Machine Learning Bayesian Force Fields and Applications to Phase Transformations

Abstract

This thesis develops machine learning Bayesian force fields for efficient and accurate molecular dynamics simulations of materials. The Gaussian process regression model provides uncertainty quantification, enabling Bayesian active learning to iteratively collect first-principle data and improve model accuracy. To overcome unfavorable scaling with training set size, the Gaussian process forces and uncertainties are mapped to low-dimensional spline functions or polynomial forms to enable high efficiency at inference time. To address the unfavorable scaling with the number of chemical elements of the descriptor dimensionality, we devised an embedding method for dimension reduction. We also parallelized the sparse GP force field using MPI, allowing for efficient use of large computational resources during training. These advances enable large-scale molecular dynamics studies of complex processes like phase transformations. The thesis investigates the 2D to 3D transition of stanene, the high-pressure phase transition of SiC, and the high-temperature decomposition and incongruent melting of SiC. The Bayesian force fields demonstrate computational speeds comparable to empirical potentials, while achieving accuracy on par with density functional theory. The atomic-level insights into stability, structure, and dynamics align well with experiments. Overall, this thesis puts forth a framework for developing transferable and systematically improvable machine learning Bayesian force fields. The integration of active learning, dimensionality reduction, and high performance computing pushes the boundaries of what is tractable in large-scale atomistic simulations. The applications showcase the ability to model complex material phenomena beyond the reach of conventional computational methods.