Magdalena Larfors, Andre Lukas, Fabian Ruehle et al.
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.
Harold Erbin, Riccardo Finotello, Robin Schneider et al.
We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi-Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi-Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for $h^{(1,1)}$ and 97% for $h^{(2,1)}$ (100% for both), 81% (96%) for $h^{(3,1)}$, and 49% (83%) for $h^{(2,2)}$. Assuming that the Euler number is known, as it is easy to compute, and taking into account the linear constraint arising from index computations, we get 100% total accuracy.