Calibration, Validation and Evaluation of Machine Learning Thermobarometers in Metamorphic Petrology: An Application to Biotite and Outlook for Future Strategy

Abstract

Geothermobarometry provides crucial constraints on the physical conditions of metamorphism, offering insights into petrogenetic processes and providing key information on thermal regimes and metamorphic depths to other geological disciplines. However, calibrating a thermobarometer from the natural record is challenging because independent pressure (P) and temperature (T) estimates are required, and the compositional variation of minerals—governed by multiple metamorphic reactions—must be captured in a complex function. This work calibrates a machine learning thermobarometer for biotite using relative P–T estimates based on mineral assemblage sequences. A neural network is used as a flexible model to fit a high-dimensional thermobarometric regression curve. To address the challenge of sparse training data, a transfer learning strategy is employed, where the model is primarily trained on a large dataset generated with phase equilibrium modelling before refinement with natural data. A general framework for calibrating machine learning thermobarometers is outlined using a neural network thermobarometer for biotite as an example. Selection of the best-performing model is guided by k-fold cross-validation alongside complementary accuracy checks using metamorphic sequences and precision assessments via Monte Carlo error propagation. Evaluation on an independent test dataset, compiled from the literature, indicates that the model is a potential biotite single-crystal thermometer with a root mean square error of ± 45°C, consistent with the estimated uncertainty of Ti-in-Bt thermometry applied to the same data. A potential barometer is affected by systematic underestimation of pressures above 0.6 GPa due to regression to the mean of the natural database, which is biased towards low-pressure metamorphism. This limits its applicability in higher-pressure regimes. This study highlights the potential of using neural networks with transfer learning in petrological applications since they are often constrained by limited natural data.