New machine learning models on reevaluation of the Ti-in-zircon thermometer via multivariate trace elements†

Since the establishment of the single-element Ti-in-zircon thermometer in 2005, it has been extensively applied to estimate the crystallization temperatures of zircon due to its simplicity and convenience. Then, the thermometer was modified in the subsequent work, considering the effect of pressure as well as the activities of SiO₂ and TiO₂, even though whether or not the other competitive trace elements can also influence the predicted temperatures remains ambiguous. Here, an advanced high-dimensional temperature prediction model has been developed, which is based on the XGBoost algorithm and utilizes comprehensive trace element concentrations within zircon, achieved through training and comparing various machine learning algorithms. This model integrates a multitude of factors, not only the activities of SiO₂ and TiO₂, but also the intricate composition of trace elements and their interactivities. Four evaluation metrics, namely R², RMSE, MAE, and EV, were utilized to assess the algorithms' capabilities. The results show that it is imperative to consider all the trace elements within zircon as an integrated system, rather than only a few specific elements for accurate temperature prediction. Moreover, an in-depth analysis of the high-dimensional model was conducted by introducing SHAP, and it exhibits either positive or negative relationships between the trace elements and temperature. Finally, this model was applied to zircons crystallized in various temperature ranges from all over the world, which unveil features characterized by “both unity and diversity”. In summary, the XGBoost model is strongly recommended for temperature prediction in comparable regions and temperature ranges.