Spherical Path Regression Through Universal Differential Equations With Applications to Paleomagnetism

Abstract Directional data analysis plays a central role in paleomagnetism, where observations lie on a spherical surface. Existing methods for analyzing directional data often fail to incorporate prior physical knowledge about plate geodynamics, significantly constraining their potential. To address this limitation, we developed a hybrid, physics‐informed machine learning model that uses a neural network to learn the underlying rotations responsible for generating directional data. Our method robustly captures the time‐dependent variability of directional data in both synthetic and real paleomagnetic data sets. Additionally, by leveraging in the differentiable programming paradigm, we can incorporate physical constraints in the form of regularizations. These results have the potential to improve future estimations of apparent polar wander paths, advancing the reconstruction of past tectonic plate motions.