Local flow estimation at the top of the Earth’s core using Physics Informed Neural Networks

The Earth’s main geomagnetic field arises from the constant motion of the fluid outer core. By assuming that the field changes are advection-dominated, and that diffusion only plays a minor role, the fluid motion at the core surface can be related to the secular variation of the geomagnetic field, providing an observational approach to understanding the motions in the deep Earth. The majority of existing core flow models are global, showing features such as an eccentric planetary gyre, with some evidence of rapid regional changes. By construction, the flow defined at any location by such a model depends on all magnetic field variations across the entire core–mantle boundary: because of this nonlocal dependence of the flow on the magnetic field, it is very challenging to interpret local structures in the flow as due to specific local changes in magnetic field. Here we present an alternative strategy in which we construct regional flow models that rely only on local secular changes. We use a novel technique based on machine learning termed Physics-Informed Neural Networks (PINNs), in which we seek a regional flow model that simultaneously fits both the local magnetic field variation and dynamical conditions assumed satisfied by the flow. Although we present results using the Tangentially Geostrophic flow constraint, we set out a modelling framework for which the physics constraint can be easily changed by altering a single line of code. After validating the PINN-based method on synthetic flows, we apply our method to the CHAOS-8.1 geomagnetic field model, itself based on data from Swarm. Constructing a global mosaic of regional flows, we reproduce the planetary gyre, providing independent evidence that the strong secular changes at high latitude and in equatorial regions are part of the same global feature. Our models also corroborate regional changes in core flows over the last decade. In our models, we find that the azimuthal flow under South America has changed sign quasi-periodically, with a recent sign change in 2022. Furthermore, our models endorse the existence of a dynamic high latitude jet, which began accelerating around 2005 but has been weakening since 2017.