41 citations · 250 across the 22 of their papers we have counts for
23 papers
Learning the Graphical Nature of Symmetries
Rashid Barket, Enrico Grimaldi, Yacoub Hendi +3
Finite groups are rigid algebraic objects, whose Cayley graphs expose a rich network geometry through which group-theoretic structure can be measured, compared, and learned. In thi…
Neural and numerical methods for -structures on contact Calabi-Yau 7-manifolds
Elli Heyes, Edward Hirst, Henrique N. Sá Earp +1
A numerical framework for approximating -structure 3-forms on contact Calabi-Yau manifolds is presented. The approach proceeds in three stages: first, existing neural…
Generating Triangulations and Fibrations with Reinforcement Learning
Per Berglund, Giorgi Butbaia, Yang-Hui He +3
We apply reinforcement learning (RL) to generate fine regular star triangulations of reflexive polytopes, that give rise to smooth Calabi-Yau (CY) hypersurfaces. We demonstrate tha…
Learning 3-Manifold Triangulations
Francesco Costantino, Yang-Hui He, Elli Heyes +1
Real 3-manifold triangulations can be uniquely represented by isomorphism signatures. Databases of these isomorphism signatures are generated for a variety of 3-manifolds and knot…
Machine learning Sasakian and topology on contact Calabi-Yau -manifolds
Daattavya Aggarwal, Yang-Hui He, Elli Heyes +3
We propose a machine learning approach to study topological quantities related to the Sasakian and -geometries of contact Calabi-Yau -manifolds. Specifically, we compute da…
Machine Learning Clifford invariants of ADE Coxeter elements
Siqi Chen, Pierre-Philippe Dechant, Yang-Hui He +3
There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric…
New Calabi-Yau Manifolds from Genetic Algorithms
Per Berglund, Yang-Hui He, Elli Heyes +3
Calabi-Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algor…
Machine Learning in Physics and Geometry
Yang-Hui He, Elli Heyes, Edward Hirst
We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the co…
Mahler Measuring the Genetic Code of Amoebae
Siqi Chen, Yang-Hui He, Edward Hirst +2
Amoebae from tropical geometry and the Mahler measure from number theory play important roles in quiver gauge theories and dimer models. Their dependencies on the coefficients of t…
Clustering Cluster Algebras with Clusters
Man-Wai Cheung, Pierre-Philippe Dechant, Yang-Hui He +3
Classification of cluster variables in cluster algebras (in particular, Grassmannian cluster algebras) is an important problem, which has direct application to computations of scat…
Machine Learning Algebraic Geometry for Physics
Jiakang Bao, Yang-Hui He, Elli Heyes +1
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 ten…
Machine Learning for Hilbert Series
Edward Hirst
Hilbert series are a standard tool in algebraic geometry, and more recently are finding many uses in theoretical physics. This summary reviews work applying machine learning to dat…
Cluster Algebras: Network Science and Machine Learning
Pierre-Philippe Dechant, Yang-Hui He, Elli Heyes +1
Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with t…
Brain Webs for Brane Webs
Guillermo Arias-Tamargo, Yang-Hui He, Elli Heyes +2
We propose a new technique for classifying 5d Superconformal Field Theories arising from brane webs in Type IIB String Theory, using technology from Machine Learning to identify di…
Machine Learning Calabi-Yau Hypersurfaces
David S. Berman, Yang-Hui He, Edward Hirst
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 tec…
Polytopes and Machine Learning
Jiakang Bao, Yang-Hui He, Edward Hirst +3
We introduce machine learning methodology to the study of lattice polytopes. With supervised learning techniques, we predict standard properties such as volume, dual volume, reflex…
Some Open Questions in Quiver Gauge Theory
Jiakang Bao, Amihay Hanany, Yang-Hui He +1
Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various re…
Neurons on Amoebae
Jiakang Bao, Yang-Hui He, Edward Hirst
We apply methods of machine-learning, such as neural networks, manifold learning and image processing, in order to study 2-dimensional amoebae in algebraic geometry and string theo…
Hilbert Series, Machine Learning, and Applications to Physics
Jiakang Bao, Yang-Hui He, Edward Hirst +3
We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ${\s…
Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
Jiakang Bao, Omar Foda, Yang-Hui He +4
We show how to map Grothendieck's dessins d'enfants to algebraic curves as Seiberg-Witten curves, then use the mirror map and the AGT map to obtain the corresponding 4d $\mathcal{N…
Quiver Mutations, Seiberg Duality and Machine Learning
Jiakang Bao, Sebastián Franco, Yang-Hui He +3
We initiate the study of applications of machine learning to Seiberg duality, focusing on the case of quiver gauge theories, a problem also of interest in mathematics in the contex…
Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curves
Yang-Hui He, Edward Hirst, Toby Peterken
We apply machine-learning to the study of dessins d'enfants. Specifically, we investigate a class of dessins which reside at the intersection of the investigations of modular subgr…
Lectures on the Calabi-Yau Landscape
Jiakang Bao, Yang-Hui He, Edward Hirst +1
In these lecture notes, we survey the landscape of Calabi-Yau threefolds, and the use of machine learning to explore it. We begin with the compact portion of the landscape, focusin…