Systematic Comparison of Genetic Algorithm and Basin Hopping Approaches to the Global Optimization of Si(111) Surface Reconstructions

Machine-learning-accelerated simulations to enable automatic surface reconstruction

Understanding material surfaces and interfaces is vital in applications such as catalysis or electronics. By combining energies from electronic structure with statistical mechanics, ab initio simulations can, in principle, predict the structure of material surfaces as a function of thermodynamic variables. However, accurate energy simulations are prohibitive when coupled to the vast phase space that must be statistically sampled. Here we present a bi-faceted computational loop to predict surface phase diagrams of multicomponent materials that accelerates both the energy scoring and statistical sampling methods. Fast, scalable and data-efficient machine learning interatomic potentials are trained on high-throughput density-functional-theory calculations through closed-loop active learning. Markov chain Monte Carlo sampling in the semigrand canonical ensemble is enabled by using virtual surface sites. The predicted surfaces for GaN(0001), Si(111) and SrTiO3(001) are in agreement with past work and indicate that the proposed strategy can model complex material surfaces and discover previously unreported surface terminations.

Cluster-MLP: An Active Learning Genetic Algorithm Framework for Accelerated Discovery of Global Minimum Configurations of Pure and Alloyed Nanoclusters

Structural characterization of nanoclusters is one of the major challenges in nanocluster modeling owing to the multitude of possible configurations of arrangement of cluster atoms. The genetic algorithm (GA), a class of evolutionary algorithms based on the principles of natural evolution, is a commonly employed search method for locating the global minimum configuration of nanoclusters. Although a GA search at the DFT level is required for the accurate description of a potential energy surface to arrive at the correct global minimum configuration of nanoclusters, computationally expensive DFT evaluation of the significantly larger number of cluster geometries limits its practicability. Recently, machine learning potentials (MLP) that are learned from DFT calculations gained significant attention as computationally cheap alternative options that provide DFT level accuracy. As the accuracy of the MLP predictions is dependent on the quality and quantity of the training DFT data, active learning (AL) strategies have gained significant momentum to bypass the need of large and representative training data. In this application note, we present Cluster-MLP, an on-the-fly active learning genetic algorithm framework that employs the Flare++ machine learning potential (MLP) for accelerating the GA search for global minima of pure and alloyed nanoclusters. We have used a modified version the Birmingham parallel genetic algorithm (BPGA) for the nanocluster GA search which is then incorporated into distributed evolutionary algorithms in Python (DEAP), an evolutionary computational framework for fast prototyping or technical experiments. We have shown that the incorporation of the AL framework in the BPGA significantly reduced the computationally expensive DFT calculations. Moreover, we have shown that both the AL-GA and DFT-GA predict the same global minima for all the clusters we tested.

Atomistic Global Optimization X: A Python package for optimization of atomistic structures

Modelling and understanding properties of materials from first principles require knowledge of the underlyingatomistic structure. This entails knowing the individual chemical identity and position of all atoms involved.Obtaining such information for macro-molecules, nano-particles, clusters, and for the surface, interface, andbulk phases of amorphous and solid materials represents a difficult high-dimensional global optimizationproblem. The rise of machine learning techniques in materials science has, however, led to many compellingdevelopments that may speed up structure searches. The complexity of such new methods has prompted aneed for an efficient way of assembling them into global optimization algorithms that can be experimentedwith. In this paper, we introduce the Atomistic Global Optimization X (AGOX) framework and code, asa customizable approach that enables efficient building and testing of global optimization algorithms. Amodular way of expressing global optimization algorithms is described and modern programming practicesare used to enable that modularity in the freely available AGOX python package. A number of examplesof global optimization approaches are implemented and analyzed. This ranges from random search andbasin-hopping to machine learning aided approaches with on-the-fly learnt surrogate energy landscapes. Themethods are show-cased on problems ranging from supported clusters over surface reconstructions to largecarbon clusters and metal-nitride clusters incorporated into graphene sheets.