Numerical Calabi-Yau metrics from holomorphic networks

Abstract

We propose machine learning inspired methods for computing numerical Calabi-Yau (Ricci flat Kähler) metrics, and implement them using Tensorflow/Keras. We compare them with previous work, and find that they are far more accurate for manifolds with little or no symmetry. We also discuss issues such as overparameterization and choice of optimization methods.

Version accepted by MSML 2021

References in corpus (5)

• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• Numerical Calabi-Yau metrics
• Numerical Kaehler-Einstein metric on the third del Pezzo
• Numerical approximations to extremal metrics on toric surfaces
• Eigenvalues and eigenforms on Calabi-Yau threefolds

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• Applying machine learning to the Calabi-Yau orientifolds with string vacua
• Calabi-Yau CFTs and Random Matrices
• Machine Learned Calabi-Yau Metrics and Curvature
• Metric Flows with Neural Networks
• Heterotic Line Bundle Models on Generalized Complete Intersection Calabi Yau Manifolds
• Explicit Soft Supersymmetry Breaking in the Heterotic M-Theory $B-L$ MSSM
• Learning Size and Shape of Calabi-Yau Spaces