5 - Data-driven acceleration of first-principles saddle point and local minimum search based on scalable Gaussian processes

Abstract

The potential energy surface (PES), the mapping from high-dimensional space of atomic positions to the free energy level of a material system, is important for building structure–property relationships at the atomistic level. The PES can be constructed by calculating the system energy with first-principles approaches such as density functional theory (DFT). Searching for local minima, saddle points, and minimum energy paths (MEPs) on the PES is the essential task in functional materials design. But it is very challenging because of the curse of dimensionality and the numerical approximation errors involved in constructing the PES. In this chapter, a first-principles local minima and saddle points searching method based on a scalable Gaussian process (GP), called GP-DFT, is described. The searching algorithm is performed based on the DFT calculation and a concurrent searching method for MEPs assisted by the GP surrogate model that approximates the PES. The concurrent searching method is able to locate multiple MEPs on the PES simultaneously. The surrogate model is composed of multiple local GPs, where each corresponds to a subset of observations in the complete dataset. The potential energy is then predicted using a weighted linear average scheme of the posterior means for each local GP. The scalable GP scheme is developed to alleviate the computational bottleneck of the classical GP method. The uncertainty associated with the potential energy prediction is quantified through the posterior variance of the surrogate model. Two computational materials examples of studying hydrogen embrittlement in Fe and FeTi systems are used to demonstrate the scalability and efficiency of the proposed searching algorithm.