Fig. 8: Error cancellation in formation energy predictions.
From: A critical examination of compound stability predictions from machine-learned formation energies

a Schematic illustration contrasting how random and systematic errors on ΔHf of the same average magnitude manifest as larger and smaller errors on predicted ground-state lines (ΔHd). b Comparing the performance on stability predictions using ML-predicted ΔHf (ΔHf,pred, filled bars) and ΔHf with perturbations drawn randomly from the distribution of ΔHf,pred errors (ΔHf,rand = ΔHf,MP + P[ΔHf,MP − ΔHf,pred], hatched bars). The mean absolute error (MAE) on ΔHd is shown by the black bars (left axis). The F1 score for classifying compounds as stable (ΔHd ≤ 0) or unstable (ΔHd > 0) is shown by the brown bars (right axis). The results for the randomly perturbed case are averaged over three random samples with the standard deviation shown as an error bar. The standard deviation is too small to see in most cases.