Investigating Lunar Melt Viscosity via Deep Learning: A Kolmogorov-Arnold Networks (KANs) Approach

Viscosity is a fundamental physical parameter governing the generation, transport, and eruption of geological melts, dictating magma ascent rates, eruption styles, and the kinetics of physicochemical processes. On Earth, melts viscosities have been widely measured from various rock samples through high T-P (temperature & pressure) experiments, and a continuous viscosity-temperature-pressure (V-T-P) dependence can be obtained by different melt viscosity models. However, due to significant compositional differences, particularly in iron and titanium oxides between lunar and terrestrial basalts, no existing model can be simply used to predict magma viscosity on the Moon.

In this study, we have collected and trained on a comprehensive dataset of 28898 hand-curated melt measurements (compositions, pressure, temperatures and viscosity), including typical lunar melt types of ferrobasaltic melts, Apollo 15C green glass, Apollo 17 orange glass, Apollo 14 black glass, as well as synthetic high-titanium mare basalts and KREEP basalts. We have employed Kolmogorov-Arnold Networks (KANs) to construct a deep learning model and established a relationship between lunar melt viscosity and its temperature, pressure, and composition (V-T-P-C). Unlike traditional Multi-Layer Perceptrons (MLPs), KANs utilize learnable spline functions rather than fixed activation functions. This architecture offers superior interpretability and generalization capabilities, making it particularly suitable for predicting viscosity under complex thermodynamic conditions.

The predicted rheological behavior of KREEP lunar silicate melts (Apollo samples) from KANs are well consistent with experimental measurements. Taking into account the compositions of basalts obtained from Chang’e 5 and 6 sampling, model suggests that the viscosity values ( Pa·s ) of young basalts (~2.0 Ga for Chang’e 5 and ~2.8 Ga for Chang’e 6) are ~2.5 orders of magnitude lower than that of relatively older Apollo-type basalts (>3.0 Ga) under the same T-P conditions.