Physics-based machine learning for mantle convection simulations

Kurzfassung

Mantle convection simulations are an essential tool for understanding how rocky planets evolve. However, the poorly known input parameters to these simulations, the non-linear dependence of transport properties on pressure and temperature, and the long integration times in excess of several billion years all pose a computational challenge for numerical solvers. We propose a physics-based machine learning approach that predicts creeping flow velocities as a function of temperature while conserving mass, thereby bypassing the numerical solution of the Stokes problem. A finite-volume solver then uses the predicted velocities to advect and diffuse the temperature field to the next time step, enabling autoregressive rollout at inference. For training, our model requires temperature-velocity snapshots from a handful of simulations (94). We consider mantle convection in a two-dimensional rectangular box with basal and internal heating, and pressure- and temperature-dependent viscosity. Overall, our model is up to 89 times faster than the numerical solver. We also show the importance of different components in our convolutional neural network architecture such as mass conservation, learned paddings on the boundaries, and loss scaling for the overall rollout performance. Finally, we test our approach on unseen scenarios and find that it is able to perform thermal evolution well despite being trained on snapshots from steady-state simulations. However, when additional compressibility effects are included in the energy equation or when the initial condition is too far out of the distribution of the training data, the network fails, leaving room for future improvements.