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Physics-based machine learning for mantle convection simulations

arXiv 2505.16041 ↗First posted 21 May 2025astro-ph.EP cs.LGcited by 0

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Abstract (arXiv)

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.

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References · 22

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
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  11. 2024On the Benefits of Memory for Modeling Time-Dependent PDEscited by 31
  12. 2020Using Machine Learning to Augment Coarse-Grid Computational Fluid Dynamics Simulationscited by 24
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  1. 2024Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulationscited by 24
  2. 2024Space-Time Continuous PDE Forecasting using Equivariant Neural Fieldscited by 18
  3. 2023A practical PINN framework for multi-scale problems with multi-magnitude loss termscited by 15
  4. 2021Effects of boundary conditions in fully convolutional networks for learning spatio-temporal dynamicscited by 14
  5. 2024P2C2Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamicscited by 13
  6. 2024Parametric Encoding with Attention and Convolution Mitigate Spectral Bias of Neural Partial Differential Equation Solverscited by 9
  7. 2022A composable machine-learning approach for steady-state simulations on high-resolution gridscited by 8
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  9. 2021Deep learning for surrogate modelling of 2D mantle convectioncited by 3
  10. 2024Accelerating the discovery of steady-states of planetary interior dynamics with machine learningcited by 3

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