Abstract
A method has been developed to measure the similarity between materials, focusing on specific physical properties. The information obtained can be utilized to understand the underlying mechanisms and support the prediction of the physical properties of materials. The method consists of three steps: variable evaluation based on nonlinear regression, regression-based clustering, and similarity measurement with a committee machine constructed from the clustering results. Three data sets of well characterized crystalline materials represented by critical atomic predicting variables are used as test beds. Herein, the focus is on the formation energy, lattice parameter and Curie temperature of the examined materials. Based on the information obtained on the similarities between the materials, a hierarchical clustering technique is applied to learn the cluster structures of the materials that facilitate interpretation of the mechanism, and an improvement in the regression models is introduced to predict the physical properties of the materials. The experiments show that rational and meaningful group structures can be obtained and that the prediction accuracy of the materials' physical properties can be significantly increased, confirming the rationality of the proposed similarity measure.
Highlights
Computational materials science encompasses a range of methods to model materials and simulate their responses on different length and time scales (Sumpter et al, 2015)
The method for measuring this similarity consists of three steps: (i) variable evaluation based on nonlinear regression, (ii) regression-based clustering and (iii) similarity measurement with a committee machine (Tresp, 2001; Opitz & Maclin, 1999) constructed based on the clustering results
The qualitative evaluations were based on the rationality and interpretability of the obtained hierarchy with reference to the domain knowledge; the quantitative evaluations were performed based on the prediction accuracy (PA) of the predictive models constructed with reference to the obtained similarity between materials
Summary
Computational materials science encompasses a range of methods to model materials and simulate their responses on different length and time scales (Sumpter et al, 2015). The first aims to predict the physical properties of materials, and the second aims to describe and interpret the underlying mechanisms (Liu et al, 2017; Lu et al, 2017; Ulissi et al, 2017). In the first task of predicting physical properties, computerbased quantum mechanics techniques (Jain et al, 2016; Kohn & Sham, 1965; Jones & Gunnarsson, 1989; Jones, 2015) in the form of well established first-principles calculations are generally performed with high accuracy and are applicable to any material, but with high computational cost. The second task, i.e. describing and interpreting the mechanisms underlying the physical properties of materials, relies mostly on the experience, insight and even luck of the experts involved. The utilization of data-mining and machinelearning techniques to discover hidden structures and latent semantics in multidimensional data (Lum et al, 2013; Landauer et al, 1998; Blei, 2012) of materials is promising, but only limited work has been reported so far (Kusne et al, 2015; Srinivasan et al, 2015; Goldsmith et al, 2017)
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