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

Kurzfassung

Simulating 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 initialize numerical time-stepping methods for different simulation parameters. For an example application, the number of time steps required to reach steady-state is reduced by a factor of 2.8, compared to typically used initializations. The benefit of this method lies in requiring very few simulations to train on, providing a steady-state solution that is numerically accurate as we initialize a numerical method, and posing minimal computational overhead at inference time. We demonstrate the effectiveness of our approach and discuss its potential for advancing mantle convection research.