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

A universal equivariant graph neural network for the elasticity tensors of any crystal system

The elasticity tensor that describes the elastic response of a material to external forces is among the most fundamental properties of materials. The availability of full elasticity tensors for inorganic crystalline compounds, however, is limited due to experimental and computational challenges. Here, we report the materials tensor (MatTen) model for rapid and accurate estimation of the full fourth-rank elasticity tensors of crystals. Based on equivariant graph neural networks, MatTen satisfies the two essential requirements for elasticity tensors: independence of the frame of reference and preservation of material symmetry. Consequently, it provides a universal treatment of elasticity tensors for all crystal systems across diverse chemical spaces. MatTen was trained on a dataset of first-principles elasticity tensors garnered by the Materials Project over the past several years (we are releasing the data herein) and has broad applications in predicting the isotropic elastic properties of polycrystalline materials, examining the anisotropic behavior of single crystals, and discovering new materials with exceptional mechanical properties. Using MatTen, we have discovered a hundred new crystals with extremely large maximum directional Young's modulus and eleven polymorphs of elemental cubic metals with unconventional spatial orientation of Young's modulus

A KIM-compliant potfit for fitting sloppy interatomic potentials : application to the EDIP model for silicon

Fitted interatomic potentials are widely used in atomistic simulations thanks to their ability to compute the energy and forces on atoms quickly. However, the simulation results crucially depend on the quality of the potential being used. Force matching is a method aimed at constructing reliable and transferable interatomic potentials by matching the forces computed by the potential as closely as possible, with those obtained from first principles calculations. The potfit program is an implementation of the force-matching method that optimizes the potential parameters using a global minimization algorithm followed by a local minimization polish. We extended potfit in two ways. First, we adapted the code to be compliant with the KIM Application Programming Interface (API) standard (part of the Knowledgebase of Interatomic Models Project). This makes it possible to use potfit to fit many KIM potential models, not just those prebuilt into the potfit code. Second, we incorporated the geodesic Levenberg–Marquardt (LM) minimization algorithm into potfit as a new local minimization algorithm. The extended potfit was tested by generating a training set using the KIM Environment-Dependent Interatomic Potential (EDIP) model for silicon and using potfit to recover the potential parameters from different initial guesses. The results show that EDIP is a “sloppy model” in the sense that its predictions are insensitive to some of its parameters, which makes fitting more difficult. We find that the geodesic LM algorithm is particularly efficient for this case. The extended potfit code is the first step in developing a KIM-based fitting framework for interatomic potentials for bulk and two-dimensional materials. The code is available for download via https://www.potfit.net

A Genome Wide Association Study Identifies Common Variants Associated with Lipid Levels in the Chinese Population

Plasma lipid levels are important risk factors for cardiovascular disease and are influenced by genetic and environmental factors. Recent genome wide association studies (GWAS) have identified several lipid-associated loci, but these loci have been identified primarily in European populations. In order to identify genetic markers for lipid levels in a Chinese population and analyze the heterogeneity between Europeans and Asians, especially Chinese, we performed a meta-analysis of two genome wide association studies on four common lipid traits including total cholesterol (TC), triglycerides (TG), low-density lipoprotein cholesterol (LDL) and high-density lipoprotein cholesterol (HDL) in a Han Chinese population totaling 3,451 healthy subjects. Replication was performed in an additional 8,830 subjects of Han Chinese ethnicity. We replicated eight loci associated with lipid levels previously reported in a European population. The loci genome wide significantly associated with TC were near DOCK7, HMGCR and ABO; those genome wide significantly associated with TG were near APOA1/C3/A4/A5 and LPL; those genome wide significantly associated with LDL were near HMGCR, ABO and TOMM40; and those genome wide significantly associated with HDL were near LPL, LIPC and CETP. In addition, an additive genotype score of eight SNPs representing the eight loci that were found to be associated with lipid levels was associated with higher TC, TG and LDL levels (P = 5.52×10-16, 1.38×10-6 and 5.59×10-9, respectively). These findings suggest the cumulative effects of multiple genetic loci on plasma lipid levels. Comparisons with previous GWAS of lipids highlight heterogeneity in allele frequency and in effect size for some loci between Chinese and European populations. The results from our GWAS provided comprehensive and convincing evidence of the genetic determinants of plasma lipid levels in a Chinese population