Figure 1
From: Accelerated crystal structure prediction of multi-elements random alloy using expandable features
Schematic representation for feature transformation module to obtain {\(n_{d}^{ex}\), \(\sigma_{d}^{ex}\)} features from {\(n_{d}\)(N), \(\sigma_{d}\)(N)} features. {\(n_{d}\)(N), \(\sigma_{d}\)(N), C, δ} features in alloy {\(M\)(N)} consist of raw features. With regression tree ensembles, {\(n_{d}\)(N), \(\sigma_{d}\)(N)} features are transformed to {\(n_{d}\) tr (N), \(\sigma_{d}\) tr (N)}. In this transformation, {C, δ} features are used in edges in the ensemble tree. Then, by vector-wise average pooling, {\(n_{d}\) tr (N), \(\sigma_{d}\) tr (N)} is reduced to {\(n_{d}^{ex}\), \(\sigma_{d}^{ex}\)} features, which used C of the constituent atom as weight. {\(n_{d}^{ex}\), \(\sigma_{d}^{ex}\)} is used for the training of the calculated binary alloy dataset. Note that {\(n_{d}\)(N), \(\sigma_{d}\)(N)} features are the information from a pure transition metal, while {\(n_{d}^{ex}\), \(\sigma_{d}^{ex}\)} features represent the information in alloy condition. After the training of the module, the {\(n_{d}^{ex}\), \(\sigma_{d}^{ex}\)} features obtained from multi-element alloys can be used for the prediction of the structural phases.
