Learning Size and Shape of Calabi-Yau Spaces
This work addresses a domain-specific problem in theoretical physics for researchers studying Calabi-Yau spaces, and it is incremental as it builds on existing numerical methods with efficiency improvements.
The authors tackled the problem of computing metrics for string compactification spaces by developing a new machine learning library that is more sample- and computation-efficient than previous numerical approximations, and they observed a linear relation between PDE optimization and vanishing Ricci curvature.
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.