Constructing and Machine Learning Calabi-Yau Five-folds

We construct all possible complete intersection Calabi-Yau five-folds in a product of four or less complex projective spaces, with up to four constraints. We obtain 27068 spaces, which are not related by permutations of rows and columns of the configuration matrix, and determine the Euler number for all of them. Excluding the 3909 product manifolds among those, we calculate the cohomological data for 12433 cases, i.e. 53.7 % of the non-product spaces, obtaining 2375 different Hodge diamonds. The dataset containing all the above information is available at https://www.dropbox.com/scl/fo/z7ii5idt6qxu36e0b8azq/h?rlkey=0qfhx3tykytduobpld510gsfy&dl=0 . The distributions of the invariants are presented, and a comparison with the lower-dimensional analogues is discussed. Supervised machine learning is performed on the cohomological data, via classifier and regressor (both fully connected and convolutional) neural networks. We find that h1,1 can be learnt very efficiently, with very high R2 score and an accuracy of 96%, i.e. 96 % of the predictions exactly match the correct values. For h1,4,h2,3, η, we also find very high R2 scores, but the accuracy is lower, due to the large ranges of possible values.