A machine-learning-based surrogate model of Mars' thermal evolution

Abstract

Constraining initial conditions and parameters of mantle convection for a planet often requires running several hundred computationally expensive simulations in order to find those matching certain 'observables', such as crustal thickness, duration of volcanism, or radial contraction. A lower fidelity alternative is to use 1-D evolution models based on scaling laws that parametrize convective heat transfer. However, this approach is often limited in the amount of physics that scaling laws can accurately represent (e.g.Temperature and pressure-dependent rheologies or mineralogical phase transitions can only be marginally simulated). We leverage neural networks to build a surrogate model that can predict the entire evolution (0-4.5 Gyr) of the 1-D temperature profile of a Mars-like planet for a wide range of values of five different parameters: reference viscosity, activation energy and activation volume of diffusion creep, enrichment factor of heat-producing elements in the crust and initial temperature of the mantle. The neural network we evaluate and present here has been trained from a subset of ∼10 000 evolution simulations of Mars ran on a 2-D quarter-cylindrical grid, from which we extracted laterally averaged 1-D temperature profiles. The temperature profiles predicted by this trained network match those of an unseen batch of 2-D simulations with an average accuracy of $99.7\, {\rm per~cent}$.