Discovering Governing Equations of Geomagnetic Storm Dynamics with Symbolic Regression

Abstract: Geomagnetic storms are large-scale disturbances of the Earth's magnetosphere driven by solar wind interactions, posing significant risks to space-based and ground-based infrastructure. The Disturbance Storm Time (Dst) index quantifies geomagnetic storm intensity by measuring global magnetic field variations. This study applies symbolic regression to derive data-driven equations describing the temporal evolution of the Dst index. We use historical data from the NASA OMNIweb database, including solar wind density, bulk velocity, convective electric field, dynamic pressure, and magnetic pressure. The PySR framework, an evolutionary algorithm-based symbolic regression library, is used to identify mathematical expressions linking dDst/dt to key solar wind. The resulting models include a hierarchy of complexity levels and enable a comparison with well-established empirical models such as the Burton-McPherron-Russell and O'Brien-McPherron models. The best-performing symbolic regression models demonstrate superior accuracy in most cases, particularly during moderate geomagnetic storms, while maintaining physical interpretability. Performance evaluation on historical storm events includes the 2003 Halloween Storm, the 2015 St. Patrick's Day Storm, and a 2017 moderate storm. The results provide interpretable, closed-form expressions that capture nonlinear dependencies and thresholding effects in Dst evolution.