Efficient global optimisation with a machine learned surrogate model

Malthe K. Bisbo and Bjørk Hammer
Aarhus University, Denmark

Knowing the exact atomic configuration of chemical systems is a prerequisite for calculating their chemical properties, making automated structure determination an important field. When using density functional theory (DFT), current search methods are however limited in either thoroughness or to relatively small systems because of the large number of expensive DFT calculations required. Inspired by the current popularity of machine learning, we propose a surrogate based search method that relies on machine learning to reduce the required number of DFT calculations by orders of magnitude. The majority of current search methods rely on locally relaxing new candidate structures with DFT, which requires multiple DFT calculations for each candidate. We use a Gaussian Process regression (GPR) [1] model as a cheap surrogate model of the potential energy surface, and train it on the fly using all DFT energies accumulated during the search. Throughout the search all local relaxations [2] are performed using this cheap surrogate model, and single DFT calculations are only made for especially promising surrogate- relaxed candidates. To quantify how promising new structures are, we take into account both the energy and uncertainty predicted by the GPR model as a means to balance exploration and exploitation in the search [3]. The orders of magnitude performance gain compared to a standard GA is exemplified on the recently discovered SnO2(110)-(4x1) surface reconstruction [4] as well as the anatase TiO2(001)-(1x4) reconstruction, for which the complexity of the problem is varied by increasing the number of bulk layers included in the search. To demonstrate the versatility of the method we proceed to address the hitherto prohibitively complex problems of determining the edge structure of graphene patches on Ir(111) as well as that of the oxidized edge. The resulting structures are used to study the atomistic mechanisms involved in intercalation of oxygen in the system.

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