Machine_learning_Dessins

We study dessin d’enfants in this report, combining mathematical analysis with machine learning techniques.3 We begins by examining mathematical foundations of dessin d’enfants, forming the basis for subsequent computational analysis. Using PCA, we try to find the data’s dimensionality to a judiciously chosen lowerdimensional space, then apply K-Means clustering to find inherent data patterns. We explore a range of cluster numbers and employ inertia analysis to identify natural clusters. We build a neural network using the MLPClassifier architecture to predict Galois orbit size from dessin representations (adjacency matrices and cyclic edge lists). We achieved an accuracy of 0.42 for adjacency matrices and 0.50 for cyclic edge list.