Unraveling the interior evolution of terrestrial planets through machine learning

Mantle convection plays a fundamental role in the long-term thermal evolution of terrestrial planets like Earth, Mars, Mercury and Venus. Yet, key parameters and initial conditions of the partial differential equations governing mantle convection are poorly constrained. This often requires a large sampling of the parameter space to determine which combinations can satisfy certain observational constraints. Traditionally, 1D models based on scaling laws used to parameterize convective heat transfer, have been used to tackle the computational bottleneck of high-fidelity forward runs in 2D or 3D. However, these are limited in the amount of physics they can model (e.g. depth dependent material properties are difficult to incorporate into these models) and predict only mean quantities such as the mean mantle temperature. In the first study, feed-forward neural networks (FNN) are trained on a large number of 2D simulations of a Mars-like planet to overcome these limitations. Given five key parameters governing mantle convection, the FNNs can reliably predict the evolution of the entire 1D laterally-averaged temperature profile in time. The five parameters that are varied throughout the thesis are: reference viscosity (which controls the overall vigor of convection), activation energy and activation volume of the diffusion creep rheology (which accounts for the pressure- and temperature-dependence of the viscosity, respectively), an enrichment factor for radiogenic elements in the crust (which controls the partitioning of the radiogenic elements in the mantle and the crust), and the initial radial distribution of the mantle temperature. In a related study, machine learning is used for probabilistic inversion. Using Mixture Density Networks (MDN), various sets of synthetic present-day observables for a Mars-like planet are inverted to infer the same five mantle convection parameters. It is shown that the constraints on a parameter can be quantified using the log-likelihood value, the negative of which is used as the loss function to train an MDN. The crustal enrichment factor of radiogenic heat sources can be constrained the best, followed by reference viscosity, when all the observables are available: core-mantle-boundary heat flux, surface heat flux, radial contraction, melt produced and duration of volcanism. The initial mantle temperature can be constrained if the radial contraction is available with at least some parts of the temperature profile. Activation energy of diffusion creep can only be weakly constrained, while the activation volume of diffusion creep cannot be constrained at all in the present setup. Different levels of uncertainty were also emulated in the observables and it was found that constraints on different parameters loosen with varying rates, with initial temperature being the most sensitive. The marginal MDN is modified to obtain a joint probability model, which captures the cross-correlations among all parameters. Finally surrogate modeling is revisited, but for predicting the full 2D temperature field, which contains more information in the form of convection structures such as rising hot plumes and sinking cold downwellings. Deep learning techniques are able to produce reliable parameterized surrogates (i.e. surrogates that predict state variables such as temperature based only on input parameters) of the solution of the underlying partial differential equations. First, convolutional autoencoders are used to compress the size of each temperature field and retain only the most important features in form of a latent space. Then, FNNs and long-short term memory networks (LSTM) are used to predict the compressed fields from the five mantle convection parameters. Proper orthogonal decomposition of the LSTM and FNN predictions shows that despite a lower mean relative accuracy, LSTMs capture the flow dynamics better than FNNs