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In this paper we propose a method for the optimal allocation of observations between an intrinsically explainable glass box model and a black box model. An optimal allocation being defined as one which, for any given explainability level (i.e. the proportion of observations for which the explainable model is the prediction function), maximizes the performance of the ensemble on the underlying task, and maximizes performance of the explainable model on the observations allocated to it, subject to the maximal ensemble performance condition. The proposed method is shown to produce such explainability optimal allocations on a benchmark suite of tabular datasets across a variety of explainable and black box model types. These learned allocations are found to consistently maintain ensemble performance at very high explainability levels (explaining 74% of observations on average), and in some cases even outperform both the component explainable and black box models while improving explainability. 

Abstract The degree of short-range order (SRO) can influence the physical and mechanical properties of refractory multi-principal element alloys (RMPEAs). Here, the effect of SRO degree on the atomic configuration and properties of the equiatomic TiTaZr RMPEA is investigated using the first-principles calculations. Their key roles on the lattice parameters, binding energy, elastic properties, electronic structure, and stacking fault energy (SFE) are analyzed. The results show the degree of SRO has a significant effect on the physical and mechanical properties of TiTaZr. During the SRO degree increasing in TiTaZr lattice, the low SRO degree exacerbates the lattice distortion and the high SRO degree reduces the lattice distortion. The high degree of SRO improves the binding energy and elastic stiffness of the TiTaZr. By analyzing the change in charge density, this change is caused by the atomic bias generated during the formation of the SRO, which leading to a change in charge-density thereby affecting the metal bond polarity and inter-atomic forces. The high SRO degree also reduces SFE, which means the capability of plastic deformation of the TiTaZr is enhanced.