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(a) shows the toric diagram for $\mathbb{C}^3/\mathbb{Z}_3$ and the corresponding ideal triangulation into unit area triangles. (b) is the corresponding dual web-diagram with normal vectors to each boundary edges of the triangulation. Notice that we have 3-vectors, given that the original toric diagram is on a plane at height 1.

The distribution of extremal vertices of toric diagrams for the set of 15,151 distinct toric Calabi-Yau 3-folds that are used as train and test sets for our machine learning models.

An example of a data entry vector for a particular toric Calabi-Yau 3-fold in our dataset. (a) shows the toric diagram obtained by cutting corners of a 5x5 lattice square and (b) shows the corresponding extremal lattice points of the toric diagram embedded in a 9x9 input matrix. The full data vector for this toric Calabi-Yau 3-fold is summarized in (c).

Illustration of the linear regression model. The features are weighted by the respective weights and added to form the output. The bias weight $w_0$ is illustrated as an additional feature, which is fixed to 1.

The $x$-axis corresponds to $E(y^{\mathcal C})$ of the 645 categories. The red curve plots the prediciton of $y$ via linear regression for the classes. The blue dots indicate the maximum $y$ taken for a class of values $\mathcal C$ and the green dots the minimum value.

The wide and deep model. The toric diagram data $\mathcal D$ is fed into a convolutional layer and further processed in two fully connected layers. The outputs are linearly combined with the output of a linear regression on the features $\hat{f}$.

The $x$-axis corresponds to the minimum volume $V_{min}$ and the y-axis to the percentage error $\epsilon$ ($\times100\%$). The blue dots correspond to the errors between the prediction and should be results for the coupled linear regression and CNN.

The $x$-axis corresponds to the minimum volume $V_{min}$ and the y-axis to the percentage error $\epsilon$ ($\times100\%$). The blue dots correspond to the errors between the prediction and should be results for the pure CNN.