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On Machine Learning Complete Intersection Calabi-Yau 3-folds

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arXiv:2404.11710v1 Announce Type: new
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 3-folds. 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.

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