A machine learning framework for constraining mantle convection parameters
Abstract
The inverse problem of constraining parameters and initial conditions governing mantle convection from observables from planetary missions is non-unique and non-linear. Hence, a probabilistic framework is advantageous. However, given the computational cost of forward simulations of thermal convection, Markov Chain Monte Carlo methods are rarely used. Some recent studies have proposed using Mixture Density Networks (MDN) (Bishop 1995) to approximate the posterior probability using only datasets of simulations run apriori (e.g. Kaufl et al. 2016, Atkins et al. 2016). Using a dataset of 6130 2D simulations for a Mars-like planet, we systematically isolate the degree to which a parameter can be constrained using different present-day synthetic observables (Agarwal et. al 2021). We randomly vary 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 temperature. The simulations include physical processes such as depth-dependent phase-transitions, pressure- and temperature-dependent viscosity as well as pressure- and temperature-dependent thermal conductivity and expansivity. The loss function (log-likelihood) used to optimize the weights of the MDN provides a robust measure of how well a parameter can be constrained. We test different numbers and combinations of observables (e.g. heat flux at the surface and core-mantle boundary, radial contraction and melt produced) to constrain the five parameters. Given all observables, reference viscosity can be constrained to within 32% of its entire range, crustal enrichment factor within 15%, activation energy within 80%, and initial mantle temperature within 39%. The activation volume cannot be constrained and requires research into new observables in space and time, as well as fields other than just temperature. Testing different levels of uncertainty in the observables, we found that constraints on different parameters loosen at different rates, with initial temperature being the most sensitive. Finally, we show that the marginal MDN can be modified to model the joint probability for all parameters, thereby providing a more comprehensive picture of all the evolution scenarios that fit the given observational constraints.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2021
- Bibcode:
- 2021AGUFM.P11B..14A