ID: 2110.12483

Machine Learning Line Bundle Connections

October 24, 2021

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Machine Learning on generalized Complete Intersection Calabi-Yau Manifolds

September 21, 2022

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Wei Cui, Xin Gao, Juntao Wang
Machine Learning

Generalized Complete Intersection Calabi-Yau Manifold (gCICY) is a new construction of Calabi-Yau manifolds established recently. However, the generation of new gCICYs using standard algebraic method is very laborious. Due to this complexity, the number of gCICYs and their classification still remain unknown. In this paper, we try to make some progress in this direction using neural network. The results showed that our trained models can have a high precision on the existing ...

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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
Machine Learning

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
Algebraic Geometry
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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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Deep Learning Gauss-Manin Connections

July 27, 2020

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Kathryn Heal, Avinash Kulkarni, Emre Can Sertöz
Machine Learning
Algebraic Geometry

The Gauss-Manin connection of a family of hypersurfaces governs the change of the period matrix along the family. This connection can be complicated even when the equations defining the family look simple. When this is the case, it is computationally expensive to compute the period matrices of varieties in the family via homotopy continuation. We train neural networks that can quickly and reliably guess the complexity of the Gauss-Manin connection of a pencil of hypersurfaces...

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Deep-Learning the Landscape

June 8, 2017

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Yang-Hui He
Algebraic Geometry
Machine Learning

We propose a paradigm to deep-learn the ever-expanding databases which have emerged in mathematical physics and particle phenomenology, as diverse as the statistics of string vacua or combinatorial and algebraic geometry. As concrete examples, we establish multi-layer neural networks as both classifiers and predictors and train them with a host of available data ranging from Calabi-Yau manifolds and vector bundles, to quiver representations for gauge theories. We find that ev...

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Machine Learning Algebraic Geometry for Physics

April 21, 2022

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Jiakang Bao, Yang-Hui He, ... , Hirst Edward
Algebraic Geometry
Machine Learning

We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised learning. Additionally, unsupervised methods can provide insight into the structure of such geometrical data. At the heart of this programme is the question of how geometry can be machine learned, and indeed how AI helps one to do mathematics...

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Gauge theory and calibrated geometry, I

October 2, 2000

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Gang Tian
Differential Geometry

The geometry of submanifolds is intimately related to the theory of functions and vector bundles. It has been of fundamental importance to find out how those two objects interact in many geometric and physical problems. A typical example of this relation is that the Picard group of line bundles on an algebraic manifold is isomorphic to the group of divisors, which is generated by holomorphic hypersurfaces modulo linear equivalence. A similar correspondence can be made between...

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David S. Berman, Yang-Hui He, Edward Hirst
Algebraic Geometry
Machine Learning

We revisit the classic database of weighted-P4s which admit Calabi-Yau 3-fold hypersurfaces equipped with a diverse set of tools from the machine-learning toolbox. Unsupervised techniques identify an unanticipated almost linear dependence of the topological data on the weights. This then allows us to identify a previously unnoticed clustering in the Calabi-Yau data. Supervised techniques are successful in predicting the topological parameters of the hypersurface from its weig...

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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Haldane Bundles: A Dataset for Learning to Predict the Chern Number of Line Bundles on the Torus

December 6, 2023

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Cody Tipton, Elizabeth Coda, Davis Brown, Alyson Bittner, Jung Lee, Grayson Jorgenson, ... , Kvinge Henry
Mesoscale and Nanoscale Phys...
Machine Learning
Algebraic Topology

Characteristic classes, which are abstract topological invariants associated with vector bundles, have become an important notion in modern physics with surprising real-world consequences. As a representative example, the incredible properties of topological insulators, which are insulators in their bulk but conductors on their surface, can be completely characterized by a specific characteristic class associated with their electronic band structure, the first Chern class. Gi...

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