A general machine learning model of aluminosilicate melt viscosity and its application to the surface properties of dry lava planets

TL;DR

This work develops a general ML model for predicting the viscosity of aluminosilicate melts across wide temperature, pressure, and compositional ranges by combining a Greybox neural network with a Gaussian process. The Greybox ANN embeds the Vogel–Tamman–Fulcher relation to constrain temperature dependence, while the GP provides accurate predictions with uncertainty quantification, achieving RMSE around 0.4–0.44 log10 Pa·s on unseen data. Trained on a large dataset of 28,898 viscosity measurements spanning room to 30 GPa, the model outperforms several baselines and remains physically plausible beyond the training domain. Applied to the magma ocean on the lava planet K2-141 b, the approach yields dayside full melting with low viscosities and a tenuous atmosphere near the substellar point, and suggests a largely solid nightside with potential geothermal-driven heat transport; these results demonstrate the method’s utility for exoplanet interior and surface investigations, while highlighting the need for more high-pressure data to improve extrapolation robustness.

Abstract

Ultra-short-period exoplanets like K2-141 b likely have magma oceans on their dayside, which play a critical role in redistributing heat within the planet. This could lead to a warm nightside surface, measurable by the James Webb Space Telescope, offering insights into the planet's structure. Accurate models of properties like viscosity, which can vary by orders of magnitude, are essential for such studies. We present a new model for predicting molten magma viscosity, applicable in diverse scenarios, including magma oceans on lava planets. Using a database of 28,898 viscosity measurements on phospho-alumino-silicate melts, spanning superliquidus to undercooled temperatures and pressures up to 30 GPa, we trained a greybox artificial neural network, refined by a Gaussian process. This model achieves high predictive accuracy (RMSE $\approx 0.4 \log_{10}$ Pa$\cdot$s) and can handle compositions from SiO$_2$ to multicomponent magmatic and industrial glasses, accounting for pressure effects up to 30 GPa for compositions such as peridotite. Applying this model, we calculated the viscosity of K2-141 b's magma ocean under different compositions. Phase diagram calculations suggest that the dayside is fully molten, with extreme temperatures primarily controlling viscosity. A tenuous atmosphere (0.1 bar) might exist around a 40° radius from the substellar point. At higher longitudes, atmospheric pressure drops, and by 90°, magma viscosity rapidly increases as solidification occurs. The nightside surface is likely solid, but previously estimated surface temperatures above 400 K imply a partly molten mantle, feeding geothermal flux through vertical convection.

Figures (9)

• Figure 1: (a) Bar plots showing the number of compositions including a particular oxide component in the database. (b) Viscosity versus temperature diagram showing all data from the full database. Data from the SciGlass database are shown in grey. Colored symbols indicate high pressure data.
• Figure 2: Viscosity against reciprocal temperature of an anorthite melt (a), and against pressure for albite melt (b). Symbols are measurements from the hand-held database ferraina2024 and lines are model predictions (see legend). Only the predictions of the three best models are represented in (b).
• Figure 3: (a) Calculated viscosity with the GP model versus measurements. The black dashed line represent the 1:1 correspondence, and the grey dashed lines the average 95 % confidence interval ($\pm 0.9$). (b), (c) and (d) Comparison between Gaussian process (GP) viscosity predictions and data available in ferraina2024 for albite NaAlSi$_3$O$_8$, wollastonite CaSiO$_3$ and peridotite melts. The viscosity at high pressure and high temperature ($\eta (T,P)$) is represented relative to that at the same temperature and 1 bar ($\eta (T,P=1\, bar)$, calculated from an interpolative fit of experimental data with the Vogel-Tammann-Fulcher equation).
• Figure 4: (a) Viscosity in Na$_2$O-SiO$_2$ melts as a function of the silica content. (b) Viscosity at 3000 K as a function of temperature for peridotite melt. Lines are predictions from three GP models; solid lines indicate that the models worked in interpolative regime, dashed lines indicate extrapolations. The grey shaded region indicates the region in which no data was available.
• Figure 5: Longitudinal temperature profile at the surface of K2-141 b. See text for details.