Modelling the Thermodynamic Properties of Melts Using Machine Learning

Thermodynamic models underpin geodynamic simulations, allowing density relationships to be described over planetary pressure and temperature scales. However, within a magma ocean setting the description of density in the liquid phase is lacking due to experimental complexities, a continuous compositional evolution of the liquid phase and scaling issues rooted in the mixing model of traditional equation of state (EoS) fitting methods. To overcome these challenges, in this thesis, datasets are constructed from density functional theory (DFT) calculations and machine learning algorithms are used to build thermodynamic models. The Guassian process regression (GPR) and artificial neural network (ANN) algorithms are used to describe the response in density to pressure and temperature, on a compositionally simple system (MgO-CaO-SiO2). This system size is typically the limit of a traditional EoS, before scaling of the mixing model parameters becomes unmanageable. It is found that the GPR algorithm outperforms the ANN, with a 21.5% decrease seen for the RMSE score on the independent cross-validation dataset. This indicates that the GPR algorithm could be more robust at handling interpolation between training compositions and is the favoured algorithm of this study. This dataset was then expanded into the NCFMAS system, which represents the major oxide components of a chondritic Earth, used as the initial magma ocean bulk composition. Corrections are also considered to the pressure results of the DFT calculations. Real world tests were constructed from published experimental and DFT density values, which show a good agreement with the model’s predicted values. Another model was also constructed from this dataset, where internal energy is also considered as a target alongside density. This multi-output model is used to perform a compositional search for the newly discovered liquid silicate layer, situated above the Martian core, by using geophysical overserved values from InSight mission data.