Toward Constraining Mars' Thermal Evolution Using Machine Learning

Abstract

• Mixture Density Networks provide a probabilistic framework for inverting observables to infer parameters of Mars' interior evolution. 10 • Reference viscosity, crustal enrichment in heat-producing elements and initial mantle 11 temperature can be well constrained. 12 • Activation energy of diffusion creep can be weakly constrained; constraining activation 13 volume requires new observational signatures.

Deep learning for surrogate modeling of two-dimensional mantle convection

“…(c) The outputs of the simulations can be processed to arrive at certain lower-dimensional observables such as (d) the horizontally averaged 1D temperature profiles or (e) more global quantities such as the surface heat flux, radial contraction, duration of volcanism, etc. ML methods have been shown to work well for these low-dimensional observables, both (f) in a forward study [27] and (g) in an inverse study [13]. In this work, we demonstrate that (h) a surrogate can model 2D mantle convection using deep learning.…”

“…It is not straightforward to predict how consequential these errors would be to constraining the parameters. Ideally, one would conduct an inverse study to test the sensitivity of uncertainties in the observables resulting from instrumentation and/or from the surrogate model [13].…”

“…A number of inverse-problem studies have attempted to overcome this computational bottleneck of expensive simulations, ranging from using modified Markov chain Monte Carlo (MCMC) methods [7,8], all the way to completely bypassing MCMC methods and directly learning the mapping between parameters and observables from simulations run prior to the inversion using mixture density networks (MDNs) [9][10][11][12][13].…”

“…In fact, Ref. [13] demonstrated that using the same setup for a Mars-like planet as in Ref. [27], the surface heat flux provides only a loose constraint for parameters governing mantle convection and even knowledge of the entire 1D temperature profile is insufficient for constraining certain parameters (e.g., the activation volume of diffusion creep rheology, which controls the pressure dependence of the viscosity).…”

Deep learning for surrogate modelling of 2D mantle convection

“…A number of inverse-problem studies have attempted to overcome this computational bottleneck of expensive simulations, ranging from using modified Markov Chain Monte Carlo (MCMC) methods (for an overview, see [8]), all the way to completely bypassing MCMC methods and directly learning the mapping between parameters and observables from simulations run prior to the inversion using Mixture Density Networks (MDN) (e.g., [9][10][11][12][13]).…”