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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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Estimation of coefficients and prediction results of the PL method in ternary alloy systems. (a) Triangular diagram of the Cu-Ni-Pt system representing the training data (circle) and test data (star). The equation for the calculation of the PCs coefficients for the test data is shown at the bottom of the figure: the equation is based on the coefficients and their weights for training alloys that most closely match the test alloy composition. (b) Maps of the weights of the coefficients of the PC vectors for the test composition (Cu_0.03Ni_0.03Pt_0.94). The weights depends on the distance between the test composition and each training composition, and they also depend on the difference of three features (n_d, CN, and F_mix) between the training and test data. (c) DOS pattern of the Cu_0.03Ni_0.03Pt_0.94 test alloy. (d) DOS pattern of the Cu_0.32Ni_0.34Pt_0.34 test alloy. Their atomic structures are shown in Supplementary Fig. S3. In (c,d), black corresponds to the DFT method, and pink corresponds to the learning method using all features including n_d, CN, and F_mix.