Data analysis of millions of Type IIB flux vacua

We study the vacuum structure of flux compactifications of type IIB string theory on the degree 18 hypersurface in ${\mathbb{C}\mathbb{P}}_{1,1,1,6,9}^4$ with two effective complex structure moduli. We scan $\mathrm{30,770,178}$ flux choices compatible with the tadpole bound, and use a gradient-based constrained minimization based on the SLSQP algorithm to identify candidates for local minima of the scalar potential, yielding a dataset of millions of candidate flux vacua. Using the $\mathrm{1,296,633}$ reliable solutions selected from this dataset, we analyze distributions and correlations of various physical quantities such as vacuum expectation values of moduli and vacuum energy. Using quadratic flux invariants as input features, we train a classifier to identify solutions satisfying the numerical SUSY criterion $\mathrm{\mid }V\mathrm{\mid }<{10}^{-4.5}$. On a randomly selected test set, selecting the top-ranked $5\mathrm{\%}$ recovers $47.2\mathrm{\%}$ of the SUSY test solutions. We also use supervised regression to predict the potential and moduli field values. In the regression comparison, quadratic flux invariant inputs improve prediction of potential value and the complex-structure coordinates, while the vanilla six flux parameters give better predictions for the axio-dilaton coordinates under the tested settings.