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Clinopyroxene ferric iron content is an important consideration for garnet-clinopyroxene geothermometry and estimations of water storage in the Earth’s interior but remains difficult and expensive to measure. Here, we develop seven classic algorithms and machine learning methods to estimate Fe3+/ΣFe in clinopyroxene using major element data from electron microprobe analyses. The models were first trained using a large data set of clinopyroxene Fe3+/ΣFe values determined by Mössbauer spectroscopy and spanning a wide compositional range, with major uncertainties ranging from 0.25 to 0.3 and root-mean-square errors on the test data set ranging from 0.071 to 0.089. After dividing the entire data set into three compositional sub-data sets, the machine learning models were trained and compared for each sub-data set. Our results suggest that ensemble learning algorithms (random forest and Extra-Trees) perform better than principal component analysis-based elastic net polynomial, artificial neural network, artificial neural network ensemble, decision trees, and linear regressions. Using a sub-data set excluding clinopyroxene in spinel peridotite and omphacite in eclogite, the new models achieved uncertainties of 0.15 to 0.2 and root-mean-square errors on the test data set ranging from 0.051 to 0.078, decreasing prediction errors by 30–40%. By incorporating compositional data on coexisting spinel, new models for clinopyroxene in spinel peridotite show improved performance, indicating the interaction between spinel and clinopyroxene in spinel peridotite. Feature importance analysis shows Na+, Ca2+, and Mg2+ to be the most important for predicting Fe3+ content, supporting the coupled substitution between Ca2+-M2+ and Na+-M3+ in natural clinopyroxenes. The application of our models to garnet-clinopyroxene geothermometry greatly improves temperature estimates, achieving uncertainties of ±50 °C, compared with uncertainties of ±250 °C using previous models assuming all Fe as Fe2+ or calculating Fe3+ by charge conservation. Differences in the ferric iron contents, as calculated using the machine learning models, of clinopyroxenes that did or did not experience hydrogen diffusion during their crystallization from basaltic magma support a redox-driven mechanism for hydrogen diffusion in clinopyroxene.

Dataset_M is the file for our training data set containing different values of pressure (GPa), temperature (°C), and melt compositions (Iron, Nickel, Sulfur, Carbon in wt%). Our objective is to predict the Carbon Concentration based on the measured values of P, T, Fe, Ni, S. For this purpose we set P, T, Fe, Ni, S to be the predictors and Carbon to be our target variable and train different ML models to find the best model (based on MAE, MSE or RMSE) for our study that can predict the Carbon values with sufficiently good accuracy. Dataset_O is our new test data whereby we predict the Cabon concentrations based on the measured values of P, T, Fe, Ni, and S from the best model (Extra Trees) obtained from training on Dataset_M Dataset_N is the predictions from the ML model we used to draw the phase boundaries. Dataset_P is the dataset incorporating the uncertainties in the measured values of predictors and the Carbon concentration. We use this as our test dataset to generate samples randomly within the uncertainty range for 1000 Monte Carlo simulations and generate the mean Carbon predictions and standard deviation (2σ variation) and correlate how the concentrations vary compared to the measured Carbon values., also available on https://github.com/ZJUEarthData/Carbon_Prediction

Dataset 1 Parent dataset of global mantle clinopyroxene compositions. Dataset 2 Labeled dataset for training the ML model to classify clinopyroxene compositions as affected or unaffected by metasomatism. Dataset 3 Application dataset. For details, please see the corresponding manuscript that describes the study and readme txt in the dataset file., For more details and updated version code see https://github.com/ZJUEarthData/BenQin_mantle-matesomatism-machine-learning