Machine learning complete intersection Calabi-Yau 3-folds

Gaussian process regression, kernel support vector regression, the random forest, extreme gradient boosting, and the generalized linear model algorithms are applied to data of complete intersection Calabi-Yau threefolds. It is shown that Gaussian process regression is the most suitable for learning the Hodge number h2,1 in terms of h1,1. The performance of this regression algorithm is such that the Pearson correlation coefficient for the validation set is R2=0.9999999995 with a root mean square error RMSE=0.0002895011. As for the train set, these two parameters are as follows: R2=0.9999999994 and RMSE=0.0002854348. The training error and the cross-validation error of this regression are 1×10−9 and 1.28×10−7, respectively. Learning the Hodge number h1,1 in terms of h2,1 yields R2=1.000000 and RMSE=7.395731×10−5 for the validation set of the Gaussian process regression. Published by the American Physical Society 2024