For each realization, a distorted chain was created by moving each atom from their position in the equilibrium geometry by a fixed displacement with a random direction. The comparison includes predictions from Hartree-Fock (HF, red, dotted), the Gaussian approximation potential framework (GAP, orange, dashed), as well as the variational continuation scheme from 5 training states of the symmetrically stretched chain (Continuation, blue, solid). Each data point corresponds to the mean over 1000 randomly generated geometries. The inset shows the mean squared force error obtained with the three methods, where the shaded area denotes the range of the errors over the random realizations. The training set of equidistant one-dimensional geometries include the equilibrium length, with an interatomic distance of 1.79 a 0 , as well as the 4 symmetric stretches of the atoms where the inter-atomic distance was increased and decreased by 0.5 a 0 and 1 a 0 . Source data are provided as a Source Data file.
