A neural network-based surrogate model to accelerate mineral phase equilibria calculations for silicate melts in arc settings

The modern view of magmatic systems includes transport and storage of melt at depths within the solid crust. An important process that directly controls the thermo-physical properties of magmatic systems is the chemical differentiation of the melt. Calculating the thermodynamic properties of the melt during its transport through the system is a well-known computational bottleneck in most multi-phase transport algorithms.

 

We present a Multi-Layer-Perceptron (MLP) surrogate model for fast prediction of thermodynamic properties of silicate melts in arc settings. The MLP takes a bulk rock composition of nine major oxides (SiO2-Al2O3-CaO-MgO-FeO-TiO2-NaO-K2O-H2O), temperature, and pressure as input variables and returns the melt fraction, composition, as well as the melt and system density. The surrogate model’s ability to predict thermodynamic properties is tested for data it has not seen during the training process. Results indicate that the MLP generalizes well within the range of the database. The melt fraction and components (i.e., major oxide concentration in the melt) are predicted with a root-mean square error (RMSE) of less than 1 wt-% and the densities with an average RMSE of ca. 5 kg/m3. 

 

The synthetic data set for training and testing the model has been generated with MAGEMin, a parallelized Gibbs energy minimization software (Riel et al., 2022). MAGEMin features adaptive mesh refinement (AMR) capabilities. This functionality allows for high resolution phase diagrams at important reaction lines with a minimum amount of computational points. Our synthetic database consists of 360’000 MAGEMin minimization points. As input parameters to MAGEMin we used anhydrous compositions from arc settings provided by the GEOROC database (Lehnert et al., 2000) varying 43-60 wt-% SiO2 and a pressure-temperature range of 650-1000°C and 1.0-10.0 kbar.

 

Predicting melt properties with the surrogate model is a point-wise operation which takes only a fraction of a second for hundreds of thousands of points. This functionality opens the door for accelerating mineral equilibria calculations within the framework of high-performance computing transport algorithms. We discuss possible application of the surrogate model within the framework of modern geodynamic algorithm architectures.

 

 

 

References:

 

Lehnert, K., Su, Y., Langmuir, C. H., Sarbas, B., & Nohl, U. (2000). A global geochemical database structure for rocks. Geochemistry, Geophysics, Geosystems, 1(5).

 

Riel, N., Kaus, B. J., Green, E. C. R., & Berlie, N. (2022). MAGEMin, an efficient Gibbs energy minimizer: application to igneous systems. Geochemistry, Geophysics, Geosystems, 23(7), e2022GC010427.