mlsanityData to 13 Oct 2026

Learning Size and Shape of Calabi-Yau Spaces

arXiv 2111.01436 ↗First posted 2 Nov 2021hep-th cs.LGcited by 28

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Abstract (arXiv)

We present a new machine learning library for computing metrics of string compactification spaces. We benchmark the performance on Monte-Carlo sampled integrals against previous numerical approximations and find that our neural networks are more sample- and computation-efficient. We are the first to provide the possibility to compute these metrics for arbitrary, user-specified shape and size parameters of the compact space and observe a linear relation between optimization of the partial differential equation we are training against and vanishing Ricci curvature.

Key facts. Cited by 28 papers in the map (data through 13 Oct 2026). Builds on 4 of its 43 references that are in the map. First posted on arXiv 2 Nov 2021.

Builds on

4 of 43 references.

References · 4

  1. 2020Scaling Laws for Neural Language Modelscited by 6,494
  2. 2020Neural Network Approximations for Calabi-Yau Metricscited by 32
  3. 2019Machine learning Calabi-Yau metricscited by 23
  4. 2020Unsupervised Neural Networks for Quantum Eigenvalue Problemscited by 15

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 3; 2022: 6; 2023: 3; 2024: 5; 2025: 4; 2026: 7.

28 papers.

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  1. 2021Machine Learning Calabi-Yau Hypersurfacescited by 15
  2. 2022Machine Learned Calabi-Yau Metrics and Curvaturecited by 14
  3. 2024Rigor with Machine Learning from Field Theory to the Poincar'e Conjecturecited by 12
  4. 2021Calabi-Yau Metrics, Energy Functionals and Machine-Learningcited by 9
  5. 2023Metric Flows with Neural Networkscited by 9
  6. 2021Machine Learning Kreuzer--Skarke Calabi--Yau Threefoldscited by 8
  7. 2025Physics-informed neural network solves minimal surfaces in curved spacetimecited by 6
  8. 2026A Machine Learning Approach to the Nirenberg Problemcited by 5
  9. 2024Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfacescited by 4
  10. 2026Neural and numerical methods for G2-structures on contact Calabi-Yau 7-manifoldscited by 4
  11. 2026Minimising Willmore Energy via Neural Flowcited by 4
  12. 2022Machine Learning Algebraic Geometry for Physicscited by 3
16 more
  1. 2024cymyc -- Calabi-Yau Metrics, Yukawas, and Curvaturecited by 3
  2. 2022From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlookcited by 2
  3. 2024Generative AI for Brane Configurations and Coamoebacited by 2
  4. 2026Minimal surfaces, Knots, and Neural Networkscited by 2
  5. 2022Intelligent Explorations of the String Theory Landscapecited by 1
  6. 2022Machine Learning on generalized Complete Intersection Calabi-Yau Manifoldscited by 1
  7. 2024Neural Network Learning and Quantum Gravitycited by 1
  8. 2025Hamiltonian Neural Networks approach to fuzzball geodesicscited by 1
  9. 2025Approximate Ricci-flat Metrics for Calabi-Yau Manifoldscited by 1
  10. 2026Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillationcited by 1
  11. 2026PINNs in More General Geometrycited by 1
  12. 2022Characterizing 4-string contact interaction using machine learningcited by 0
  13. 2023Calabi-Yau Four/Five/Six-folds as mathbbPnw Hypersurfaces: Machine Learning, Approximation, and Generationcited by 0
  14. 2023Learning to be Simplecited by 0
  15. 2025Machine Learning the 6d Supergravity Landscapecited by 0
  16. 2026GlobalCY I: A JAX Framework for Globally Defined and Symmetry-Aware Neural K"ahler Potentialscited by 0