ID: 2108.02221

Deep multi-task mining Calabi-Yau four-folds

August 4, 2021

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Topological Invariants and Fibration Structure of Complete Intersection Calabi-Yau Four-Folds

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James Gray, Alexander S. Haupt, Andre Lukas
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We investigate the mathematical properties of the class of Calabi-Yau four-folds recently found in [arXiv:1303.1832]. This class consists of 921,497 configuration matrices which correspond to manifolds that are described as complete intersections in products of projective spaces. For each manifold in the list, we compute the full Hodge diamond as well as additional topological invariants such as Chern classes and intersection numbers. Using this data, we conclude that there a...

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Machine Learning Kreuzer--Skarke Calabi--Yau Threefolds

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Per Berglund, Ben Campbell, Vishnu Jejjala
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Using a fully connected feedforward neural network we study topological invariants of a class of Calabi--Yau manifolds constructed as hypersurfaces in toric varieties associated with reflexive polytopes from the Kreuzer--Skarke database. In particular, we find the existence of a simple expression for the Euler number that can be learned in terms of limited data extracted from the polytope and its dual.

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Numerical Calabi-Yau metrics from holomorphic networks

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Michael R. Douglas, Subramanian Lakshminarasimhan, Yidi Qi
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We propose machine learning inspired methods for computing numerical Calabi-Yau (Ricci flat K\"ahler) metrics, and implement them using Tensorflow/Keras. We compare them with previous work, and find that they are far more accurate for manifolds with little or no symmetry. We also discuss issues such as overparameterization and choice of optimization methods.

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Distinguishing Elliptic Fibrations with AI

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Yang-Hui He, Seung-Joo Lee
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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...

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The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning

December 7, 2018

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Yang-Hui He
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We present a pedagogical introduction to the recent advances in the computational geometry, physical implications, and data science of Calabi-Yau manifolds. Aimed at the beginning research student and using Calabi-Yau spaces as an exciting play-ground, we intend to teach some mathematics to the budding physicist, some physics to the budding mathematician, and some machine-learning to both. Based on various lecture series, colloquia and seminars given by the author in the past...

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On Machine Learning Complete Intersection Calabi-Yau 3-folds

April 17, 2024

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Kaniba Mady Keita
High Energy Physics - Theory

Gaussian Process Regression, Kernel Support Vector Regression, the random forest, extreme gradient boosting and the generalized linear model algorithms are applied to data of Complete Intersection Calabi-Yau 3-folds. It is shown that Gaussian process regression is the most suitable for learning the Hodge number h^(2,1)in terms of h^(1,1). The performance of this regression algorithm is such that the Pearson correlation coefficient for the validation set is R^2 = 0.9999999995 ...

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Identifying equivalent Calabi--Yau topologies: A discrete challenge from math and physics for machine learning

February 15, 2022

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Vishnu Jejjala, Washington Taylor, Andrew Turner
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We review briefly the characteristic topological data of Calabi--Yau threefolds and focus on the question of when two threefolds are equivalent through related topological data. This provides an interesting test case for machine learning methodology in discrete mathematics problems motivated by physics.

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Machine Learning CICY Threefolds

June 8, 2018

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Kieran Bull, Yang-Hui He, ... , Mishra Challenger
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The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbers and report a remarkable improvement over previous efforts, (2) query for favourability, and (3) predict discrete symmetries, a highly imbalanced problem to w...

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Machine Learning Line Bundle Cohomology

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Callum R. Brodie, Andrei Constantin, ... , Lukas Andre
High Energy Physics - Theory

We investigate different approaches to machine learning of line bundle cohomology on complex surfaces as well as on Calabi-Yau three-folds. Standard function learning based on simple fully connected networks with logistic sigmoids is reviewed and its main features and shortcomings are discussed. It has been observed recently that line bundle cohomology can be described by dividing the Picard lattice into certain regions in each of which the cohomology dimension is described b...

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Machine Learned Calabi-Yau Metrics and Curvature

November 17, 2022

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Per Berglund, Giorgi Butbaia, Tristan Hübsch, Vishnu Jejjala, Damián Mayorga Peña, ... , Tan Justin
Machine Learning
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Finding Ricci-flat (Calabi-Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural networks to engineer approximations to the Calabi-Yau metric within a given K\"ahler class. In this paper we investigate numerical Ricci-flat metrics over smooth and singular K3 surfaces and Calabi-Yau threefolds. Using these Ricci-flat metric approximations for the Cefal\'u family of quartic twofol...

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