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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.

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The universal mathematical form of machine-learning potentials (MLPs) shifts the core of development of interatomic potentials to collecting proper training data. Ideally, the training set should encompass diverse local atomic environments but conventional approaches are prone to sampling similar configurations repeatedly, mainly due to the Boltzmann statistics. As such, practitioners handpick a large pool of distinct configurations manually, stretching the development period significantly. To overcome this hurdle, methods are being proposed that automatically generate training data. Herein, we suggest a sampling method optimized for gathering diverse yet relevant configurations semi-automatically. This is achieved by applying the metadynamics with the descriptor for the local atomic environment as a collective variable. As a result, the simulation is automatically steered toward unvisited local environment space such that each atom experiences diverse chemical environments without redundancy. We apply the proposed metadynamics sampling to H:Pt(111), GeTe, and Si systems. Throughout these examples, a small number of metadynamics trajectories can provide reference structures necessary for training high-fidelity MLPs. By proposing a semi-automatic sampling method tuned for MLPs, the present work paves the way to wider applications of MLPs to many challenging applications.

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