This dissertation presents a framework for developing neural-network interatomic potential models for use in large-scale atomistic simulations of materials. The goal is to minimize the number of descriptors and thus enhance the speed with accuracy comparable to that achieved in other machine-learned models. We also seek to provide a framework that is readily generalizable to multicomponent systems.

One of the aims of this dissertation is to present a new type of descriptor that has the potential to uniquely describe the radial and angular distribution functions of atomic configurations. Other descriptors that are based on similar radial and angular distribution functions have not been proven to be able to uniquely describe these distribution functions. Moreover, when used to describe systems with multiple species, previous such descriptors invariably introduce either informational degeneracy or must be expanded in number. The former introduces a source for loss of accuracy while the latter added computational cost. The descriptor proposed in this work avoids both problems.

Using a Response Surface Methodology, we show that, given a descriptor length, an optimization of the hyperparameters of our descriptors leads to a reduction in errors in forces and energies, i.e., a better description of the underlying potential energy surface. This differs from the current norm of using a predetermined sets of hyperparameters for the descriptors.We implemented a two-stage procedure to perform highly parallelized multi-nodal hyperparameter tuning for the descriptors, as well as the training of our Species-separated Gaussian Coefficient Neural Network Potential (SSGC NNP). When compared to a Spectral Neighbor Analysis Potential (SNAP) trained on the same dataset of density- functional theory (DFT) energies and forces for elemental Molybdenum (Mo), our SSGC NNP formalism produces lower errors in energies and forces. Mean absolute error in energies and forces of SSGC NNP are 7.0 meV/atom and 0.335 eV/Å, while that of SNAP are 8.6 meV/atom and 0.604 eV/ Å, respectively. It achieves this accuracy with slightly less than half the number of descriptors. Our NNP also displays smaller errors in predictions than the SNAP potential for properties that it was not fitted on. Similar results are obtained for a SSGC NNP trained on a previously developed database of DFT energies and forces for elemental Rhenium (Re). This is achieved with with the computational cost of SSGC NNP being about half that of SNAP for Mo and one tenth that for Re.

We employ the Re SSGC NNP to investigate the relaxed core structure of a edge dislocation in hcp Re. We show direct evidence of {112-1} twin nucleation from the dislocation under applied stress, which supports previous theoretical investigations suggesting this mechanism as being a source for the predominance of the {112-1} deformation twinning mode observed in experimental compression mechanical tests in polycrystalline samples. Furthermore, when a c-axis tensile stress is applied, the {112-1} twin grows initially, but its growth becomes coupled with the formation and growth of a {112-2} twin at high stress values. The {112-2} twin is not observed in the simulations when the stress is applied off the c-axis. The results not only provide new insights into deformation twinning in Re, but also demonstrate the scale of simulations that can be readily addressed with the SSGC NNP formalism.

The significance of this dissertation is that it shows the efficacy of a proposed novel descriptor formalism and associated highly parallelized training workflow in producing machine-learning potentials with sufficient accuracy to be used in simulations that contain millions of atoms and beyond. Our method produces highly accurate potentials with computational speed that is only about four times more than that of a MEAM potential for Mo and an EAM potential for Re. This opens up the possibility for long-time and long- length scale simulations with our SSGC NNP formalism, in a manner that is anticipated to scale extremely well with the number of distinct atomic species.