibility Measure for Eternal Inflation: Dynamical Criticality and Higgs Metastability
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• Deep multi-task mining Calabi-Yau four-folds
• Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyer
• Lectures on the Calabi-Yau Landscape
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• Graph Laplacians, Riemannian Manifolds and their Machine-Learning
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