A Machine Learning-Based Approach to Clinopyroxene Thermobarometry: Model Optimization and Distribution for Use in Earth Sciences

Thermobarometry is a fundamental tool to quantitatively interrogate magma plumbing systems and broaden our appreciation of volcanic processes. Developments in random forest-based machine learning lend themselves to a data-driven approach to clinopyroxene thermobarometry, allowing users to access large experimental data sets that can be tailored to individual applications in Earth Sciences. We present a methodological assessment of random forest thermobarometry using the R freeware package extraTrees. We investigate the model performance, the effect of hyperparameter tuning, and assess different methods for calculating uncertainties. Deviating from the default hyperparameters used in the extraTrees package results in little difference in overall model performance (<0.2 kbar and <3°C difference in standard error estimate, SEE). However, accuracy is greatly affected by how the final value from the distribution of trees in the random forest is selected (mean, median, or mode). Using the mean value leads to higher residuals between experimental and predicted P and T, whereas using median values produces smaller residuals. Additionally, this work provides two scripts for users to apply the methodology to natural data sets. The first script permits modification and filtering of the model calibration data set. The second script contains premade models, where users can rapidly input their data to recover PT estimates (SEE clinopyroxene-only model: 3.2 kbar, 72.5°C and liquid-clinopyroxene model: 2.7 kbar, 44.9°C). Additionally, the scripts allow the user to estimate the uncertainty for each analysis, which in some cases is significantly smaller than the reported SEE. These scripts are open source and can be accessed at https://github.com/corinjorgenson/RandomForest-cpx-thermobarometer.