Physics-Based Machine Learning: Opportunities and Challenges for Mantle Convection

Abstract

Abstract. Geodynamic research revolves around understanding the Earth's subsurface, which often requires solving complex partial differential equations to produce numerical models. Using state-of-the-art solvers to tackle these high-dimensional problems can be computationally demanding, or even prohibitive. A potential solution is to use surrogate models–methods that reduce the dimensionality of the problem while maintaining its general characteristics. In this work, we focus on developing reliable and efficient surrogate models via physics-based machine learning techniques for mantle convection applications, thus mitigating the computational challenges inherent in direct forward modeling of mantle convection. For this purpose, we employ the non-intrusive reduced basis method (NI-RB), which maintains the accuracy of traditional simulations while significantly reducing computational complexity. The performance of these models is compared against high-dimensional finite element mantle convection models generated from ASPECT, an open-source geodynamical simulation software. We show that the adopted approach significantly speeds up simulations of mantle temperature distribution-enabling rapid multi-query analyses such as global sensitivity studies and uncertainty quantification-while overcoming typical model reduction issues in geodynamics. The results indicate that our surrogate models not only capture the essential dynamics of mantle convection but also offer a balance of computational efficiency and quality of the model. With the potential to transform how geodynamic modeling studies are conducted, these surrogate models hold promise for a more efficient and effective exploration of Earth's subsurface processes in future studies.

Authors 5

1. Marilina Valatsou Aachen Institute for Computational Geoscience

   ETH Zurich · Institute for Particle Physics and Astrophysics · RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute for Computational Geoscience, Geothermics and Reservoir Geophysics, Mathieustraße 30, 52074 Aachen, Germany

   now at: Institute for Particle Physics and Astrophysics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland

2. Denise Degen corresponding

   Technische Universität Darmstadt · GFZ Helmholtz Centre for Geosciences

   Affiliation as printed

   GFZ Helmholtz Centre for Geosciences (Potsdam, Germany)

   Technische Universität Darmstadt (Darmstadt, Germany)

3. Juliane Dannberg

   Christian-Albrechts-Universität zu Kiel · GEOMAR Helmholtz Centre for Ocean Research Kiel

   Affiliation as printed

   Christian-Albrecht University of Kiel, Institute of Geosciences, Kiel, Germany

   GEOMAR Helmholtz Centre for Ocean Research, Kiel, Germany

4. René Gassmöller

   GEOMAR Helmholtz Centre for Ocean Research Kiel

   Affiliation as printed

   GEOMAR Helmholtz Centre for Ocean Research, Kiel, Germany

5. Florian Wellmann Aachen Institute for Computational Geoscience

   Fraunhofer Research Institution for Energy Infrastructures and Geotechnologies IEG · RWTH Aachen University

   Affiliation as printed

   Fraunhofer Research Institution for Energy Infrastructures and Geothermal Systems (IEG), Am Hochschulcampus 1, 44801 Bochum, Germany

   RWTH Aachen University, Institute for Computational Geoscience, Geothermics and Reservoir Geophysics, Mathieustraße 30, 52074 Aachen, Germany