A Set of Moment Tensor Potentials for Zirconium with Increasing Complexity

Machine learning force fields (MLFFs) are an increasingly popular choice for atomistic simulations due to their high fidelity and improvable nature. Here we propose a hybrid small-cell approach that combines attributes of both offline and active learning to systematically expand a quantum-mechanical (QM) database while constructing MLFFs with increasing model complexity. Our MLFFs employ the moment tensor potential formalism. During this process, we quantitatively assessed the structural properties, elastic properties, dimer potential energies, melting temperatures, phase stability, point defect formation energies, point defect migration energies, free surface energies, and generalized stacking fault (GSF) energies of Zr as predicted by our MLFFs. Unsurprisingly, the model complexity has a positive correlation with prediction accuracy. We also find that the MLFFs were able to predict the properties of out-of-sample configurations without directly including these specific configurations in the training dataset. Additionally, we generated 100 MLFFs of high complexity (1513 parameters each) that reached different local optima during training. Their predictions cluster around the benchmark DFT values, but subtle physical features such as the location of local minima on the GSF energy surface are washed out by statistical noise.