Toward Constraining Mars' Thermal Evolution Using Machine Learning

Abstract

Abstract The thermal and convective evolution of terrestrial planets like Mars is governed by a number of initial conditions and parameters, which are poorly constrained. We use Mixture Density Networks (MDN) to invert various sets of synthetic present-day observables and infer five parameters: reference viscosity, activation energy and activation volume of the diffusion creep rheology, an enrichment factor for radiogenic elements in the crust, and initial mantle temperature. The data set comes from 6,130 two-dimensional simulations of the thermal evolution of Mars' interior. We quantify the possibility of constraining a parameter using the log-likelihood value from the MDN. Reference viscosity can be constrained to within 32% of its entire range (10^19 − 10^22 Pa s), when all the observables are available: core-mantle-boundary heat flux, surface heat flux, radial contraction, melt produced, and duration of volcanism. Furthermore, crustal enrichment factor (1–50) can be constrained, at best, to within 15%, and the activation energy (10^5 − 5 × 10^5 J mol−1) to within 80%. Initial mantle temperature can be constrained to within 39% of its range (1,600–1,800 K). Using the full present-day temperature profile or parts of it as an observable tightens the constraints further. The activation volume (4 × 10^−6 − 10 × 10^−6 m3 mol−1) cannot be constrained. We also tested different levels of uncertainty in the observables and found that constraints on different parameters loosen differently, with initial temperature being the most sensitive. Finally, we present how a joint probability model for all parameters can be obtained from the MDN.