Toward Constraining Mars' Thermal Evolution Using Machine Learning

• Published in: Earth and space science (Hoboken, N.J.) Vol. 8; no. 4
• Main Authors: Agarwal, S., Tosi, N., Kessel, P., Padovan, S., Breuer, D., Montavon, G.
• Format: Journal Article
• Language: English
• Published: Hoboken John Wiley & Sons, Inc 01.04.2021; American Geophysical Union (AGU)
• Subjects: Earth; Heat; inverse problem; Inverse problems; Lithosphere; Machine learning; mantle convection; Mars; mixture density networks; Partial differential equations; Rheology; Simulation; Viscosity
• ISSN: 2333-5084; 2333-5084
• DOI: 10.1029/2020EA001484

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 (1019 − 1022 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 (105 − 5 × 105 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. Plain Language Summary The mantle of rocky planets like Mars behaves like a highly viscous fluid over geological time scales. Key parameters and initial conditions for the non‐linear partial differential equations governing mantle flow are poorly known. Machine Learning (ML) can help us avoid running several thousand computationally expensive fluid dynamic simulations each time to determine if an observable can constrain a parameter. Using an ML approach, we invert a set of synthetic observables such as present‐day surface heat flux, duration of volcanism and radial contraction to constrain important parameters controlling the long‐term evolution of the planet's interior, such as the reference mantle viscosity or the partitioning of radiogenic heat sources between mantle and crust. We demonstrate that by training a probabilistic ML algorithm on the data and applying it, we can quantify the constraints on parameters. This provides a high‐dimensional framework for analyzing inverse problems in geodynamics. Key Points Mixture Density Networks provide a probabilistic framework for inverting observables to infer parameters of Mars' interior evolution Reference viscosity, crustal enrichment in heat‐producing elements and initial mantle temperature can be well constrained Activation energy of diffusion creep can be weakly constrained; constraining activation volume requires new observational signatures