Machine learning is all you need: A surrogate model for phase equilibrium prediction for planetary-scale models

Geodynamic models require constraints from phase equilibria to infer how changes in phase abundance and composition affect physical properties. When applying such models on a planetary scale, performance becomes especially crucial. Therefore, computationally costly methods, such as Gibbs free energy minimisation, are no longer a viable option for predicting phase equilibria directly. We present a machine learning (ML) surrogate that can approximate phase equilibrium predictions for silicate mantles of rocky planets. ML surrogates have proven to be useful tools for approximating complex physics-based simulations in various fields, as they are computationally efficient, highly scalable, and fully compliant with GPU-based computation in high-performance computing clusters and automatic differentiation.

We calibrated a neural network surrogate on a large synthetic dataset (n = 2.0×10⁶) generated using MAGEMin (Riel et al., 2022) and the thermodynamic dataset from Stixrude and Lithgow-Bertelloni (2022). The training dataset ranges over typical upper to transition-zone mantle conditions in terms of pressure, temperature, and bulk rock composition. The model architecture and calibration strategy presented can accurately predict the molar proportions and molar oxide composition of multicomponent solid solutions from pressure, temperature, and bulk rock composition. Constraints on mass balance and closure of compositional variables are actively enforced during calibration through additional physics-informed misfits, in addition to the data-driven convergence. Evaluation of the model indicates uncertainties of less than ±0.02 molmol^-1 for the prediction of phase fractions and less than ±0.005 molmol^-1 for most compositional variables within solid solutions for the phases considered. The performance assessment shows a systematic increase in computational speed of two orders of magnitude when comparing the prediction between the ML surrogate and MAGEMin. Moving the computation to a GPU can improve performance by up to 5 orders of magnitude, <100ns per point, for large data sets of 10⁵ points, compared to the Gibbs free energy minimiser.

In this presentation, the ML surrogate will be used to map the stability of wadsleyite, ringwoodite and akimotoite within the Martian mantle. This ultra-fast prediction method enables the incorporation of poorly constrained minor components (e.g. Na₂O) using a Monte Carlo approach. Our results demonstrate the significant influence of these minor components on phase stability. This, in turn, determines seismic velocities and can be associated with water storage in nominally anhydrous minerals.

 

[1] Riel, N., Kaus, B. J. P., Green, E. C. R., & Berlie, N. (2022). MAGEMin, an efficient Gibbs energy minimizer: Application to igneous systems. Geochemistry, Geophysics, Geosystems, 23.

[2] Stixrude, L. & Lithgow-Bertelloni, C. (2022), Thermal expansivity, heat capacity and bulk modulus of the mantle, Geophysical Journal International, 228 (2), 1119–1149.