Parameter-Free and Electron Counting Satisfied Material Representation for Machine Learning Potential Energy and...

We proposed a parameter-free volume element representation that satisfies the electron counting model and obtains accurate machine learning potential energy and direct force fitting of randomly perturbed hexagonal BN. Our method preserves permutational, translational, and rotational invariance and can be extended to three-dimensional systems, verified by a system of bulk Si. As a result, we obtained 0.57 meV/atom potential energy root mean squared error (RMSE) and 59 meV/Å force RMSE for perturbed bulk BN systems and 0.43 meV/atom potential energy RMSE and 36 meV/Å force RMSE for perturbed Si systems. In addition, an unbiased perturbation-based data set construction scheme is introduced and a continuous population distribution is obtained with a training data set of 4500, which is about 1 order of magnitude smaller than standard methods based on first-principles molecular dynamics simulations and saves a large amount of computing resources. General validity of our model is verified by structure optimization, molecular dynamics simulations, and extrapolations.