Machine Learning-Based Predictions for Half-Heusler Phases

Abstract

Machine learning models (Support Vector Regression) were applied for predictions of several targets for 18-electron half-Heusler phases: a lattice parameter, a bulk modulus, a band gap, and a lattice thermal conductivity. The training subset, which consisted of 47 stable phases, was studied with the use of Density Functional Theory calculations with two Exchange-Correlation Functionals employed (GGA, MBJGGA). The predictors for machine learning models were defined among the basic properties of the elements. The most optimal combinations of predictors for each target were proposed and discussed. Root Mean Squared Errors obtained for the best combinations of predictors for the particular targets are as follows: 0.1 Å (lattice parameters), 11–12 GPa (bulk modulus), 0.22 eV (band gaps, GGA and MBJGGA), and 9–9.5 W/mK (lattice thermal conductivity). The final results of the predictions for a large set of 74 semiconducting half-Heusler compounds were disclosed and compared to the available literature and experimental data. The findings presented in this work encourage further studies with the use of combined machine learning and ab initio calculations.

Machine Learning-Based Predictions of Power Factor for Half-Heusler Phases

“…Nevertheless, the general hint on the crucial elemental factors for the target may be the fact that over 150 favourable combinations (from RMSE of 0.319 mW/K 2 m for [n, r, k, i(I), VEC] and [n, i(I), VEC] to RMSE of 0.339 mW/K 2 m for [g, k, i(III), VEC]) included at least one of the following predictors: n, i(I), and VEC. The significance of the indicated properties is in accord with the favourable features found in SVR modelling of other parameters of hH phases [3], i.e., i(I) and VEC were crucial for band gaps. Whereas n and i(I) may reflect the width of a band gap and the effective mass, VEC may be connected with some characteristic features of band structures, e.g., the number and shape of valence bands.…”

“…Neither the most nor the least numerous combinations of predictors minimize RMSE for the particular model, which justifies the requirement of testing of various combinations of predictors. Analogous observations were reported for SVR models for different physical properties of hH systems [3]. Nevertheless, the general hint on the crucial elemental factors for the target may be the fact that over 150 favourable combinations (from RMSE of 0.319 mW/K 2 m for [n, r, k, i(I), VEC] and [n, i(I), VEC] to RMSE of 0.339 mW/K 2 m for [g, k, i(III), VEC]) included at least one of the following predictors: n, i(I), and VEC.…”

“…As the predictors for SVR models, the following features of the elements in the XYZ phases were employed: atomic mass u, atomic radius r, molar volume V, density of a solid g, electronegativity n, Debye temperature T, thermal conductivity k, I-III ionization energies: i(I), i(II), i(III), and Valence Electron Count VEC. According to the previous ML studies [2,3,7,8], these features were found to be relevant for modelling of various properties of hH phases. The targets examined based on the listed predictors were PF and ZT at 300 K in the p and n-regimes.…”

“…Machine Learning (ML) models are increasingly used as support for ab initio calculations of various properties of half-Heusler (hH) alloys [1][2][3]. Depending on the relations and character of the parameters investigated, different ML methods are employed, e.g., Boosted Decision Tree Regression, Multiple Linear Regression [2], or Random Forest Regression [1].…”

“…Careful investigations among 2000 combinations of eleven elemental properties of ions present in ternary hH compounds (up to 33-dimensional feature space) as potential predictors of structural and electronic properties for arbitrarily chosen subsets of hH systems (47 hH phases as the train-test records and 74 hH systems for predictions) were presented in the recent study [3]. The root mean squared errors of ML-based predictions for the lattice parameters (0.1 Å), bulk modulus (11)(12), band gap (0.22 eV), and the lattice thermal conductivity (9-9.5 W/mK) proved general ability of the Support Vector Regression (SVR) methods to predict various properties of hH materials.…”