Machine learning methods for geometry optimization of atomic structures

In this thesis, a series of novel methods for the identification of the optimal geometry of atomic structures are introduced. The geometry of a material or molecule, that is, the arrangement of its atoms in space, determines all its properties. Thus, the determination of the geometry of an atomic system is the first step in any computational study and the development of computationally efficient methods is important in order to accelerate research in materials science.

Even though methods for the identification of the structures with minimum energy (both locally and globally) and transition states are abundant in literature, these methods often rely on quantum chemistry methods, such as density functional theory (DFT), which can be computationally very expensive. The methods presented in this thesis address this issue by using machine learning methods to model the potential energy surface. The machine learning model can then be used to guide the search of the optimal geometry and, thus, reduce the computational time.

An important subfield of geometry optimization of atomic structures is the identification of a local minimum of the potential energy surface, that is, a structure with no internal forces on the atoms. For this problem, we introduce two new minimization methods, which consistently achieve a reduction of the number of DFT calculations. For one of these methods, we show that this reduction can be of up to a factor two for adsorption systems. We further show that the reuse of the trajectories from former local optimizations and transition state search methods can further speed up the calculations.

For many applications, however, it is not enough to use a local optimization method, since the approximate structure of the system studied is not known. In this thesis we present two different methods to tackle this problem. We have proposed a method that uses a message-passing neural network to determine the optimal prototype for a material. This can be used in the context of computational screening. Furthermore, we have extended the Gaussian process regression formalism used in local optimization so that it can be used for the global optimization problem. In this way, we have created a novel global optimization method that can identify the global minimum in a fraction of the DFT evaluations needed by other methods, and used it to identify the optimal structure of Ta₆O₁₅ clusters and the oxidized structure of ZrN.