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 $h^{1,1}$ can be learnt very efficiently, with very high $R^2$ score and an accuracy of $96\%$, i.e. $96 \%$ of the predictions exactly match the correct values. For $h^{1,4},h^{2,3}, \eta$, we also find very high $R^2$ scores, but the accuracy is lower, due to the large ranges of possible values.

翻译：我们在至多四个复射影空间的乘积中构造了所有可能的完全交卡拉比-丘五重流形，约束条件不超过四个。共得到$27068$个空间（这些空间不通过配置矩阵的行列置换相关联），并计算了所有空间的欧拉数。排除其中$3909$个乘积流形后，我们计算了$12433$个情形（即非乘积空间的$53.7\%$）的上同调数据，获得了$2375$个不同的霍奇钻石。包含上述所有信息的数据集可在 https://www.dropbox.com/scl/fo/z7ii5idt6qxu36e0b8azq/h?rlkey=0qfhx3tykytduobpld510gsfy&dl=0 获取。本文展示了不变量的分布，并讨论了与低维类似情形的比较。基于分类器和回归器（包括全连接和卷积）神经网络，对上同调数据进行了监督学习。我们发现$h^{1,1}$的学习效率极高，$R^2$得分非常高且准确率达到$96\%$，即$96\%$的预测值与真实值完全匹配。对于$h^{1,4},h^{2,3}, \eta$，虽也获得较高的$R^2$得分，但由于可能取值区间较大，准确率有所降低。