Polytopes and Machine Learning

Abstract

We introduce machine learning methodology to the study of lattice polytopes. With supervised learning techniques, we predict standard properties such as volume, dual volume, reflexivity, etc, with accuracies up to 100%. We focus on 2d polygons and 3d polytopes with Plücker coordinates as input, which out-perform the usual vertex representation.

arXiv comment33 pages, 26 figures

References in corpus (14)

• Machine Learning in the String Landscape
• Machine Learning of Calabi-Yau Volumes
• A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List
• Evolving neural networks with genetic algorithms to study the String Landscape
• On the Classification of Reflexive Polyhedra
• Canonical toric Fano threefolds
• Quiver Mutations, Seiberg Duality and Machine Learning
• Estimating Calabi-Yau Hypersurface and Triangulation Counts with Equation Learners
• Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curves
• Calabi-Yau Volumes and Reflexive Polytopes
• Hilbert Series, Machine Learning, and Applications to Physics
• Neurons on Amoebae
• Reflexive polytopes of higher index and the number 12
• Patterns in Calabi-Yau Distributions

Cited by in corpus (4)

• Applying machine learning to the Calabi-Yau orientifolds with string vacua
• Calabi-Yau Four/Five/Six-folds as ${\mathbb{P}}_{\text{w}}^n$ Hypersurfaces: Machine Learning, Approximation, and Generation
• Totally Positive Matrices and the Highest-Order Coefficients of the Characteristic Polynomial
• Learning 3-Manifold Triangulations