Deep learning for surrogate modelling of 2D mantle convection

Kurzfassung

The key parameters to mantle convection simulations are poorly constrained. Whereas the outputs can sometimes be observed directly or indirectly using geophysical and geochemical data obtained via planetary space missions. Hence, the “observables” can be used to constrain parameters governing mantle convection. Given the computational cost of running each forward model in 2D or 3D (on the scale of hours to days), it is often impractical to run several thousands of simulations to determine which parameters can satisfy a set of given observational constraints. Traditionally, scaling laws have been used as a low-fidelity alternative to overcome this computational bottleneck. However, they are limited in the amount of physics they can capture and only predict mean quantities such as surface heat flux and mantle temperature instead of spatio-temporally resolved flows. Using a dataset of 10,000 2D mantle convection simulations for a Mars-like planet, we show that deep learning can be used to reliably predict the entire 2D temperature field at any point in the evolution. We first use convolutional autoencoders to compress each temperature field by a factor of 140 to a latent space representation, which is easier to predict. We test feedforward neural networks (FNN) to predict the compressed temperature fields from five input parameters plus time. While the mean accuracy of the predicted temperature fields was high (99.30%), FNN was unable to capture the sharper downwelling structures and their advection. To address this, we use long short-term memory networks (LSTM), which have recently been shown to work in a variety of fluid dynamics problems. In comparison to the FNN, LSTM achieved a slightly lower mean relative accuracy, but captured the spatio-temporal dynamics more accurately.