Development of Interatomic Potentials with Uncertainty Quantification: Applications to Two-dimensional Materials

University of Minnesota Ph.D. dissertation.July 2019. Major: Aerospace Engineering and Mechanics. Advisor: Ellad Tadmor. 1 computer file (PDF); xiii, 198 pages.Atomistic simulation is a powerful computational tool to investigate materials on the microscopic scale and is widely employed to study a large variety of problems in science and engineering. Empirical interatomic potentials have proven to be an indis- pensable part of atomistic simulation due to their unrivaled computational efficiency in describing the interactions between atoms, which produce the forces governing atomic motion and deformation. Atomistic simulation with interatomic potentials, however, has historically been viewed as a tool limited to provide only qualitative insight. A key reason is that in such simulations there are many sources of uncertainty that are difficult to quantify, thus failing to give confidence interval on the obtained results. This thesis presents my research work on the development of interatomic potentials with the ability to quantify the uncertainty in simulation results. The methods to train interatomic po- tentials and quantify the uncertainty are demonstrated via two-dimensional materials and heterostructures throughout this thesis, whose low-dimensional nature makes them distinct from their three-dimensional counterparts in many aspects. Both physics-based and machine learning interatomic potentials are developed for MoS2 and multilayer graphene structures. The new potentials accurately model the interactions in these systems, reproducing a number of structural, energetic, elastic, and thermal properties obtained from first-principles calculations and experiments. For physics-based poten- tials, a method based on Fisher information theory is used to analyze the parametric sensitivity and the uncertainty in material properties obtained from phase average. We show that the dropout technique can be applied to train neural network potentials and demonstrate how to obtain the predictions and the associated uncertainties of material properties practically and efficiently from such potentials. Putting all these ingredients of my research work together, we create an open-source fitting framework to train inter- atomic potentials and hope it can make the development and deployment of interatomic potentials easier and less error prone for other researchers