Physics-based machine learning for mantle convection simulations

TL;DR

This paper introduces a physics-based machine learning method that predicts mantle convection flow velocities to significantly accelerate simulations while maintaining physical accuracy, enabling faster planetary evolution modeling.

Contribution

It presents a novel ML approach that predicts flow velocities conserving mass, reducing computational time by up to 89 times compared to traditional numerical solvers.

Findings

Model achieves up to 89x speedup over numerical methods.

Incorporates mass conservation and boundary conditions in neural network.

Demonstrates robustness on unseen mantle convection scenarios.

Abstract

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, 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 to demonstrate some of its strengths and weaknesses.