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

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.