A machine learning-based selective sampling procedure for identifying the low energy region in a potential energy surface: a case study on proton conduction in oxides

In this paper, we propose a selective sampling procedure to preferentially evaluate a potential energy surface (PES) in a part of the configuration space governing a physical property of interest. The proposed sampling procedure is based on a machine-learning method called the Gaussian process, which is used to construct a statistical model of the PES for identifying the region of interest in the configuration space. We demonstrate the efficacy of the proposed procedure for atomic diffusion and ionic conduction, specifically, the proton conduction in a well-studied proton-conducting oxide, barium zirconate $({\mathrm{BaZrO}}_{3})$. The results of the demonstration study indicate that our procedure can efficiently identify the low-energy region characterizing the proton conduction in the host crystal lattice and that the descriptors used for the statistical PES model have a great influence on the performance.