Deep learning for surrogate modelling of 2D mantle convection

Exploring the high-dimensional parameter space governing 2D or 3D mantle convection simulations of terrestrial planets is computationally challenging. Hence, surrogates are helpful. Using 10,500 simulations of Mars’ thermal evolution carried out in a 2D cylindrical-shell geometry, we demonstrated that feedforward neural networks (FNN) can take five key parameters (initial temperature, radial distribution of  radiogenic elements, reference viscosity, pressure- and temperature-dependence of the viscosity) plus time as an additional variable, and predict the 1D horizontally-averaged temperature profile at any time during 4.5 billion years of evolution (Agarwal et al. 2020). We now extend this work to predict the entire 2D temperature field which contains more information than the 1D profile such as the structure of plumes and downwellings. First, we compress the temperature fields by a factor of ~140 using a convolutional autoencoder. Then, we compare the use of FNN and long-short term memory networks (LSTM) for predicting this compressed state. While FNN predictions are slightly more accurate, LSTMs ultimately capture the flow dynamics significantly better. The entire spatio-temporal evolution of the temperature field can thus be predicted for a wide range of parameters.