Title:

Prediciting Calabi-Yau Threefold Topology from the Kreuzer-Starke List of 4D Reflexive Polytopes

A neural network is used on a sample of 1,000,000 four dimensional reflexive polytopes out of 473,800,776 from the Kreuzer-Starke list to predict the Euler number and first and second Hodge numbers of the corresponding Calabi-Yau threefolds. For the input data, vertex coordinates are used along with features including number of dual vertices and number of dual lattice points. A fully connected network with rectified non-linearity is employed. The model is able to predict the exact Euler number, and first and second Hodge numbers with an accuracy of 36.35%, 40.62%, and 34.54%, respectively. The mean difference between actual and predicted are -0.33631 \pm 6.63236 for the Euler number, 0.58364 \pm 6.63748 for the first Hodge number, and 0.83766 \pm 7.66044 for the second Hodge number. The model is predicting each ontology at least better than first order. For instance, the difference between first order and predicted first Hodge number is about 5.0759 \pm 9.7083. Using layer-wise relevance propagation, we found that the most relevant input data is the number of dual lattice points, and feature data generally. Removing the vertex data and including more features may increase the accuracy.

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