Efficient Atomic-Resolution Uncertainty Estimation for Neural Network Potentials Using a Replica Ensemble

Neural network potentials (NNPs) are gaining much attention as they enable fast molecular dynamics (MD) simulations for a wide range of systems while maintaining the accuracy of density functional theory calculations. Since NNP is constructed by machine learning on training data, its prediction uncertainty increases drastically as atomic environments deviate from training points. Therefore, it is essential to monitor the uncertainty level during MD simulations to judge the soundness of the results. In this work, we propose an uncertainty estimator based on the replica ensemble in which NNPs are trained over atomic energies of a reference NNP that drives MD simulations. The replica ensemble is trained quickly, and its standard deviation provides atomic-resolution uncertainties. We apply this method to a highly reactive silicidation process of Si(001) overlaid with Ni thin films and confirm that the replica ensemble can spatially and temporally trace simulation errors at atomic resolution, which in turn guides the augmentation of the training set. The refined NNP completes a 3.6 ns simulation without any noticeable problems. By suggesting an efficient and atomic-resolution uncertainty indicator, this work will contribute to achieving reliable MD simulations by NNPs.