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.
Highlights
Introduction and summaryEver since the birth of string theory its compactifications on compact Calabi-Yau manifolds have been a subject of constant interest to theoretical physicists and algebraic geometers alike
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
The purpose of this letter is to report that this problem of recognizing elliptic fibrations within Calabi-Yau manifolds, using complete intersection 3-folds and 4-folds within products of projective spaces as a playground, appear to belong to the class of problems which can be addressed by machine-learning to high precision
Summary
Ever since the birth of string theory its compactifications on compact Calabi-Yau manifolds have been a subject of constant interest to theoretical physicists and algebraic geometers alike. In the meantime various dualities amongst Calabi-Yau compactifications have been influential in exciting development in enumerative and algebraic geometry [17,18] as well as many other branches of pure mathematics Such string dualities oftentimes base on elliptic fibration structures within the internal. The purpose of this letter is to report that this problem of recognizing elliptic fibrations within Calabi-Yau manifolds (and presumably more arbitrary dataset of algebraic varieties), using complete intersection 3-folds and 4-folds within products of projective spaces as a playground, appear to belong to the class of problems which can be addressed by machine-learning to high precision. Like computing cohomology of bundles over varieties, distinguishing elliptic fibrations appears to be a pattern recognizable by the likes of a neural network - completely without any knowledge of algebraic geometry or expensive algorithms needed to deterministically address the problem.
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