Machine learning complete intersection Calabi-Yau 3-folds

TL;DR

This paper applies various machine learning algorithms to data on complete intersection Calabi-Yau threefolds, finding Gaussian process regression to be highly effective in predicting Hodge numbers with near-perfect accuracy.

Contribution

The study demonstrates the effectiveness of Gaussian process regression in accurately learning Hodge numbers of Calabi-Yau threefolds, outperforming other machine learning methods.

Findings

Gaussian process regression achieves R^2 ≈ 1 for predicting Hodge numbers.

The method yields extremely low RMSE, indicating high prediction accuracy.

Gaussian process regression outperforms other algorithms in this context.

Abstract

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 h^(2,1)in terms of h^(1,1). The performance of this regression algorithm is such that the Pearson correlation coefficient for the validation set is R^2 = 0.9999999995 with a Root Mean Square Error RMSE = 0.0002895011. As for the calibration set, these two parameters are as follows: R^2 = 0.9999999994 and RMSE = 0.0002854348. The training error and the cross-validation error of this regression are 10^(-9) and 1.28 * 10^(-7), respectively. Learning the Hodge number h^(1,1)in terms of h^(2,1) yields R^2 = 1.000000 and RMSE = 7.395731 * 10^(-5) for the validation set of the Gaussian Process regression.