  We apply machine-learning to the study of dessins d'enfants. Specifically, we
investigate a class of dessins which reside at the intersection of the
investigations of modular subgroups, Seiberg-Witten curves and extremal
elliptic K3 surfaces. A deep feed-forward neural network with simple structure
and standard activation functions without prior knowledge of the underlying
mathematics is established and imposed onto the classification of extension
degree over the rationals, known to be a difficult problem. The classifications
reached 0.92 accuracy with 0.03 standard error relatively quickly. The
Seiberg-Witten curves for those with rational coefficients are also tabulated.
