Fig. 4.

Results and insights from ML model. a The fitting results of test bandgaps $E_{\mathrm{g}}^{\mathrm{PBE}}$ and predicted bandgaps $E_{\mathrm{g}}^{\mathrm{ML}}$. Coefficient of determination (R²), Pearson coefficient (r) and mean squared error (MSE) are computed to estimate the prediction errors. The subplot is the convergence of model accuracy for five cross-validation split of the data. b Scatter plots of tolerance factors against the bandgaps for the prediction dataset from trained ML model (blue, red and dark gray plots represent train, test and prediction set, respectively). Data visualization of predicted bandgaps for all possible HOIPs (one color represents a class of halogen perovskites) with (c) tolerance factor, (d) octahedral factor, (e) ionic polarizability for the A-site ions, and (f) electronegativity of B-site ions. The dotted box represents the most appropriate range for each feature