ID: 2111.01436

Learning Size and Shape of Calabi-Yau Spaces

November 2, 2021

View on ArXiv

Similar papers 3

A physics-informed search for metric solutions to Ricci flow, their embeddings, and visualisation

November 30, 2022

85% Match
Aarjav Jain, Challenger Mishra, Pietro Liò
Neural and Evolutionary Comp...
Mathematical Physics

Neural networks with PDEs embedded in their loss functions (physics-informed neural networks) are employed as a function approximators to find solutions to the Ricci flow (a curvature based evolution) of Riemannian metrics. A general method is developed and applied to the real torus. The validity of the solution is verified by comparing the time evolution of scalar curvature with that found using a standard PDE solver, which decreases to a constant value of 0 on the whole man...

Find SimilarView on arXiv

CYJAX: A package for Calabi-Yau metrics with JAX

November 22, 2022

85% Match
Mathis Gerdes, Sven Krippendorf
High Energy Physics - Theory

We present the first version of CYJAX, a package for machine learning Calabi-Yau metrics using JAX. It is meant to be accessible both as a top-level tool and as a library of modular functions. CYJAX is currently centered around the algebraic ansatz for the K\"ahler potential which automatically satisfies K\"ahlerity and compatibility on patch overlaps. As of now, this implementation is limited to varieties defined by a single defining equation on one complex projective space....

Find SimilarView on arXiv

Deep Learning Calabi-Yau four folds with hybrid and recurrent neural network architectures

May 27, 2024

85% Match
H. L. Dao
Machine Learning
Algebraic Geometry

In this work, we report the results of applying deep learning based on hybrid convolutional-recurrent and purely recurrent neural network architectures to the dataset of almost one million complete intersection Calabi-Yau four-folds (CICY4) to machine-learn their four Hodge numbers $h^{1,1}, h^{2,1}, h^{3,1}, h^{2,2}$. In particular, we explored and experimented with twelve different neural network models, nine of which are convolutional-recurrent (CNN-RNN) hybrids with the R...

Find SimilarView on arXiv

Physical Yukawa Couplings in Heterotic String Compactifications

January 26, 2024

84% Match
Giorgi Butbaia, Damián Mayorga Peña, Justin Tan, Per Berglund, Tristan Hübsch, ... , Mishra Challenger
High Energy Physics - Theory
High Energy Physics - Phenom...

One of the challenges of heterotic compactification on a Calabi-Yau threefold is to determine the physical $(\mathbf{27})^3$ Yukawa couplings of the resulting four-dimensional $\mathcal{N}=1$ theory. In general, the calculation necessitates knowledge of the Ricci-flat metric. However, in the standard embedding, which references the tangent bundle, we can compute normalized Yukawa couplings from the Weil-Petersson metric on the moduli space of complex structure deformations of...

Find SimilarView on arXiv

Deep learning complete intersection Calabi-Yau manifolds

November 20, 2023

84% Match
Harold Erbin, Riccardo Finotello
Machine Learning
Algebraic Geometry

We review advancements in deep learning techniques for complete intersection Calabi-Yau (CICY) 3- and 4-folds, with the aim of understanding better how to handle algebraic topological data with machine learning. We first discuss methodological aspects and data analysis, before describing neural networks architectures. Then, we describe the state-of-the art accuracy in predicting Hodge numbers. We include new results on extrapolating predictions from low to high Hodge numbers,...

Find SimilarView on arXiv

Deep-Learning the Landscape

June 8, 2017

84% Match
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...

Find SimilarView on arXiv

Deep multi-task mining Calabi-Yau four-folds

August 4, 2021

84% Match
Harold Erbin, Riccardo Finotello, ... , Tamaazousti Mohamed
Machine Learning
Algebraic Geometry

We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi-Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi-Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using...

Find SimilarView on arXiv

Calabi-Yau Four/Five/Six-folds as $\mathbb{P}^n_\textbf{w}$ Hypersurfaces: Machine Learning, Approximation, and Generation

November 28, 2023

84% Match
Edward Hirst, Tancredi Schettini Gherardini
Algebraic Geometry
Machine Learning

Calabi-Yau four-folds may be constructed as hypersurfaces in weighted projective spaces of complex dimension 5 defined via weight systems of 6 weights. In this work, neural networks were implemented to learn the Calabi-Yau Hodge numbers from the weight systems, where gradient saliency and symbolic regression then inspired a truncation of the Landau-Ginzburg model formula for the Hodge numbers of any dimensional Calabi-Yau constructed in this way. The approximation always prov...

Find SimilarView on arXiv
Anthony Ashmore, Rehan Deen, ... , Ovrut Burt A.
High Energy Physics - Theory

We study the use of machine learning for finding numerical hermitian Yang-Mills connections on line bundles over Calabi-Yau manifolds. Defining an appropriate loss function and focusing on the examples of an elliptic curve, a K3 surface and a quintic threefold, we show that neural networks can be trained to give a close approximation to hermitian Yang-Mills connections.

Inception Neural Network for Complete Intersection Calabi-Yau 3-folds

July 27, 2020

84% Match
Harold Erbin, Riccardo Finotello
Machine Learning
Algebraic Geometry

We introduce a neural network inspired by Google's Inception model to compute the Hodge number $h^{1,1}$ of complete intersection Calabi-Yau (CICY) 3-folds. This architecture improves largely the accuracy of the predictions over existing results, giving already 97% of accuracy with just 30% of the data for training. Moreover, accuracy climbs to 99% when using 80% of the data for training. This proves that neural networks are a valuable resource to study geometric aspects in b...

Find SimilarView on arXiv