Figure 23.

Atom-wise force regularization leads to high accuracy for phonon computations in silicon.¹⁹⁴ The general-purpose GAP-18 model already predicts accurate phonon frequencies for diamond-type silicon (“mp-149” identifier in the Materials Project database;¹⁹⁵ < 0.2 THz RMS error) but performs substantially worse for other allotropes, because it has not been fitted for those. The asterisk (*) indicates a structure which is erroneously predicted to be dynamically unstable. The extended GAP-18C model, which added specifically selected crystalline configurations, including supercells describing individual displacements with atom-wise force regularization, shows accurate phonon predictions throughout. Adapted from ref (194). Original work published under the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).