Accelerating the Discovery of Steady‐States of Planetary Interior Dynamics With Machine Learning

AbstractSimulating mantle convection often requires reaching a computationally expensive steady‐state, crucial for deriving scaling laws for thermal and dynamical flow properties and benchmarking numerical solutions. The strong temperature dependence of the rheology of mantle rocks causes viscosity variations of several orders of magnitude, leading to a slow‐evolving “stagnant lid” where heat conduction dominates, overlying a rapidly evolving and strongly convecting region. Time‐stepping methods, while effective for fluids with constant viscosity, are hindered by the Courant criterion, which restricts the time step based on the system's maximum velocity and grid size. Consequently, achieving steady‐state requires a large number of time steps due to the disparate time scales governing the stagnant and convecting regions. We present a concept for accelerating mantle convection simulations using machine learning. We generate a data set of 128 two‐dimensional simulations with mixed basal and internal heating, and pressure‐ and temperature‐dependent viscosity. We train a feedforward neural network on 97 simulations to predict steady‐state temperature profiles. These can then be used to