Fig. 2: The active learning workflow and the accuracy verification of the constructed neural network potential (NNP).

a The integration of three steps of the training of NNP models, exploration of new configuration, and calculation of energies and forces at density functional theory (DFT) level. Besides, the structure of the NNP models is also presented, where Ri is the Cartesian coordinate, Di is the descriptor, and Ei is the energy. The comparison of phonon dispersion of (b) BAs and (c) GaN between NNP and DFT. d–i The comparison of energies and forces of BAs, GaN, GaN-BAs heterostructures from NNP predictions and DFT calculations, where color indicates the number density of points.