Cluster-formula-embedded machine learning for design of multicomponent β-Ti alloys with low Young’s modulus

The present work formulated a materials design approach, a cluster-formula-embedded machine learning (ML) model, to search for body-centered-cubic (BCC) β-Ti alloys with low Young’s modulus (E) in the Ti–Mo–Nb–Zr–Sn–Ta system. The characteristic parameters, including the Mo equivalence and the cluster-formula approach, are implemented into the ML to ensure the accuracy of prediction, in which the former parameter represents the BCC-β structural stability, and the latter reflects the interactions among elements expressed with a composition formula. Both auxiliary gradient-boosting regression tree and genetic algorithm methods were adopted to deal with the optimization problem in the ML model. This cluster-formula-embedded ML can not only predict alloy property in the forward design, but also design and optimize alloy compositions with desired properties in multicomponent systems efficiently and accurately. By setting different objective functions, several new β-Ti alloys with either the lowest E (E = 48 GPa) or a specific E (E = 55 and 60 GPa) were predicted by ML and then validated by a series of experiments, including the microstructural characterization and mechanical measurements. It could be found that the experimentally obtained E of predicted alloys by ML could reach the desired objective E, which indicates that the cluster-formula-embedded ML model can make the prediction and optimization of composition and property more accurate, effective, and controllable.