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. 2019 Apr 10;9:5879. doi: 10.1038/s41598-019-42277-9

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Scheme of the PL method for the DOS representation of surface structures and the predicted results. (a) Two-dimensional cleaved lattice structure to represent the plane vectors of the (011) and (111) low-index surface and the (211) high-index surface. Here, red, green, and violet nodes represent the atoms on the surface layer for the (211), (111), and (011) plane vector, respectively. The dotted lines represent the periodicities of the (111) and (011) lattice vectors. (b) Three-dimensional cubic diagram of the lattice plane vectors in the coordinate system for the inverse of miller indices h′, k′, and l′ representing the training (black circle) and test (red star) data. (c) DOS pattern of the Cu (211) surface. (d) DOS pattern of the Cu_0.375Ni_0.625 (211) surface. In (c,d), black corresponds to the DFT method, and pink corresponds to the learning method (use of three PCs) using the inverse value of the miller index as a feature. The atomic structures of each surfaces can be found in Supplementary Fig. S4.