Deep learning for surrogate modeling of two-dimensional mantle convection

Traditionally, 1D models based on scaling laws have been used to parameterized convective heat transfer rocks in the interior of terrestrial planets like Earth, Mars, Mercury and Venus tackle computational bottleneck high-fidelity forward runs 2D or 3D. However, these are limited amount physics they can model (e.g. depth dependent material properties) predict only mean quantities such as mantle temperature. We recently showed that feedforward neural networks (FNN) trained using a large number simulations overcome this limitation reliably evolution entire laterally-averaged temperature profile time for complex models. now extend approach full field, which contains more information form convection structures hot plumes cold downwellings. Using dataset 10,525 two-dimensional thermal Mars-like planet, we show deep learning techniques produce reliable surrogates (i.e. state variables parameters) underlying partial differential equations. first use convolutional autoencoders compress fields by factor 142 then FNN long-short term memory (LSTM) compressed fields. On average, predictions 99.30% LSTM 99.22% accurate with respect unseen simulations. Proper orthogonal decomposition (POD) shows despite lower absolute relative accuracy, LSTMs capture flow dynamics better than FNNs. When summed, POD coefficients from 96.51% 97.66% original simulations, respectively.