mlsanityData to 13 Oct 2026

Machine Learning Calabi-Yau Hypersurfaces

arXiv 2112.06350 ↗First posted 12 Dec 2021hep-th math.AG stat.MLcited by 15

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Abstract (arXiv)

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 weights with an accuracy of R^2 > 95%. Supervised learning also allows us to identify weighted-P4s which admit Calabi-Yau hypersurfaces to 100% accuracy by making use of partitioning supported by the clustering behaviour.

Key facts. Cited by 15 papers in the map (data through 13 Oct 2026). Builds on 22 of its 61 references that are in the map. First posted on arXiv 12 Dec 2021.

Builds on

22 of 61 references.

References · 22

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,093
  2. 2020Detecting Symmetries with Neural Networkscited by 34
  3. 2020Neural Network Approximations for Calabi-Yau Metricscited by 32
  4. 2021Learning Size and Shape of Calabi-Yau Spacescited by 28
  5. 2021Building Quantum Field Theories Out of Neuronscited by 28
  6. 2021Machine-Learning Mathematical Structurescited by 25
  7. 2018Machine Learning CICY Threefoldscited by 22
  8. 2017Deep-Learning the Landscapecited by 21
  9. 2018The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learningcited by 19
  10. 2020Quiver Mutations, Seiberg Duality and Machine Learningcited by 19
  11. 2020Machine learning for complete intersection Calabi-Yau manifolds: a methodological studycited by 17
  12. 2020Machine Learning Calabi-Yau Four-foldscited by 17
10 more
  1. 2019Learning Algebraic Structures: Preliminary Investigationscited by 15
  2. 2020Inception Neural Network for Complete Intersection Calabi-Yau 3-foldscited by 14
  3. 2020Graph Laplacians, Riemannian Manifolds and their Machine-Learningcited by 12
  4. 2021Neurons on Amoebaecited by 11
  5. 2021Deep multi-task mining Calabi-Yau four-foldscited by 11
  6. 2019Searching the Landscape of Flux Vacua with Genetic Algorithmscited by 10
  7. 2020Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curvescited by 10
  8. 2019Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyercited by 8
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  10. 2019SO(8) Supergravity and the Magic of Machine Learningcited by 1

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Citing papers per year: 2022: 4; 2023: 5; 2024: 6.

15 papers.

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  1. 2022Cluster Algebras: Network Science and Machine Learningcited by 9
  2. 2024Can Transformers Do Enumerative Geometry?cited by 8
  3. 2023Machine Learning Clifford invariants of ADE Coxeter elementscited by 6
  4. 2023Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-foldscited by 5
  5. 2024A Triumvirate of AI Driven Theoretical Discoverycited by 5
  6. 2023Constructing and Machine Learning Calabi-Yau Five-foldscited by 4
  7. 2022Machine Learning Algebraic Geometry for Physicscited by 3
  8. 2022Identifying equivalent Calabi--Yau topologies: A discrete challenge from math and physics for machine learningcited by 2
  9. 2024Deep Learning Calabi-Yau four folds with hybrid and recurrent neural network architecturescited by 2
  10. 2024Generative AI for Brane Configurations and Coamoebacited by 2
  11. 2022Intelligent Explorations of the String Theory Landscapecited by 1
  12. 2024Learning 3-Manifold Triangulationscited by 1
3 more
  1. 2024Machine Learning Mutation-Acyclicity of Quiverscited by 1
  2. 2023Black holes and the loss landscape in machine learningcited by 0
  3. 2023Calabi-Yau Four/Five/Six-folds as mathbbPnw Hypersurfaces: Machine Learning, Approximation, and Generationcited by 0