Physics-informed neural networks for geomagnetic data assimilation

We present a physics-informed neural network (PINN) framework for geomagnetic data assimilation, aimed at reconstructing the time-dependent state of the Earth’s outer core, consistent with both geomagnetic observations and the governing equations of the geodynamo. The method incorporates the quasi-geostrophic magneto–Archimedean–Coriolis (QG–MAC) balance, together with the magnetic induction and thermal diffusion equations, as embedded physical constraints within the neural network training. Flow, magnetic, and temperature fields are represented using a poloidal–toroidal spectral decomposition, enabling an efficient description of large-scale core dynamics in a rotating spherical shell.

Synthetic assimilation experiments based on benchmark dynamo models demonstrate that the proposed framework can successfully recover the temporal evolution of the core state from magnetic field observations, with the reconstructed flow and magnetic fields reproducing the main characteristics of the reference solutions. The results further indicate that the method is capable of recovering small-scale magnetic field features at the core–mantle boundary. The framework is subsequently applied to geomagnetic data assimilation using observations from the COV-OBS geomagnetic field model. Using approximately 180 years of historical geomagnetic observations, we reconstruct the structure of the Earth’s core state and perform short-term (20 years) predictions of the magnetic field evolution.