Machine-learning dessins d’enfants: Explorations via modular and Seiberg–Witten curves
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Volume
54
DOI
10.1088/1751-8121/abbc4f
Journal
Journal of Physics A: Mathematical and Theoretical
Issue
ISSN
1751-8113
Metadata
Show full item recordAbstract
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 (SW) 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 SW curves for those with rational coefficients are also tabulated.
Authors
He, YH; Hirst, E; Peterken, TCollections
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