Deep learning for surrogate modeling of two-dimensional mantle convection

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Abstract

Mantle convection, the buoyancy-driven creeping flow of silicate rocks in the interior of terrestrial planets like Earth, Mars, Mercury, and Venus plays a fundamental role in the long-term thermal evolution of these bodies. 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 parameterized convective heat transfer have been used to tackle the computational bottleneck of high-fidelity forward runs in two or three dimensions. However, these are limited in the amount of physics they can model (e.g., depth-dependent material properties) and predict only mean quantities such as the mean mantle temperature. A recent machine learning study has shown that feedforward neural networks (FNNs) trained using a large number of 2D simulations can overcome this limitation and reliably predict the evolution of entire 1D laterally averaged temperature profile in time for complex models. We now extend that approach to predict the full 2D temperature field, which contains more information in the form of convection structures such as hot plumes and cold downwellings. Using a data set of 10525 2D simulations of the thermal evolution of the mantle of a Mars-like planet, we show that deep learning techniques can produce reliable parameterized surrogates (i.e., surrogates that predict state variables such as temperature based only on parameters) of the underlying partial differential equations. We first use convolutional autoencoders to compress the size of each temperature field by a factor of 142 and then use FNNs and long-short-term memory networks (LSTMs) to predict the compressed fields. On average, the FNN predictions are 99.30% and the LSTM predictions are 99.22% accurate with respect to unseen simulations. Proper orthogonal decomposition (POD) of the LSTM and FNN predictions shows that despite a lower mean relative accuracy, LSTMs capture the flow dynamics better than FNNs. When summed, the POD coefficients from FNN predictions and from LSTM predictions amount to 96.51% and 97.66% relative to the coefficients of the original simulations, respectively.

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• Deep learning for surrogate modeling of two-dimensional mantle convection. (deposited 26 Nov 2021 13:08) [Currently Displayed]