Fig. 1: Domains of applicability of three 2d-models of a noisy third-degree polynomial.
From: Identifying domains of applicability of machine learning models for materials science
Three different models, linear (top), radial basis function (rbf, center), and polynomial (poly, bottom), are shown approximating the same distribution of two independent features x1 ~ N(0, 2) and x2 ~ N(0, 2), and the target property \(y \sim {x}_{1}^{3}-{x}_{1}+N(0,\exp ({x}_{2}/2))\), where N(μ, ϵ2) denotes a normal distribution with mean μ and standard deviation ϵ. Test points are plotted in 3d plots against the prediction surface of the models (color corresponds to absolute error) where the DA is highlighted in gray. The distributions of individual errors for the DA (gray) and globally (black) are shown in the 2d plots of each panel with the mean error (solid) and the 95th percentile (95 perc./dashed) marked by vertical lines. Note that the global error distribution of the linear model has a considerably long tail, which is capped in the image.
